Quizbank/University Physics Semester 2/T1

University Physics Semester 2/T1 ID153341821922

For more information visit Quizbank/University Physics Semester 2

Exams:  A0  A1  A2   B0  B1  B2   C0  C1  C2   D0  D1  D2   E0  E1  E2   F0  F1  F2   G0  G1  G2   H0  H1  H2   I0  I1  I2   J0  J1  J2   K0  K1  K2   L0  L1  L2   M0  M1  M2   N0  N1  N2   O0  O1  O2   P0  P1  P2   Q0  Q1  Q2   R0  R1  R2   S0  S1  S2   T0  T1  T2   U0  U1  U2   V0  V1  V2   W0  W1  W2   X0  X1  X2   Y0  Y1  Y2   Z0  Z1  Z2  

Answers:   A0  A1  A2   B0  B1  B2   C0  C1  C2   D0  D1  D2   E0  E1  E2   F0  F1  F2   G0  G1  G2   H0  H1  H2   I0  I1  I2   J0  J1  J2   K0  K1  K2   L0  L1  L2   M0  M1  M2   N0  N1  N2   O0  O1  O2   P0  P1  P2   Q0  Q1  Q2   R0  R1  R2   S0  S1  S2   T0  T1  T2   U0  U1  U2   V0  V1  V2   W0  W1  W2   X0  X1  X2   Y0  Y1  Y2   Z0  Z1  Z2  

78 Tests = 3 versions x 26 variations: Each of the 26 variations (A, B, ...) represents a different random selection of questions taken from the study guide.The 3 versions (0,1,..) all have the same questions but in different order and with different numerical inputs. Unless all students take version "0" it is best to reserve it for the instructor because the questions are grouped according to the order in which they appear on the study guide.

Links:   Quizbank/Instructions   Study guide   file:QB-University Physics Semester 2-T1.pdf

Contact me at User talk:Guy vandegrift if you need any help.

T1 A0

1)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.4{\text{ m}}$ and the surface charge density is $\sigma =6{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=0.56{\text{ m}}$.

a) 2.567E+01 V/m²

b) 2.824E+01 V/m²

c) 3.106E+01 V/m²

d) 3.417E+01 V/m²

e) 3.759E+01 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-8e$, and $q_{3}=2e$?

a) 3.876E-14 N

b) 4.263E-14 N

c) 4.690E-14 N

d) 5.159E-14 N

e) 5.675E-14 N

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-7e$, and $q_{3}=5e$?

a) 4.357E+01 degrees

b) 4.793E+01 degrees

c) 5.272E+01 degrees

d) 5.799E+01 degrees

e) 6.379E+01 degrees

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 2.86 x 10^-1

b) 3.47 x 10^-1

c) 4.2 x 10^-1

d) 5.09 x 10^-1

e) 6.17 x 10^-1

5) What angle does the electric field at the origin make with the x-axis if a 2 nC charge is placed at x = -8 m, and a 1.4 nC charge is placed at y = -9.3 m?

a) 2.37 x 10¹degrees

b) 2.74 x 10¹degrees

c) 3.16 x 10¹degrees

d) 3.65 x 10¹degrees

e) 4.22 x 10¹degrees

6) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−7

b) 3−s

c) 7−s

d) s−3

e) 8

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) −3

b) −7

c) −3

d) 2

e) 3

8) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 5−s

b) 5

c) s−1

d) 1−s

e) s−4

9) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

a) 4

b) 2

c) 8

d) 1/2

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 3/2

b) 3

c) 1/2

d) 2

T1 A1

1) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) −7

b) −3

c) 3

d) −3

e) 2

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-9e$, and $q_{3}=5e$?

a) 5.272E+01 degrees

b) 5.799E+01 degrees

c) 6.379E+01 degrees

d) 7.017E+01 degrees

e) 7.719E+01 degrees

3) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8

b) s−3

c) 3−s

d) 7−s

e) s−7

4) What angle does the electric field at the origin make with the x-axis if a 1.9 nC charge is placed at x = -5.4 m, and a 1.5 nC charge is placed at y = -7.1 m?

a) 1.38 x 10¹degrees

b) 1.59 x 10¹degrees

c) 1.84 x 10¹degrees

d) 2.13 x 10¹degrees

e) 2.45 x 10¹degrees

5) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

a) 2

b) 1/2

c) 8

d) 4

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 3/2

b) 1/2

c) 2

d) 3

7) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 5

b) 1−s

c) s−4

d) 5−s

e) s−1

8)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.8{\text{ m}}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=1.9{\text{ m}}$.

a) 4.295E+00 V/m²

b) 4.724E+00 V/m²

c) 5.196E+00 V/m²

d) 5.716E+00 V/m²

e) 6.288E+00 V/m²

9) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 1.95 x 10^-1 unit

b) 2.36 x 10^-1 unit

c) 2.86 x 10^-1 unit

d) 3.47 x 10^-1 unit

e) 4.2 x 10^-1 unit

10)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-8e$, and $q_{3}=2e$?

a) 3.876E-14 N

b) 4.263E-14 N

c) 4.690E-14 N

d) 5.159E-14 N

e) 5.675E-14 N

T1 A2

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=5e$?

a) 9.958E-15 N

b) 1.095E-14 N

c) 1.205E-14 N

d) 1.325E-14 N

e) 1.458E-14 N

2) What angle does the electric field at the origin make with the x-axis if a 1.8 nC charge is placed at x = -6.9 m, and a 2.5 nC charge is placed at y = -7.5 m?

a) 2.79 x 10¹degrees

b) 3.22 x 10¹degrees

c) 3.72 x 10¹degrees

d) 4.3 x 10¹degrees

e) 4.96 x 10¹degrees

3) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 2.36 x 10^-1 unit

b) 2.86 x 10^-1 unit

c) 3.47 x 10^-1 unit

d) 4.2 x 10^-1 unit

e) 5.09 x 10^-1 unit

4) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) 3

b) −3

c) 2

d) −7

e) −3

5) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 2

b) 1/2

c) 3

d) 3/2

6) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−4

b) 1−s

c) s−1

d) 5−s

e) 5

7) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 3−s

b) s−7

c) 8

d) s−3

e) 7−s

8)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-8e$, and $q_{3}=6e$?

a) 5.243E+01 degrees

b) 5.767E+01 degrees

c) 6.343E+01 degrees

d) 6.978E+01 degrees

e) 7.676E+01 degrees

9) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

a) 4

b) 1/2

c) 2

d) 8

10)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.3{\text{ m}}$ and the surface charge density is $\sigma =5{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=5.3{\text{ m}}$.

a) 1.022E+00 V/m²

b) 1.125E+00 V/m²

c) 1.237E+00 V/m²

d) 1.361E+00 V/m²

e) 1.497E+00 V/m²

T1 B0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-9e$, and $q_{3}=6e$?

a) 1.308E-13 N

b) 1.439E-13 N

c) 1.583E-13 N

d) 1.741E-13 N

e) 1.915E-13 N

2)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.9{\text{ m}}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=4.3{\text{ m}}$.

a) 8.924E-01 V/m²

b) 9.816E-01 V/m²

c) 1.080E+00 V/m²

d) 1.188E+00 V/m²

e) 1.307E+00 V/m²

3) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 2.357E+01 N/C

b) 2.593E+01 N/C

c) 2.852E+01 N/C

d) 3.137E+01 N/C

e) 3.451E+01 N/C

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 3a) is βkQ/a², where β equals

a) 3.38 x 10^-3 unit

b) 4.1 x 10^-3 unit

c) 4.96 x 10^-3 unit

d) 6.01 x 10^-3 unit

e) 7.28 x 10^-3 unit

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 3.47 x 10^-1 unit

b) 4.2 x 10^-1 unit

c) 5.09 x 10^-1 unit

d) 6.17 x 10^-1 unit

e) 7.47 x 10^-1 unit

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 3

b) 1/2

c) 3/2

d) 2

7) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 7² + (2-s)²

b) 2² + (7-s)²

c) 2² + (9-s)²

d) 9² + (7-s)²

e) 9² + (2-s)²

8) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) −3

b) 2

c) −7

d) −3

e) 3

9) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s − 2

b) 9 − s

c) 2 − s

d) s − 9

e) 2

10) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−4

b) s−8

c) 8−s

d) 4−s

e) 4

T1 B1

1) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) −3

b) −7

c) 2

d) 3

e) −3

2) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 3.47 x 10^-1 unit

b) 4.2 x 10^-1 unit

c) 5.09 x 10^-1 unit

d) 6.17 x 10^-1 unit

e) 7.47 x 10^-1 unit

3) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 2

b) 3/2

c) 3

d) 1/2

4) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−4

b) 8−s

c) 4−s

d) s−8

e) 4

5) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 2² + (9-s)²

b) 7² + (2-s)²

c) 9² + (7-s)²

d) 2² + (7-s)²

e) 9² + (2-s)²

6) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 6.171E+01 N/C

b) 6.788E+01 N/C

c) 7.467E+01 N/C

d) 8.214E+01 N/C

e) 9.035E+01 N/C

7) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 6a) is βkQ/a², where β equals

a) 1.52 x 10^-4 unit

b) 1.85 x 10^-4 unit

c) 2.24 x 10^-4 unit

d) 2.71 x 10^-4 unit

e) 3.28 x 10^-4 unit

8)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=6e$?

a) 2.544E-14 N

b) 2.798E-14 N

c) 3.078E-14 N

d) 3.385E-14 N

e) 3.724E-14 N

9)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.0{\text{ m}}$ and the surface charge density is $\sigma =8{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=2.0{\text{ m}}$.

a) 9.459E+00 V/m²

b) 1.040E+01 V/m²

c) 1.145E+01 V/m²

d) 1.259E+01 V/m²

e) 1.385E+01 V/m²

10) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s − 2

b) 9 − s

c) s − 9

d) 2 − s

e) 2

T1 B2

1) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) −3

b) 2

c) −3

d) 3

e) −7

2) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 5a, 4a) is βkQ/a², where β equals

a) 1.76 x 10^-3 unit

b) 2.13 x 10^-3 unit

c) 2.59 x 10^-3 unit

d) 3.13 x 10^-3 unit

e) 3.79 x 10^-3 unit

3) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 2

b) 2 − s

c) s − 2

d) s − 9

e) 9 − s

4)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=9.1{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=6.2{\text{ m}}$.

a) 4.961E-01 V/m²

b) 5.457E-01 V/m²

c) 6.002E-01 V/m²

d) 6.603E-01 V/m²

e) 7.263E-01 V/m²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=6e$?

a) 1.028E-14 N

b) 1.130E-14 N

c) 1.244E-14 N

d) 1.368E-14 N

e) 1.505E-14 N

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 3

b) 2

c) 1/2

d) 3/2

7) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 2.36 x 10^-1 unit

b) 2.86 x 10^-1 unit

c) 3.47 x 10^-1 unit

d) 4.2 x 10^-1 unit

e) 5.09 x 10^-1 unit

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−8

b) 4

c) 4−s

d) 8−s

e) s−4

9) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

a) 5.647E+01 N/C

b) 6.212E+01 N/C

c) 6.833E+01 N/C

d) 7.516E+01 N/C

e) 8.268E+01 N/C

10) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 9² + (7-s)²

b) 7² + (2-s)²

c) 9² + (2-s)²

d) 2² + (9-s)²

e) 2² + (7-s)²

T1 C0

1) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 3.214E+01 N/C

b) 3.536E+01 N/C

c) 3.889E+01 N/C

d) 4.278E+01 N/C

e) 4.706E+01 N/C

2)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.3 m (on axis) away from the loop's center?

a) 4.788E+09 N/C²

b) 5.267E+09 N/C²

c) 5.793E+09 N/C²

d) 6.373E+09 N/C²

e) 7.010E+09 N/C²

3)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.3{\text{ m}}$ and the surface charge density is $\sigma =4{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=2.0{\text{ m}}$.

a) 6.877E+00 V/m²

b) 7.565E+00 V/m²

c) 8.321E+00 V/m²

d) 9.153E+00 V/m²

e) 1.007E+01 V/m²

4) What is the magnitude of the electric field at the origin if a 1.4 nC charge is placed at x = 8.2 m, and a 2.3 nC charge is placed at y = 5.9 m?

a) 5.39 x 10^-1N/C

b) 6.23 x 10^-1N/C

c) 7.19 x 10^-1N/C

d) 8.31 x 10^-1N/C

e) 9.59 x 10^-1N/C

5) What angle does the electric field at the origin make with the x-axis if a 2 nC charge is placed at x = -8 m, and a 1.4 nC charge is placed at y = -9.3 m?

a) 2.37 x 10¹degrees

b) 2.74 x 10¹degrees

c) 3.16 x 10¹degrees

d) 3.65 x 10¹degrees

e) 4.22 x 10¹degrees

6) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−8

b) 4

c) s−4

d) 8−s

e) 4−s

7) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 3−s

b) 7−s

c) s−7

d) 8

e) s−3

8) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 2/3

b) 2

c) 3/2

d) 3

e) 1/2

9) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

a) 1/2

b) 2

c) 8

d) 4

10) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8−s

b) 4−s

c) 4

d) s−4

e) s−8

T1 C1

1)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=9.1{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=6.2{\text{ m}}$.

a) 4.961E-01 V/m²

b) 5.457E-01 V/m²

c) 6.002E-01 V/m²

d) 6.603E-01 V/m²

e) 7.263E-01 V/m²

2) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−8

b) 4−s

c) 8−s

d) s−4

e) 4

3) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

a) 1/2

b) 8

c) 4

d) 2

4) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 3

b) 1/2

c) 2

d) 3/2

e) 2/3

5)

A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.73 m (on axis) away from the loop's center?

a) 7.415E+09 N/C²

b) 8.156E+09 N/C²

c) 8.972E+09 N/C²

d) 9.869E+09 N/C²

e) 1.086E+10 N/C²

6) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 6.534E+01 N/C

b) 7.187E+01 N/C

c) 7.906E+01 N/C

d) 8.696E+01 N/C

e) 9.566E+01 N/C

7) What angle does the electric field at the origin make with the x-axis if a 2.8 nC charge is placed at x = -9.8 m, and a 2.8 nC charge is placed at y = -5.8 m?

a) 7.07 x 10¹degrees

b) 8.16 x 10¹degrees

c) 9.43 x 10¹degrees

d) 1.09 x 10²degrees

e) 1.26 x 10²degrees

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8−s

b) s−8

c) 4−s

d) 4

e) s−4

9) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−7

b) 7−s

c) 8

d) 3−s

e) s−3

10) What is the magnitude of the electric field at the origin if a 1.8 nC charge is placed at x = 9.6 m, and a 2 nC charge is placed at y = 8.7 m?

a) 2.95 x 10^-1N/C

b) 3.41 x 10^-1N/C

c) 3.94 x 10^-1N/C

d) 4.55 x 10^-1N/C

e) 5.25 x 10^-1N/C

T1 C2

1)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=4.3{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=2.4{\text{ m}}$.

a) 5.647E+00 V/m²

b) 6.212E+00 V/m²

c) 6.833E+00 V/m²

d) 7.517E+00 V/m²

e) 8.268E+00 V/m²

2) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8−s

b) s−8

c) s−4

d) 4−s

e) 4

3) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−3

b) 7−s

c) 3−s

d) s−7

e) 8

4) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 3

b) 1/2

c) 3/2

d) 2/3

e) 2

5) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 4

b) s−4

c) 8−s

d) s−8

e) 4−s

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

a) 5.647E+01 N/C

b) 6.212E+01 N/C

c) 6.833E+01 N/C

d) 7.516E+01 N/C

e) 8.268E+01 N/C

7) What is the magnitude of the electric field at the origin if a 3.1 nC charge is placed at x = 6.2 m, and a 2.6 nC charge is placed at y = 6 m?

a) 5.47 x 10^-1N/C

b) 6.32 x 10^-1N/C

c) 7.3 x 10^-1N/C

d) 8.43 x 10^-1N/C

e) 9.73 x 10^-1N/C

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

a) 4

b) 2

c) 8

d) 1/2

9)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

a) 2.013E+09 N/C²

b) 2.214E+09 N/C²

c) 2.435E+09 N/C²

d) 2.679E+09 N/C²

e) 2.947E+09 N/C²

10) What angle does the electric field at the origin make with the x-axis if a 2.6 nC charge is placed at x = -8.3 m, and a 2.5 nC charge is placed at y = -9.6 m?

a) 2.32 x 10¹degrees

b) 2.68 x 10¹degrees

c) 3.09 x 10¹degrees

d) 3.57 x 10¹degrees

e) 4.12 x 10¹degrees

T1 D0

1)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

a) 2.013E+09 N/C²

b) 2.214E+09 N/C²

c) 2.435E+09 N/C²

d) 2.679E+09 N/C²

e) 2.947E+09 N/C²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=3e$?

a) 2.036E-14 N

b) 2.240E-14 N

c) 2.464E-14 N

d) 2.710E-14 N

e) 2.981E-14 N

3)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m. Evaluate $f(x,y)$ at x=0.52 m if a=0.88 m, b=1.3 m. The total charge on the rod is 6 nC.

a) 6.804E+00 V/m²

b) 7.485E+00 V/m²

c) 8.233E+00 V/m²

d) 9.056E+00 V/m²

e) 9.962E+00 V/m²

4) What is the magnitude of the electric field at the origin if a 2.1 nC charge is placed at x = 7 m, and a 2.1 nC charge is placed at y = 8.6 m?

a) 3 x 10^-1N/C

b) 3.47 x 10^-1N/C

c) 4 x 10^-1N/C

d) 4.62 x 10^-1N/C

e) 5.34 x 10^-1N/C

5) What angle does the electric field at the origin make with the x-axis if a 2.9 nC charge is placed at x = -7.3 m, and a 1.7 nC charge is placed at y = -8.1 m?

a) 2.55 x 10¹degrees

b) 2.94 x 10¹degrees

c) 3.4 x 10¹degrees

d) 3.92 x 10¹degrees

e) 4.53 x 10¹degrees

6) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 4

b) s−4

c) 8−s

d) 4−s

e) s−8

7) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 7² + (3−s)²

b) (7-s)² + 8²

c) 7² + 8²

d) 7² + (8−s)²

e) 3² + 8²

8) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8

b) s−7

c) 3−s

d) 7−s

e) s−3

9) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 2

b) s − 2

c) s − 9

d) 9 − s

e) 2 − s

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) −3

b) −3

c) −7

d) 3

e) 2

T1 D1

1)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.3 m (on axis) away from the loop's center?

a) 4.788E+09 N/C²

b) 5.267E+09 N/C²

c) 5.793E+09 N/C²

d) 6.373E+09 N/C²

e) 7.010E+09 N/C²

2) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−3

b) s−7

c) 8

d) 3−s

e) 7−s

3) What angle does the electric field at the origin make with the x-axis if a 2.6 nC charge is placed at x = -8.3 m, and a 2.5 nC charge is placed at y = -9.6 m?

a) 2.32 x 10¹degrees

b) 2.68 x 10¹degrees

c) 3.09 x 10¹degrees

d) 3.57 x 10¹degrees

e) 4.12 x 10¹degrees

4) What is the magnitude of the electric field at the origin if a 1.9 nC charge is placed at x = 9.7 m, and a 3.1 nC charge is placed at y = 5.5 m?

a) 5.28 x 10^-1N/C

b) 6.1 x 10^-1N/C

c) 7.04 x 10^-1N/C

d) 8.13 x 10^-1N/C

e) 9.39 x 10^-1N/C

5) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) 3

b) −7

c) −3

d) 2

e) −3

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-9e$, and $q_{3}=4e$?

a) 5.014E-14 N

b) 5.515E-14 N

c) 6.067E-14 N

d) 6.674E-14 N

e) 7.341E-14 N

7) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 3² + 8²

b) 7² + (8−s)²

c) 7² + (3−s)²

d) (7-s)² + 8²

e) 7² + 8²

8)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=1.0 m if a=1.0 m, b=1.8 m. The total charge on the rod is 6 nC.

a) 3.610E+00 V/m²

b) 3.971E+00 V/m²

c) 4.368E+00 V/m²

d) 4.804E+00 V/m²

e) 5.285E+00 V/m²

9) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8−s

b) s−8

c) 4−s

d) s−4

e) 4

10) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 9 − s

b) 2

c) s − 2

d) s − 9

e) 2 − s

T1 D2

1) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s − 2

b) 9 − s

c) 2

d) 2 − s

e) s − 9

2) What angle does the electric field at the origin make with the x-axis if a 1.4 nC charge is placed at x = -8.7 m, and a 2.7 nC charge is placed at y = -8.3 m?

a) 4.85 x 10¹degrees

b) 5.61 x 10¹degrees

c) 6.47 x 10¹degrees

d) 7.48 x 10¹degrees

e) 8.63 x 10¹degrees

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-8e$, and $q_{3}=2e$?

a) 3.876E-14 N

b) 4.263E-14 N

c) 4.690E-14 N

d) 5.159E-14 N

e) 5.675E-14 N

4) What is the magnitude of the electric field at the origin if a 1.9 nC charge is placed at x = 9.7 m, and a 3.1 nC charge is placed at y = 5.5 m?

a) 5.28 x 10^-1N/C

b) 6.1 x 10^-1N/C

c) 7.04 x 10^-1N/C

d) 8.13 x 10^-1N/C

e) 9.39 x 10^-1N/C

5) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−3

b) 8

c) 7−s

d) s−7

e) 3−s

6) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 7² + 8²

b) (7-s)² + 8²

c) 3² + 8²

d) 7² + (8−s)²

e) 7² + (3−s)²

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) 2

b) −3

c) −7

d) 3

e) −3

8)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.6 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.64 m, b=1.8 m. The total charge on the rod is 3 nC.

a) 2.955E+00 V/m²

b) 3.250E+00 V/m²

c) 3.575E+00 V/m²

d) 3.933E+00 V/m²

e) 4.326E+00 V/m²

9) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 4−s

b) 4

c) 8−s

d) s−4

e) s−8

10)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.3 m (on axis) away from the loop's center?

a) 4.788E+09 N/C²

b) 5.267E+09 N/C²

c) 5.793E+09 N/C²

d) 6.373E+09 N/C²

e) 7.010E+09 N/C²

T1 E0

1)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.8{\text{ m}}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=1.9{\text{ m}}$.

a) 4.295E+00 V/m²

b) 4.724E+00 V/m²

c) 5.196E+00 V/m²

d) 5.716E+00 V/m²

e) 6.288E+00 V/m²

2) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 3.428E+01 N/C

b) 3.771E+01 N/C

c) 4.148E+01 N/C

d) 4.563E+01 N/C

e) 5.020E+01 N/C

3)

A ring is uniformly charged with a net charge of 8 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.32 m (on axis) away from the loop's center?

a) 3.339E+09 N/C²

b) 3.673E+09 N/C²

c) 4.041E+09 N/C²

d) 4.445E+09 N/C²

e) 4.889E+09 N/C²

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 3.47 x 10^-1 unit

b) 4.2 x 10^-1 unit

c) 5.09 x 10^-1 unit

d) 6.17 x 10^-1 unit

e) 7.47 x 10^-1 unit

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 5a) is βkQ/a², where β equals

a) 6.11 x 10^-4

b) 7.4 x 10^-4

c) 8.97 x 10^-4

d) 1.09 x 10^-3

e) 1.32 x 10^-3

6) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 2² + (7-s)²

b) 9² + (7-s)²

c) 9² + (2-s)²

d) 7² + (2-s)²

e) 2² + (9-s)²

7) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s − 2

b) 2 − s

c) s − 9

d) 2

e) 9 − s

8) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 7² + 8²

b) 3² + 8²

c) 7² + (3−s)²

d) 7² + (8−s)²

e) (7-s)² + 8²

9) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 5−s

b) 1−s

c) s−1

d) s−4

e) 5

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 1/2

b) 3

c) 2

d) 3/2

T1 E1

1) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 3/2

b) 3

c) 1/2

d) 2

2)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.9{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=5.1{\text{ m}}$.

a) 8.253E-01 V/m²

b) 9.079E-01 V/m²

c) 9.987E-01 V/m²

d) 1.099E+00 V/m²

e) 1.208E+00 V/m²

3) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 6a) is βkQ/a², where β equals

a) 1.52 x 10^-4 unit

b) 1.85 x 10^-4 unit

c) 2.24 x 10^-4 unit

d) 2.71 x 10^-4 unit

e) 3.28 x 10^-4 unit

4) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 9² + (7-s)²

b) 7² + (2-s)²

c) 9² + (2-s)²

d) 2² + (9-s)²

e) 2² + (7-s)²

5) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−4

b) 1−s

c) 5−s

d) 5

e) s−1

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 7.701E+01 N/C

b) 8.471E+01 N/C

c) 9.318E+01 N/C

d) 1.025E+02 N/C

e) 1.127E+02 N/C

7) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s − 9

b) 2 − s

c) s − 2

d) 9 − s

e) 2

8) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 1.95 x 10^-1 unit

b) 2.36 x 10^-1 unit

c) 2.86 x 10^-1 unit

d) 3.47 x 10^-1 unit

e) 4.2 x 10^-1 unit

9)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.99 m (on axis) away from the loop's center?

a) 2.429E+09 N/C²

b) 2.672E+09 N/C²

c) 2.939E+09 N/C²

d) 3.233E+09 N/C²

e) 3.556E+09 N/C²

10) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 7² + (3−s)²

b) 7² + (8−s)²

c) 7² + 8²

d) (7-s)² + 8²

e) 3² + 8²

T1 E2

1) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 2² + (7-s)²

b) 9² + (7-s)²

c) 2² + (9-s)²

d) 7² + (2-s)²

e) 9² + (2-s)²

2) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 5−s

b) 1−s

c) 5

d) s−4

e) s−1

3) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 1.95 x 10^-1 unit

b) 2.36 x 10^-1 unit

c) 2.86 x 10^-1 unit

d) 3.47 x 10^-1 unit

e) 4.2 x 10^-1 unit

4) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 2.357E+01 N/C

b) 2.593E+01 N/C

c) 2.852E+01 N/C

d) 3.137E+01 N/C

e) 3.451E+01 N/C

5) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 7² + (8−s)²

b) 7² + 8²

c) 3² + 8²

d) (7-s)² + 8²

e) 7² + (3−s)²

6) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

a) 1.09 x 10^-3 unit

b) 1.33 x 10^-3 unit

c) 1.61 x 10^-3 unit

d) 1.95 x 10^-3 unit

e) 2.36 x 10^-3 unit

7)

A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.73 m (on axis) away from the loop's center?

a) 7.415E+09 N/C²

b) 8.156E+09 N/C²

c) 8.972E+09 N/C²

d) 9.869E+09 N/C²

e) 1.086E+10 N/C²

8) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s − 9

b) 9 − s

c) 2 − s

d) s − 2

e) 2

9) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 3/2

b) 3

c) 2

d) 1/2

10)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=4.3{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=2.4{\text{ m}}$.

a) 5.647E+00 V/m²

b) 6.212E+00 V/m²

c) 6.833E+00 V/m²

d) 7.517E+00 V/m²

e) 8.268E+00 V/m²

T1 F0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=1e$, $q_{2}=-8e$, and $q_{3}=3e$?

a) 3.629E+01 degrees

b) 3.992E+01 degrees

c) 4.391E+01 degrees

d) 4.830E+01 degrees

e) 5.313E+01 degrees

2)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.2{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=2.2{\text{ m}}$.

a) 3.228E+00 V/m²

b) 3.551E+00 V/m²

c) 3.906E+00 V/m²

d) 4.297E+00 V/m²

e) 4.727E+00 V/m²

3) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 4.492E+01 N/C

b) 4.941E+01 N/C

c) 5.435E+01 N/C

d) 5.979E+01 N/C

e) 6.577E+01 N/C

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 2a) is βkQ/a², where β equals

a) 7.31 x 10^-3 unit

b) 8.86 x 10^-3 unit

c) 1.07 x 10^-2 unit

d) 1.3 x 10^-2 unit

e) 1.57 x 10^-2 unit

5) What is the magnitude of the electric field at the origin if a 1.9 nC charge is placed at x = 9.7 m, and a 3.1 nC charge is placed at y = 5.5 m?

a) 5.28 x 10^-1N/C

b) 6.1 x 10^-1N/C

c) 7.04 x 10^-1N/C

d) 8.13 x 10^-1N/C

e) 9.39 x 10^-1N/C

6) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 3/2

b) 1/2

c) 3

d) 2/3

e) 2

7) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 2² + (9-s)²

b) 2² + (7-s)²

c) 9² + (2-s)²

d) 9² + (7-s)²

e) 7² + (2-s)²

8) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) 3

b) −3

c) −3

d) 2

e) −7

9) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 7² + (3−s)²

b) 7² + (8−s)²

c) 7² + 8²

d) (7-s)² + 8²

e) 3² + 8²

10) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

a) 8

b) 1/2

c) 2

d) 4

T1 F1

1) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 2² + (7-s)²

b) 2² + (9-s)²

c) 9² + (2-s)²

d) 7² + (2-s)²

e) 9² + (7-s)²

2) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

a) 1/2

b) 8

c) 4

d) 2

3)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.8{\text{ m}}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=1.1{\text{ m}}$.

a) 7.517E+00 V/m²

b) 8.269E+00 V/m²

c) 9.096E+00 V/m²

d) 1.001E+01 V/m²

e) 1.101E+01 V/m²

4) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 8.471E+01 N/C

b) 9.318E+01 N/C

c) 1.025E+02 N/C

d) 1.127E+02 N/C

e) 1.240E+02 N/C

5) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 3

b) 2/3

c) 3/2

d) 2

e) 1/2

6) What is the magnitude of the electric field at the origin if a 1.9 nC charge is placed at x = 9.7 m, and a 3.1 nC charge is placed at y = 5.5 m?

a) 5.28 x 10^-1N/C

b) 6.1 x 10^-1N/C

c) 7.04 x 10^-1N/C

d) 8.13 x 10^-1N/C

e) 9.39 x 10^-1N/C

7) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 5a) is βkQ/a², where β equals

a) 6.11 x 10^-4

b) 7.4 x 10^-4

c) 8.97 x 10^-4

d) 1.09 x 10^-3

e) 1.32 x 10^-3

8) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) 3

b) 2

c) −7

d) −3

e) −3

9)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-9e$, and $q_{3}=5e$?

a) 5.272E+01 degrees

b) 5.799E+01 degrees

c) 6.379E+01 degrees

d) 7.017E+01 degrees

e) 7.719E+01 degrees

10) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 7² + (3−s)²

b) 7² + (8−s)²

c) 7² + 8²

d) 3² + 8²

e) (7-s)² + 8²

T1 F2

1) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

a) 2

b) 8

c) 4

d) 1/2

2)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.8{\text{ m}}$ and the surface charge density is $\sigma =6{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=3.6{\text{ m}}$.

a) 1.258E+00 V/m²

b) 1.384E+00 V/m²

c) 1.522E+00 V/m²

d) 1.674E+00 V/m²

e) 1.842E+00 V/m²

3) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 4a) is βkQ/a², where β equals

a) 2.22 x 10^-3 unit

b) 2.69 x 10^-3 unit

c) 3.26 x 10^-3 unit

d) 3.95 x 10^-3 unit

e) 4.79 x 10^-3 unit

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=5e$?

a) 5.569E+01 degrees

b) 6.125E+01 degrees

c) 6.738E+01 degrees

d) 7.412E+01 degrees

e) 8.153E+01 degrees

5) What is the magnitude of the electric field at the origin if a 1.8 nC charge is placed at x = 5.2 m, and a 3.1 nC charge is placed at y = 7.6 m?

a) 7.69 x 10^-1N/C

b) 8.88 x 10^-1N/C

c) 1.03 x 10⁰N/C

d) 1.18 x 10⁰N/C

e) 1.37 x 10⁰N/C

6) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) (7-s)² + 8²

b) 7² + (3−s)²

c) 7² + (8−s)²

d) 3² + 8²

e) 7² + 8²

7) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

a) 3.214E+01 N/C

b) 3.536E+01 N/C

c) 3.889E+01 N/C

d) 4.278E+01 N/C

e) 4.706E+01 N/C

8) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 2

b) 3

c) 1/2

d) 2/3

e) 3/2

9) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) 3

b) −7

c) −3

d) 2

e) −3

10) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 9² + (7-s)²

b) 2² + (7-s)²

c) 7² + (2-s)²

d) 9² + (2-s)²

e) 2² + (9-s)²

T1 G0

1)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.65 m if a=0.85 m, b=1.8 m. The total charge on the rod is 5 nC.

a) 3.959E+00 V/m²

b) 4.355E+00 V/m²

c) 4.790E+00 V/m²

d) 5.269E+00 V/m²

e) 5.796E+00 V/m²

2) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 4.821E+01 N/C

b) 5.303E+01 N/C

c) 5.834E+01 N/C

d) 6.417E+01 N/C

e) 7.059E+01 N/C

3)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.35 m (on axis) away from the loop's center?

a) 4.142E+09 N/C²

b) 4.556E+09 N/C²

c) 5.012E+09 N/C²

d) 5.513E+09 N/C²

e) 6.064E+09 N/C²

4) What is the magnitude of the electric field at the origin if a 3 nC charge is placed at x = 8.8 m, and a 2.9 nC charge is placed at y = 6.9 m?

a) 4.87 x 10^-1N/C

b) 5.62 x 10^-1N/C

c) 6.49 x 10^-1N/C

d) 7.49 x 10^-1N/C

e) 8.65 x 10^-1N/C

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 1.95 x 10^-1 unit

b) 2.36 x 10^-1 unit

c) 2.86 x 10^-1 unit

d) 3.47 x 10^-1 unit

e) 4.2 x 10^-1 unit

6) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 7−s

b) 8

c) 3−s

d) s−3

e) s−7

7) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 1/2

b) 2

c) 3

d) 2/3

e) 3/2

8) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−4

b) 5−s

c) 5

d) 1−s

e) s−1

9) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 4

b) s−8

c) 8−s

d) s−4

e) 4−s

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 2

b) 1/2

c) 3/2

d) 3

T1 G1

1) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 3.47 x 10^-1 unit

b) 4.2 x 10^-1 unit

c) 5.09 x 10^-1 unit

d) 6.17 x 10^-1 unit

e) 7.47 x 10^-1 unit

2)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.99 m (on axis) away from the loop's center?

a) 2.429E+09 N/C²

b) 2.672E+09 N/C²

c) 2.939E+09 N/C²

d) 3.233E+09 N/C²

e) 3.556E+09 N/C²

3) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 3−s

b) 7−s

c) 8

d) s−7

e) s−3

4) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 2

b) 3/2

c) 1/2

d) 3

5) What is the magnitude of the electric field at the origin if a 1.8 nC charge is placed at x = 9.6 m, and a 2 nC charge is placed at y = 8.7 m?

a) 2.95 x 10^-1N/C

b) 3.41 x 10^-1N/C

c) 3.94 x 10^-1N/C

d) 4.55 x 10^-1N/C

e) 5.25 x 10^-1N/C

6) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 6.171E+01 N/C

b) 6.788E+01 N/C

c) 7.467E+01 N/C

d) 8.214E+01 N/C

e) 9.035E+01 N/C

7) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−4

b) 8−s

c) 4

d) s−8

e) 4−s

8) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 3

b) 1/2

c) 2/3

d) 3/2

e) 2

9) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 5

b) 1−s

c) 5−s

d) s−4

e) s−1

10)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.6 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.64 m, b=1.8 m. The total charge on the rod is 3 nC.

a) 2.955E+00 V/m²

b) 3.250E+00 V/m²

c) 3.575E+00 V/m²

d) 3.933E+00 V/m²

e) 4.326E+00 V/m²

T1 G2

1) What is the magnitude of the electric field at the origin if a 3.1 nC charge is placed at x = 6.2 m, and a 2.6 nC charge is placed at y = 6 m?

a) 5.47 x 10^-1N/C

b) 6.32 x 10^-1N/C

c) 7.3 x 10^-1N/C

d) 8.43 x 10^-1N/C

e) 9.73 x 10^-1N/C

2) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 4

b) s−8

c) 8−s

d) s−4

e) 4−s

3)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m. Evaluate $f(x,y)$ at x=0.76 m if a=1.1 m, b=1.6 m. The total charge on the rod is 8 nC.

a) 5.267E+00 V/m²

b) 5.794E+00 V/m²

c) 6.374E+00 V/m²

d) 7.011E+00 V/m²

e) 7.712E+00 V/m²

4) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 3−s

b) s−3

c) 7−s

d) 8

e) s−7

5)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.2 m (on axis) away from the loop's center?

a) 6.925E+09 N/C²

b) 7.617E+09 N/C²

c) 8.379E+09 N/C²

d) 9.217E+09 N/C²

e) 1.014E+10 N/C²

6) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 2.36 x 10^-1 unit

b) 2.86 x 10^-1 unit

c) 3.47 x 10^-1 unit

d) 4.2 x 10^-1 unit

e) 5.09 x 10^-1 unit

7) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 2

b) 3

c) 3/2

d) 1/2

e) 2/3

8) A large thin isolated square plate has an area of 3 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 1.694E+02 N/C

b) 1.864E+02 N/C

c) 2.050E+02 N/C

d) 2.255E+02 N/C

e) 2.480E+02 N/C

9) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 5−s

b) s−1

c) s−4

d) 5

e) 1−s

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 2

b) 3/2

c) 1/2

d) 3

T1 H0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=1e$, $q_{2}=-8e$, and $q_{3}=4e$?

a) 3.719E+01 degrees

b) 4.091E+01 degrees

c) 4.500E+01 degrees

d) 4.950E+01 degrees

e) 5.445E+01 degrees

2)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.3 m (on axis) away from the loop's center?

a) 1.764E+09 N/C²

b) 1.941E+09 N/C²

c) 2.135E+09 N/C²

d) 2.348E+09 N/C²

e) 2.583E+09 N/C²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-9e$, and $q_{3}=4e$?

a) 5.014E-14 N

b) 5.515E-14 N

c) 6.067E-14 N

d) 6.674E-14 N

e) 7.341E-14 N

4) What is the magnitude of the electric field at the origin if a 1.2 nC charge is placed at x = 5.9 m, and a 3.1 nC charge is placed at y = 6.1 m?

a) 7.02 x 10^-1N/C

b) 8.11 x 10^-1N/C

c) 9.36 x 10^-1N/C

d) 1.08 x 10⁰N/C

e) 1.25 x 10⁰N/C

5) What angle does the electric field at the origin make with the x-axis if a 1.9 nC charge is placed at x = -5.4 m, and a 1.5 nC charge is placed at y = -7.1 m?

a) 1.38 x 10¹degrees

b) 1.59 x 10¹degrees

c) 1.84 x 10¹degrees

d) 2.13 x 10¹degrees

e) 2.45 x 10¹degrees

6) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 7² + 8²

b) 3² + 8²

c) 7² + (8−s)²

d) (7-s)² + 8²

e) 7² + (3−s)²

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 3

b) 2

c) 1/2

d) 3/2

8) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 9² + (2-s)²

b) 2² + (9-s)²

c) 7² + (2-s)²

d) 9² + (7-s)²

e) 2² + (7-s)²

9) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8

b) 7−s

c) s−7

d) 3−s

e) s−3

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) 3

b) −3

c) 2

d) −3

e) −7

T1 H1

1) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 7² + 8²

b) 7² + (3−s)²

c) (7-s)² + 8²

d) 3² + 8²

e) 7² + (8−s)²

2) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) −7

b) 3

c) −3

d) 2

e) −3

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=1e$, $q_{2}=-8e$, and $q_{3}=3e$?

a) 3.629E+01 degrees

b) 3.992E+01 degrees

c) 4.391E+01 degrees

d) 4.830E+01 degrees

e) 5.313E+01 degrees

4) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 7−s

b) s−3

c) 3−s

d) 8

e) s−7

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=6e$?

a) 2.544E-14 N

b) 2.798E-14 N

c) 3.078E-14 N

d) 3.385E-14 N

e) 3.724E-14 N

6) What angle does the electric field at the origin make with the x-axis if a 1.2 nC charge is placed at x = -6.7 m, and a 1.7 nC charge is placed at y = -6.1 m?

a) 4.47 x 10¹degrees

b) 5.17 x 10¹degrees

c) 5.97 x 10¹degrees

d) 6.89 x 10¹degrees

e) 7.96 x 10¹degrees

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 1/2

b) 3/2

c) 2

d) 3

8) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 7² + (2-s)²

b) 9² + (7-s)²

c) 9² + (2-s)²

d) 2² + (9-s)²

e) 2² + (7-s)²

9)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 3.159E+09 N/C²

b) 3.475E+09 N/C²

c) 3.823E+09 N/C²

d) 4.205E+09 N/C²

e) 4.626E+09 N/C²

10) What is the magnitude of the electric field at the origin if a 1.4 nC charge is placed at x = 8.2 m, and a 2.3 nC charge is placed at y = 5.9 m?

a) 5.39 x 10^-1N/C

b) 6.23 x 10^-1N/C

c) 7.19 x 10^-1N/C

d) 8.31 x 10^-1N/C

e) 9.59 x 10^-1N/C

T1 H2

1) What is the magnitude of the electric field at the origin if a 2.5 nC charge is placed at x = 5.3 m, and a 1.9 nC charge is placed at y = 5.6 m?

a) 7.26 x 10^-1N/C

b) 8.38 x 10^-1N/C

c) 9.68 x 10^-1N/C

d) 1.12 x 10⁰N/C

e) 1.29 x 10⁰N/C

2) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 2² + (7-s)²

b) 2² + (9-s)²

c) 9² + (7-s)²

d) 7² + (2-s)²

e) 9² + (2-s)²

3)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 3.159E+09 N/C²

b) 3.475E+09 N/C²

c) 3.823E+09 N/C²

d) 4.205E+09 N/C²

e) 4.626E+09 N/C²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-7e$, and $q_{3}=3e$?

a) 4.743E+01 degrees

b) 5.217E+01 degrees

c) 5.739E+01 degrees

d) 6.313E+01 degrees

e) 6.944E+01 degrees

5) What angle does the electric field at the origin make with the x-axis if a 2.9 nC charge is placed at x = -7.3 m, and a 1.7 nC charge is placed at y = -8.1 m?

a) 2.55 x 10¹degrees

b) 2.94 x 10¹degrees

c) 3.4 x 10¹degrees

d) 3.92 x 10¹degrees

e) 4.53 x 10¹degrees

6) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 7² + (8−s)²

b) 7² + (3−s)²

c) 3² + 8²

d) (7-s)² + 8²

e) 7² + 8²

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 1/2

b) 3/2

c) 2

d) 3

8) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8

b) s−3

c) 3−s

d) 7−s

e) s−7

9)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=5e$?

a) 8.259E-15 N

b) 9.085E-15 N

c) 9.993E-15 N

d) 1.099E-14 N

e) 1.209E-14 N

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) −7

b) 3

c) 2

d) −3

e) −3

T1 I0

1) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 7.701E+01 N/C

b) 8.471E+01 N/C

c) 9.318E+01 N/C

d) 1.025E+02 N/C

e) 1.127E+02 N/C

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=5e$?

a) 8.259E-15 N

b) 9.085E-15 N

c) 9.993E-15 N

d) 1.099E-14 N

e) 1.209E-14 N

3)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.3 m (on axis) away from the loop's center?

a) 4.788E+09 N/C²

b) 5.267E+09 N/C²

c) 5.793E+09 N/C²

d) 6.373E+09 N/C²

e) 7.010E+09 N/C²

4) What is the magnitude of the electric field at the origin if a 3 nC charge is placed at x = 5.1 m, and a 2 nC charge is placed at y = 8.6 m?

a) 7.99 x 10^-1N/C

b) 9.22 x 10^-1N/C

c) 1.07 x 10⁰N/C

d) 1.23 x 10⁰N/C

e) 1.42 x 10⁰N/C

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 1.95 x 10^-1 unit

b) 2.36 x 10^-1 unit

c) 2.86 x 10^-1 unit

d) 3.47 x 10^-1 unit

e) 4.2 x 10^-1 unit

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

a) s−3

b) s−7

c) 3

d) 7−s

e) 3−s

7) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s − 9

b) 2

c) 9 − s

d) 2 − s

e) s − 2

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−4

b) 8−s

c) 4−s

d) s−8

e) 4

9) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−1

b) 5

c) s−4

d) 5−s

e) 1−s

10) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 2/3

b) 1/2

c) 3

d) 3/2

e) 2

T1 I1

1) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

a) 7−s

b) 3−s

c) 3

d) s−3

e) s−7

2) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 2/3

b) 3/2

c) 1/2

d) 3

e) 2

3) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 3.47 x 10^-1 unit

b) 4.2 x 10^-1 unit

c) 5.09 x 10^-1 unit

d) 6.17 x 10^-1 unit

e) 7.47 x 10^-1 unit

4) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 2.571E+01 N/C

b) 2.828E+01 N/C

c) 3.111E+01 N/C

d) 3.422E+01 N/C

e) 3.765E+01 N/C

5) What is the magnitude of the electric field at the origin if a 1.8 nC charge is placed at x = 9.6 m, and a 2 nC charge is placed at y = 8.7 m?

a) 2.95 x 10^-1N/C

b) 3.41 x 10^-1N/C

c) 3.94 x 10^-1N/C

d) 4.55 x 10^-1N/C

e) 5.25 x 10^-1N/C

6) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 2

b) 9 − s

c) 2 − s

d) s − 9

e) s − 2

7) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−8

b) 8−s

c) 4−s

d) 4

e) s−4

8)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=5e$?

a) 2.248E-14 N

b) 2.473E-14 N

c) 2.721E-14 N

d) 2.993E-14 N

e) 3.292E-14 N

9) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−1

b) s−4

c) 1−s

d) 5−s

e) 5

10)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 5.581E+09 N/C²

b) 6.139E+09 N/C²

c) 6.753E+09 N/C²

d) 7.428E+09 N/C²

e) 8.171E+09 N/C²

T1 I2

1) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 7.701E+01 N/C

b) 8.471E+01 N/C

c) 9.318E+01 N/C

d) 1.025E+02 N/C

e) 1.127E+02 N/C

2) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s − 9

b) 2

c) 2 − s

d) s − 2

e) 9 − s

3) What is the magnitude of the electric field at the origin if a 3 nC charge is placed at x = 8.8 m, and a 2.9 nC charge is placed at y = 6.9 m?

a) 4.87 x 10^-1N/C

b) 5.62 x 10^-1N/C

c) 6.49 x 10^-1N/C

d) 7.49 x 10^-1N/C

e) 8.65 x 10^-1N/C

4) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

a) s−7

b) 7−s

c) s−3

d) 3

e) 3−s

5) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−8

b) 8−s

c) 4−s

d) 4

e) s−4

6)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.99 m (on axis) away from the loop's center?

a) 2.429E+09 N/C²

b) 2.672E+09 N/C²

c) 2.939E+09 N/C²

d) 3.233E+09 N/C²

e) 3.556E+09 N/C²

7) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 3/2

b) 2

c) 3

d) 1/2

e) 2/3

8) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 1.95 x 10^-1 unit

b) 2.36 x 10^-1 unit

c) 2.86 x 10^-1 unit

d) 3.47 x 10^-1 unit

e) 4.2 x 10^-1 unit

9) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−1

b) s−4

c) 5−s

d) 1−s

e) 5

10)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-7e$, and $q_{3}=2e$?

a) 3.391E-14 N

b) 3.731E-14 N

c) 4.104E-14 N

d) 4.514E-14 N

e) 4.965E-14 N

T1 J0

1)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.54 m if a=1.0 m, b=2.0 m. The total charge on the rod is 3 nC.

a) 1.665E+00 V/m²

b) 1.831E+00 V/m²

c) 2.014E+00 V/m²

d) 2.216E+00 V/m²

e) 2.437E+00 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=4e$?

a) 5.914E+01 degrees

b) 6.506E+01 degrees

c) 7.157E+01 degrees

d) 7.872E+01 degrees

e) 8.659E+01 degrees

3)

A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.4 m (on axis) away from the loop's center?

a) 7.119E+09 N/C²

b) 7.831E+09 N/C²

c) 8.614E+09 N/C²

d) 9.476E+09 N/C²

e) 1.042E+10 N/C²

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 1.61 x 10^-1 unit

b) 1.95 x 10^-1 unit

c) 2.36 x 10^-1 unit

d) 2.86 x 10^-1 unit

e) 3.47 x 10^-1 unit

5) What angle does the electric field at the origin make with the x-axis if a 2 nC charge is placed at x = -8.7 m, and a 2.7 nC charge is placed at y = -5.2 m?

a) 4.23 x 10¹degrees

b) 4.88 x 10¹degrees

c) 5.64 x 10¹degrees

d) 6.51 x 10¹degrees

e) 7.52 x 10¹degrees

6) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

a) 8

b) 1/2

c) 4

d) 2

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) −3

b) 3

c) 2

d) −7

e) −3

8) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 7² + (3−s)²

b) 7² + (8−s)²

c) 7² + 8²

d) (7-s)² + 8²

e) 3² + 8²

9) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 5

b) 1−s

c) s−4

d) s−1

e) 5−s

10) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s − 2

b) 9 − s

c) s − 9

d) 2

e) 2 − s

T1 J1

1) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) −7

b) −3

c) 2

d) −3

e) 3

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-7e$, and $q_{3}=3e$?

a) 4.743E+01 degrees

b) 5.217E+01 degrees

c) 5.739E+01 degrees

d) 6.313E+01 degrees

e) 6.944E+01 degrees

3)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.4 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.69 m, b=2.2 m. The total charge on the rod is 6 nC.

a) 3.161E+00 V/m²

b) 3.477E+00 V/m²

c) 3.825E+00 V/m²

d) 4.208E+00 V/m²

e) 4.628E+00 V/m²

4) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 2 − s

b) s − 9

c) 9 − s

d) s − 2

e) 2

5) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 7² + (8−s)²

b) (7-s)² + 8²

c) 7² + 8²

d) 3² + 8²

e) 7² + (3−s)²

6) What angle does the electric field at the origin make with the x-axis if a 2.6 nC charge is placed at x = -8.3 m, and a 2.5 nC charge is placed at y = -9.6 m?

a) 2.32 x 10¹degrees

b) 2.68 x 10¹degrees

c) 3.09 x 10¹degrees

d) 3.57 x 10¹degrees

e) 4.12 x 10¹degrees

7) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 2.86 x 10^-1

b) 3.47 x 10^-1

c) 4.2 x 10^-1

d) 5.09 x 10^-1

e) 6.17 x 10^-1

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

a) 8

b) 1/2

c) 2

d) 4

9)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 5.581E+09 N/C²

b) 6.139E+09 N/C²

c) 6.753E+09 N/C²

d) 7.428E+09 N/C²

e) 8.171E+09 N/C²

10) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−4

b) 5

c) 5−s

d) 1−s

e) s−1

T1 J2

1) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 1.95 x 10^-1 unit

b) 2.36 x 10^-1 unit

c) 2.86 x 10^-1 unit

d) 3.47 x 10^-1 unit

e) 4.2 x 10^-1 unit

2)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.96 m if a=0.95 m, b=1.8 m. The total charge on the rod is 7 nC.

a) 3.385E+00 V/m²

b) 3.724E+00 V/m²

c) 4.096E+00 V/m²

d) 4.506E+00 V/m²

e) 4.957E+00 V/m²

3)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

a) 2.013E+09 N/C²

b) 2.214E+09 N/C²

c) 2.435E+09 N/C²

d) 2.679E+09 N/C²

e) 2.947E+09 N/C²

4) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s − 2

b) 2 − s

c) 2

d) s − 9

e) 9 − s

5) What angle does the electric field at the origin make with the x-axis if a 1.8 nC charge is placed at x = -6.9 m, and a 2.5 nC charge is placed at y = -7.5 m?

a) 2.79 x 10¹degrees

b) 3.22 x 10¹degrees

c) 3.72 x 10¹degrees

d) 4.3 x 10¹degrees

e) 4.96 x 10¹degrees

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) −7

b) −3

c) 2

d) 3

e) −3

7)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-9e$, and $q_{3}=6e$?

a) 5.767E+01 degrees

b) 6.343E+01 degrees

c) 6.978E+01 degrees

d) 7.676E+01 degrees

e) 8.443E+01 degrees

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

a) 8

b) 2

c) 1/2

d) 4

9) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 7² + (8−s)²

b) (7-s)² + 8²

c) 7² + 8²

d) 3² + 8²

e) 7² + (3−s)²

10) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−1

b) 1−s

c) s−4

d) 5−s

e) 5

T1 K0

1)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.7{\text{ m}}$ and the surface charge density is $\sigma =7{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=5.8{\text{ m}}$.

a) 3.722E-01 V/m²

b) 4.094E-01 V/m²

c) 4.504E-01 V/m²

d) 4.954E-01 V/m²

e) 5.450E-01 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-9e$, and $q_{3}=5e$?

a) 3.961E+01 degrees

b) 4.357E+01 degrees

c) 4.793E+01 degrees

d) 5.272E+01 degrees

e) 5.799E+01 degrees

3)

A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 5.402E+09 N/C²

b) 5.943E+09 N/C²

c) 6.537E+09 N/C²

d) 7.191E+09 N/C²

e) 7.910E+09 N/C²

4) What is the magnitude of the electric field at the origin if a 3 nC charge is placed at x = 5.1 m, and a 2 nC charge is placed at y = 8.6 m?

a) 7.99 x 10^-1N/C

b) 9.22 x 10^-1N/C

c) 1.07 x 10⁰N/C

d) 1.23 x 10⁰N/C

e) 1.42 x 10⁰N/C

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 4a) is βkQ/a², where β equals

a) 1.33 x 10^-3 unit

b) 1.61 x 10^-3 unit

c) 1.95 x 10^-3 unit

d) 2.37 x 10^-3 unit

e) 2.87 x 10^-3 unit

6) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 7² + (2-s)²

b) 9² + (7-s)²

c) 2² + (9-s)²

d) 2² + (7-s)²

e) 9² + (2-s)²

7) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 5

b) 1−s

c) s−4

d) s−1

e) 5−s

8) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 5−s

b) 5

c) 1−s

d) s−4

e) s−1

9) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) 3

b) −3

c) 2

d) −3

e) −7

10) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 3−s

b) 7−s

c) s−7

d) 8

e) s−3

T1 K1

1) What is the magnitude of the electric field at the origin if a 2.7 nC charge is placed at x = 9.1 m, and a 2.5 nC charge is placed at y = 5.9 m?

a) 3.99 x 10^-1N/C

b) 4.6 x 10^-1N/C

c) 5.32 x 10^-1N/C

d) 6.14 x 10^-1N/C

e) 7.09 x 10^-1N/C

2) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−1

b) 5

c) 1−s

d) 5−s

e) s−4

3) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−3

b) 7−s

c) 3−s

d) 8

e) s−7

4) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 5−s

b) 5

c) s−4

d) s−1

e) 1−s

5) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 7² + (2-s)²

b) 2² + (9-s)²

c) 2² + (7-s)²

d) 9² + (7-s)²

e) 9² + (2-s)²

6) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 2a) is βkQ/a², where β equals

a) 7.31 x 10^-3 unit

b) 8.86 x 10^-3 unit

c) 1.07 x 10^-2 unit

d) 1.3 x 10^-2 unit

e) 1.57 x 10^-2 unit

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) 2

b) −7

c) 3

d) −3

e) −3

8)

A ring is uniformly charged with a net charge of 8 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.32 m (on axis) away from the loop's center?

a) 3.339E+09 N/C²

b) 3.673E+09 N/C²

c) 4.041E+09 N/C²

d) 4.445E+09 N/C²

e) 4.889E+09 N/C²

9)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.9{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=5.1{\text{ m}}$.

a) 8.253E-01 V/m²

b) 9.079E-01 V/m²

c) 9.987E-01 V/m²

d) 1.099E+00 V/m²

e) 1.208E+00 V/m²

10)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=4e$?

a) 5.377E+01 degrees

b) 5.914E+01 degrees

c) 6.506E+01 degrees

d) 7.157E+01 degrees

e) 7.872E+01 degrees

T1 K2

1) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−4

b) 5

c) 1−s

d) s−1

e) 5−s

2)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.0{\text{ m}}$ and the surface charge density is $\sigma =8{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=2.0{\text{ m}}$.

a) 9.459E+00 V/m²

b) 1.040E+01 V/m²

c) 1.145E+01 V/m²

d) 1.259E+01 V/m²

e) 1.385E+01 V/m²

3) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 9² + (2-s)²

b) 9² + (7-s)²

c) 7² + (2-s)²

d) 2² + (7-s)²

e) 2² + (9-s)²

4)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.2 m (on axis) away from the loop's center?

a) 6.925E+09 N/C²

b) 7.617E+09 N/C²

c) 8.379E+09 N/C²

d) 9.217E+09 N/C²

e) 1.014E+10 N/C²

5) What is the magnitude of the electric field at the origin if a 2.7 nC charge is placed at x = 9.1 m, and a 2.5 nC charge is placed at y = 5.9 m?

a) 3.99 x 10^-1N/C

b) 4.6 x 10^-1N/C

c) 5.32 x 10^-1N/C

d) 6.14 x 10^-1N/C

e) 7.09 x 10^-1N/C

6) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−3

b) 8

c) 7−s

d) s−7

e) 3−s

7) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 4a) is βkQ/a², where β equals

a) 2.22 x 10^-3 unit

b) 2.69 x 10^-3 unit

c) 3.26 x 10^-3 unit

d) 3.95 x 10^-3 unit

e) 4.79 x 10^-3 unit

8) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) −3

b) 3

c) 2

d) −3

e) −7

9) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 5

b) s−4

c) s−1

d) 1−s

e) 5−s

10)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-7e$, and $q_{3}=5e$?

a) 4.357E+01 degrees

b) 4.793E+01 degrees

c) 5.272E+01 degrees

d) 5.799E+01 degrees

e) 6.379E+01 degrees

T1 L0

1)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.0{\text{ m}}$ and the surface charge density is $\sigma =8{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=2.0{\text{ m}}$.

a) 9.459E+00 V/m²

b) 1.040E+01 V/m²

c) 1.145E+01 V/m²

d) 1.259E+01 V/m²

e) 1.385E+01 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=5e$?

a) 2.248E-14 N

b) 2.473E-14 N

c) 2.721E-14 N

d) 2.993E-14 N

e) 3.292E-14 N

3) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 3.428E+01 N/C

b) 3.771E+01 N/C

c) 4.148E+01 N/C

d) 4.563E+01 N/C

e) 5.020E+01 N/C

4) What angle does the electric field at the origin make with the x-axis if a 2.8 nC charge is placed at x = -9.8 m, and a 2.8 nC charge is placed at y = -5.8 m?

a) 7.07 x 10¹degrees

b) 8.16 x 10¹degrees

c) 9.43 x 10¹degrees

d) 1.09 x 10²degrees

e) 1.26 x 10²degrees

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

a) 1.09 x 10^-3 unit

b) 1.33 x 10^-3 unit

c) 1.61 x 10^-3 unit

d) 1.95 x 10^-3 unit

e) 2.36 x 10^-3 unit

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) −3

b) 2

c) −3

d) 3

e) −7

7) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 4

b) 4−s

c) 8−s

d) s−4

e) s−8

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−8

b) s−4

c) 4

d) 8−s

e) 4−s

9) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

a) 3

b) 7−s

c) s−7

d) s−3

e) 3−s

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 3/2

b) 1/2

c) 3

d) 2

T1 L1

1) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 4a) is βkQ/a², where β equals

a) 2.22 x 10^-3 unit

b) 2.69 x 10^-3 unit

c) 3.26 x 10^-3 unit

d) 3.95 x 10^-3 unit

e) 4.79 x 10^-3 unit

2) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 4.821E+01 N/C

b) 5.303E+01 N/C

c) 5.834E+01 N/C

d) 6.417E+01 N/C

e) 7.059E+01 N/C

3)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=4.3{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=2.4{\text{ m}}$.

a) 5.647E+00 V/m²

b) 6.212E+00 V/m²

c) 6.833E+00 V/m²

d) 7.517E+00 V/m²

e) 8.268E+00 V/m²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=5e$?

a) 9.958E-15 N

b) 1.095E-14 N

c) 1.205E-14 N

d) 1.325E-14 N

e) 1.458E-14 N

5) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8−s

b) s−4

c) 4−s

d) 4

e) s−8

6) What angle does the electric field at the origin make with the x-axis if a 2.8 nC charge is placed at x = -9.8 m, and a 2.8 nC charge is placed at y = -5.8 m?

a) 7.07 x 10¹degrees

b) 8.16 x 10¹degrees

c) 9.43 x 10¹degrees

d) 1.09 x 10²degrees

e) 1.26 x 10²degrees

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

a) 3

b) 7−s

c) s−3

d) s−7

e) 3−s

8) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) −3

b) −3

c) −7

d) 2

e) 3

9) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 2

b) 3

c) 1/2

d) 3/2

10) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 4−s

b) s−8

c) 8−s

d) s−4

e) 4

T1 L2

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=5e$?

a) 8.259E-15 N

b) 9.085E-15 N

c) 9.993E-15 N

d) 1.099E-14 N

e) 1.209E-14 N

2) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8−s

b) 4

c) s−8

d) 4−s

e) s−4

3) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 4

b) s−4

c) s−8

d) 4−s

e) 8−s

4) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) 2

b) −3

c) −3

d) 3

e) −7

5) What angle does the electric field at the origin make with the x-axis if a 1.4 nC charge is placed at x = -5.5 m, and a 2.8 nC charge is placed at y = -6.8 m?

a) 3.95 x 10¹degrees

b) 4.56 x 10¹degrees

c) 5.26 x 10¹degrees

d) 6.08 x 10¹degrees

e) 7.02 x 10¹degrees

6)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.8{\text{ m}}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=0.83{\text{ m}}$.

a) 2.898E+01 V/m²

b) 3.188E+01 V/m²

c) 3.507E+01 V/m²

d) 3.857E+01 V/m²

e) 4.243E+01 V/m²

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

a) s−3

b) 3−s

c) 7−s

d) s−7

e) 3

8) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 3a, 5a) is βkQ/a², where β equals

a) 1.08 x 10^-3 unit

b) 1.31 x 10^-3 unit

c) 1.59 x 10^-3 unit

d) 1.93 x 10^-3 unit

e) 2.34 x 10^-3 unit

9) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 1/2

b) 3

c) 3/2

d) 2

10) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 6.534E+01 N/C

b) 7.187E+01 N/C

c) 7.906E+01 N/C

d) 8.696E+01 N/C

e) 9.566E+01 N/C

T1 M0

1)

A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.73 m (on axis) away from the loop's center?

a) 7.415E+09 N/C²

b) 8.156E+09 N/C²

c) 8.972E+09 N/C²

d) 9.869E+09 N/C²

e) 1.086E+10 N/C²

2) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

a) 9.546E+01 N/C

b) 1.050E+02 N/C

c) 1.155E+02 N/C

d) 1.271E+02 N/C

e) 1.398E+02 N/C

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-8e$, and $q_{3}=2e$?

a) 1.172E-14 N

b) 1.290E-14 N

c) 1.419E-14 N

d) 1.561E-14 N

e) 1.717E-14 N

4) What is the magnitude of the electric field at the origin if a 2.5 nC charge is placed at x = 5.3 m, and a 1.9 nC charge is placed at y = 5.6 m?

a) 7.26 x 10^-1N/C

b) 8.38 x 10^-1N/C

c) 9.68 x 10^-1N/C

d) 1.12 x 10⁰N/C

e) 1.29 x 10⁰N/C

5) What angle does the electric field at the origin make with the x-axis if a 1.4 nC charge is placed at x = -5.5 m, and a 2.8 nC charge is placed at y = -6.8 m?

a) 3.95 x 10¹degrees

b) 4.56 x 10¹degrees

c) 5.26 x 10¹degrees

d) 6.08 x 10¹degrees

e) 7.02 x 10¹degrees

6) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−3

b) 7−s

c) s−7

d) 3−s

e) 8

7) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 2

b) 3

c) 3/2

d) 2/3

e) 1/2

8) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 2

b) s − 9

c) 2 − s

d) 9 − s

e) s − 2

9) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 9² + (2-s)²

b) 9² + (7-s)²

c) 2² + (9-s)²

d) 2² + (7-s)²

e) 7² + (2-s)²

10) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−8

b) s−4

c) 4

d) 8−s

e) 4−s

T1 M1

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=6e$?

a) 1.028E-14 N

b) 1.130E-14 N

c) 1.244E-14 N

d) 1.368E-14 N

e) 1.505E-14 N

2) What is the magnitude of the electric field at the origin if a 3.1 nC charge is placed at x = 6.2 m, and a 2.6 nC charge is placed at y = 6 m?

a) 5.47 x 10^-1N/C

b) 6.32 x 10^-1N/C

c) 7.3 x 10^-1N/C

d) 8.43 x 10^-1N/C

e) 9.73 x 10^-1N/C

3) What angle does the electric field at the origin make with the x-axis if a 2.8 nC charge is placed at x = -9.8 m, and a 2.8 nC charge is placed at y = -5.8 m?

a) 7.07 x 10¹degrees

b) 8.16 x 10¹degrees

c) 9.43 x 10¹degrees

d) 1.09 x 10²degrees

e) 1.26 x 10²degrees

4) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 2/3

b) 1/2

c) 3/2

d) 2

e) 3

5) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 4.492E+01 N/C

b) 4.941E+01 N/C

c) 5.435E+01 N/C

d) 5.979E+01 N/C

e) 6.577E+01 N/C

6) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 9 − s

b) s − 9

c) 2

d) s − 2

e) 2 − s

7) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8

b) 7−s

c) 3−s

d) s−3

e) s−7

8) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 7² + (2-s)²

b) 2² + (9-s)²

c) 9² + (2-s)²

d) 2² + (7-s)²

e) 9² + (7-s)²

9)

A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.73 m (on axis) away from the loop's center?

a) 7.415E+09 N/C²

b) 8.156E+09 N/C²

c) 8.972E+09 N/C²

d) 9.869E+09 N/C²

e) 1.086E+10 N/C²

10) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 4−s

b) 8−s

c) s−4

d) 4

e) s−8

T1 M2

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-7e$, and $q_{3}=2e$?

a) 3.426E-15 N

b) 3.768E-15 N

c) 4.145E-15 N

d) 4.560E-15 N

e) 5.015E-15 N

2) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 2/3

b) 3

c) 2

d) 3/2

e) 1/2

3) What angle does the electric field at the origin make with the x-axis if a 2.9 nC charge is placed at x = -6.3 m, and a 2.1 nC charge is placed at y = -8.8 m?

a) 1.32 x 10¹degrees

b) 1.53 x 10¹degrees

c) 1.76 x 10¹degrees

d) 2.04 x 10¹degrees

e) 2.35 x 10¹degrees

4) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8−s

b) 4

c) s−4

d) 4−s

e) s−8

5) What is the magnitude of the electric field at the origin if a 1.7 nC charge is placed at x = 6.4 m, and a 3 nC charge is placed at y = 8 m?

a) 4.22 x 10^-1N/C

b) 4.87 x 10^-1N/C

c) 5.63 x 10^-1N/C

d) 6.5 x 10^-1N/C

e) 7.51 x 10^-1N/C

6) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 2² + (9-s)²

b) 9² + (7-s)²

c) 2² + (7-s)²

d) 7² + (2-s)²

e) 9² + (2-s)²

7) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 8.471E+01 N/C

b) 9.318E+01 N/C

c) 1.025E+02 N/C

d) 1.127E+02 N/C

e) 1.240E+02 N/C

8) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 9 − s

b) s − 2

c) s − 9

d) 2

e) 2 − s

9)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.35 m (on axis) away from the loop's center?

a) 4.142E+09 N/C²

b) 4.556E+09 N/C²

c) 5.012E+09 N/C²

d) 5.513E+09 N/C²

e) 6.064E+09 N/C²

10) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 7−s

b) s−7

c) 3−s

d) 8

e) s−3

T1 N0

1)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 5.581E+09 N/C²

b) 6.139E+09 N/C²

c) 6.753E+09 N/C²

d) 7.428E+09 N/C²

e) 8.171E+09 N/C²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=3e$?

a) 2.036E-14 N

b) 2.240E-14 N

c) 2.464E-14 N

d) 2.710E-14 N

e) 2.981E-14 N

3)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.0{\text{ m}}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=1.2{\text{ m}}$.

a) 8.933E+00 V/m²

b) 9.826E+00 V/m²

c) 1.081E+01 V/m²

d) 1.189E+01 V/m²

e) 1.308E+01 V/m²

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 2.86 x 10^-1

b) 3.47 x 10^-1

c) 4.2 x 10^-1

d) 5.09 x 10^-1

e) 6.17 x 10^-1

5) What angle does the electric field at the origin make with the x-axis if a 2.9 nC charge is placed at x = -7.3 m, and a 1.7 nC charge is placed at y = -8.1 m?

a) 2.55 x 10¹degrees

b) 2.94 x 10¹degrees

c) 3.4 x 10¹degrees

d) 3.92 x 10¹degrees

e) 4.53 x 10¹degrees

6) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 2

b) 3/2

c) 3

d) 1/2

e) 2/3

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 1/2

b) 3/2

c) 2

d) 3

8) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−1

b) 1−s

c) 5−s

d) s−4

e) 5

9) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 3−s

b) 8

c) 7−s

d) s−3

e) s−7

10) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−8

b) 8−s

c) 4−s

d) s−4

e) 4

T1 N1

1) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 3

b) 3/2

c) 2

d) 1/2

2) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−3

b) 7−s

c) s−7

d) 3−s

e) 8

3) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 1−s

b) s−1

c) s−4

d) 5−s

e) 5

4)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=4.3{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=2.4{\text{ m}}$.

a) 5.647E+00 V/m²

b) 6.212E+00 V/m²

c) 6.833E+00 V/m²

d) 7.517E+00 V/m²

e) 8.268E+00 V/m²

5) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8−s

b) 4−s

c) s−4

d) 4

e) s−8

6) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 1.95 x 10^-1 unit

b) 2.36 x 10^-1 unit

c) 2.86 x 10^-1 unit

d) 3.47 x 10^-1 unit

e) 4.2 x 10^-1 unit

7)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-8e$, and $q_{3}=3e$?

a) 5.243E-14 N

b) 5.768E-14 N

c) 6.344E-14 N

d) 6.979E-14 N

e) 7.677E-14 N

8)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.5 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.33 m (on axis) away from the loop's center?

a) 1.353E+09 N/C²

b) 1.488E+09 N/C²

c) 1.637E+09 N/C²

d) 1.801E+09 N/C²

e) 1.981E+09 N/C²

9) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 3

b) 3/2

c) 2/3

d) 2

e) 1/2

10) What angle does the electric field at the origin make with the x-axis if a 1.4 nC charge is placed at x = -5.5 m, and a 2.8 nC charge is placed at y = -6.8 m?

a) 3.95 x 10¹degrees

b) 4.56 x 10¹degrees

c) 5.26 x 10¹degrees

d) 6.08 x 10¹degrees

e) 7.02 x 10¹degrees

T1 N2

1) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 1/2

b) 3

c) 2

d) 3/2

2) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 2

b) 3

c) 1/2

d) 3/2

e) 2/3

3) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 5

b) 1−s

c) s−1

d) s−4

e) 5−s

4)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.4{\text{ m}}$ and the surface charge density is $\sigma =6{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=0.56{\text{ m}}$.

a) 2.567E+01 V/m²

b) 2.824E+01 V/m²

c) 3.106E+01 V/m²

d) 3.417E+01 V/m²

e) 3.759E+01 V/m²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-7e$, and $q_{3}=3e$?

a) 4.171E-14 N

b) 4.588E-14 N

c) 5.047E-14 N

d) 5.551E-14 N

e) 6.107E-14 N

6) What angle does the electric field at the origin make with the x-axis if a 2.8 nC charge is placed at x = -8 m, and a 1.5 nC charge is placed at y = -8.7 m?

a) 2.44 x 10¹degrees

b) 2.81 x 10¹degrees

c) 3.25 x 10¹degrees

d) 3.75 x 10¹degrees

e) 4.33 x 10¹degrees

7) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8−s

b) 4−s

c) 4

d) s−4

e) s−8

8) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 3.47 x 10^-1 unit

b) 4.2 x 10^-1 unit

c) 5.09 x 10^-1 unit

d) 6.17 x 10^-1 unit

e) 7.47 x 10^-1 unit

9)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 8.336E+09 N/C²

b) 9.170E+09 N/C²

c) 1.009E+10 N/C²

d) 1.110E+10 N/C²

e) 1.220E+10 N/C²

10) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8

b) s−7

c) 3−s

d) 7−s

e) s−3

T1 O0

1) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 3.500E+01 N/C

b) 3.850E+01 N/C

c) 4.235E+01 N/C

d) 4.659E+01 N/C

e) 5.125E+01 N/C

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=6e$?

a) 2.544E-14 N

b) 2.798E-14 N

c) 3.078E-14 N

d) 3.385E-14 N

e) 3.724E-14 N

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-9e$, and $q_{3}=5e$?

a) 5.272E+01 degrees

b) 5.799E+01 degrees

c) 6.379E+01 degrees

d) 7.017E+01 degrees

e) 7.719E+01 degrees

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 1.95 x 10^-1 unit

b) 2.36 x 10^-1 unit

c) 2.86 x 10^-1 unit

d) 3.47 x 10^-1 unit

e) 4.2 x 10^-1 unit

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 2a) is βkQ/a², where β equals

a) 7.31 x 10^-3 unit

b) 8.86 x 10^-3 unit

c) 1.07 x 10^-2 unit

d) 1.3 x 10^-2 unit

e) 1.57 x 10^-2 unit

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) −3

b) −7

c) 3

d) 2

e) −3

7) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 5−s

b) 5

c) 1−s

d) s−1

e) s−4

8) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 1−s

b) 5−s

c) 5

d) s−4

e) s−1

9) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 1/2

b) 2/3

c) 3/2

d) 3

e) 2

10) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−7

b) 7−s

c) 3−s

d) 8

e) s−3

T1 O1

1) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 1.61 x 10^-1 unit

b) 1.95 x 10^-1 unit

c) 2.36 x 10^-1 unit

d) 2.86 x 10^-1 unit

e) 3.47 x 10^-1 unit

2) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 3a, 5a) is βkQ/a², where β equals

a) 1.08 x 10^-3 unit

b) 1.31 x 10^-3 unit

c) 1.59 x 10^-3 unit

d) 1.93 x 10^-3 unit

e) 2.34 x 10^-3 unit

3) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 7−s

b) 8

c) 3−s

d) s−7

e) s−3

4) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 6.534E+01 N/C

b) 7.187E+01 N/C

c) 7.906E+01 N/C

d) 8.696E+01 N/C

e) 9.566E+01 N/C

5) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 5

b) s−4

c) s−1

d) 1−s

e) 5−s

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) 2

b) −3

c) 3

d) −3

e) −7

7)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-9e$, and $q_{3}=5e$?

a) 6.125E+01 degrees

b) 6.738E+01 degrees

c) 7.412E+01 degrees

d) 8.153E+01 degrees

e) 8.968E+01 degrees

8) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 2

b) 3/2

c) 1/2

d) 2/3

e) 3

9) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 5

b) s−4

c) s−1

d) 5−s

e) 1−s

10)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=5e$?

a) 8.259E-15 N

b) 9.085E-15 N

c) 9.993E-15 N

d) 1.099E-14 N

e) 1.209E-14 N

T1 O2

1) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) 2

b) −3

c) −7

d) −3

e) 3

2) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 2/3

b) 1/2

c) 3/2

d) 2

e) 3

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-7e$, and $q_{3}=3e$?

a) 4.743E+01 degrees

b) 5.217E+01 degrees

c) 5.739E+01 degrees

d) 6.313E+01 degrees

e) 6.944E+01 degrees

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=4e$?

a) 8.613E-15 N

b) 9.474E-15 N

c) 1.042E-14 N

d) 1.146E-14 N

e) 1.261E-14 N

5) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

a) 5.647E+01 N/C

b) 6.212E+01 N/C

c) 6.833E+01 N/C

d) 7.516E+01 N/C

e) 8.268E+01 N/C

6) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 5−s

b) s−1

c) 5

d) s−4

e) 1−s

7) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−3

b) 7−s

c) s−7

d) 8

e) 3−s

8) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

a) 1.09 x 10^-3 unit

b) 1.33 x 10^-3 unit

c) 1.61 x 10^-3 unit

d) 1.95 x 10^-3 unit

e) 2.36 x 10^-3 unit

9) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 5

b) 5−s

c) 1−s

d) s−1

e) s−4

10) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 1.95 x 10^-1 unit

b) 2.36 x 10^-1 unit

c) 2.86 x 10^-1 unit

d) 3.47 x 10^-1 unit

e) 4.2 x 10^-1 unit

T1 P0

1)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.5 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.33 m (on axis) away from the loop's center?

a) 1.353E+09 N/C²

b) 1.488E+09 N/C²

c) 1.637E+09 N/C²

d) 1.801E+09 N/C²

e) 1.981E+09 N/C²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-8e$, and $q_{3}=6e$?

a) 5.243E+01 degrees

b) 5.767E+01 degrees

c) 6.343E+01 degrees

d) 6.978E+01 degrees

e) 7.676E+01 degrees

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-7e$, and $q_{3}=3e$?

a) 1.473E-14 N

b) 1.620E-14 N

c) 1.782E-14 N

d) 1.960E-14 N

e) 2.156E-14 N

4) What is the magnitude of the electric field at the origin if a 1.8 nC charge is placed at x = 9.6 m, and a 2 nC charge is placed at y = 8.7 m?

a) 2.95 x 10^-1N/C

b) 3.41 x 10^-1N/C

c) 3.94 x 10^-1N/C

d) 4.55 x 10^-1N/C

e) 5.25 x 10^-1N/C

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 6a) is βkQ/a², where β equals

a) 1.52 x 10^-4 unit

b) 1.85 x 10^-4 unit

c) 2.24 x 10^-4 unit

d) 2.71 x 10^-4 unit

e) 3.28 x 10^-4 unit

6) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−1

b) 1−s

c) s−4

d) 5−s

e) 5

7) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

a) 8

b) 1/2

c) 2

d) 4

8) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 9² + (7-s)²

b) 9² + (2-s)²

c) 2² + (9-s)²

d) 2² + (7-s)²

e) 7² + (2-s)²

9) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 2

b) s − 2

c) 2 − s

d) s − 9

e) 9 − s

10) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 3

b) 2/3

c) 2

d) 1/2

e) 3/2

T1 P1

1) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

a) 8

b) 4

c) 2

d) 1/2

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=4e$?

a) 5.914E+01 degrees

b) 6.506E+01 degrees

c) 7.157E+01 degrees

d) 7.872E+01 degrees

e) 8.659E+01 degrees

3)

A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 5.402E+09 N/C²

b) 5.943E+09 N/C²

c) 6.537E+09 N/C²

d) 7.191E+09 N/C²

e) 7.910E+09 N/C²

4) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 5−s

b) 5

c) s−4

d) s−1

e) 1−s

5) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 2

b) 3

c) 2/3

d) 3/2

e) 1/2

6) What is the magnitude of the electric field at the origin if a 2.1 nC charge is placed at x = 7 m, and a 2.1 nC charge is placed at y = 8.6 m?

a) 3 x 10^-1N/C

b) 3.47 x 10^-1N/C

c) 4 x 10^-1N/C

d) 4.62 x 10^-1N/C

e) 5.34 x 10^-1N/C

7) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

a) 1.61 x 10^-3 unit

b) 1.95 x 10^-3 unit

c) 2.36 x 10^-3 unit

d) 2.86 x 10^-3 unit

e) 3.46 x 10^-3 unit

8)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-7e$, and $q_{3}=3e$?

a) 1.473E-14 N

b) 1.620E-14 N

c) 1.782E-14 N

d) 1.960E-14 N

e) 2.156E-14 N

9) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 9 − s

b) s − 9

c) 2

d) 2 − s

e) s − 2

10) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 9² + (2-s)²

b) 2² + (7-s)²

c) 2² + (9-s)²

d) 7² + (2-s)²

e) 9² + (7-s)²

T1 P2

1)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 8.336E+09 N/C²

b) 9.170E+09 N/C²

c) 1.009E+10 N/C²

d) 1.110E+10 N/C²

e) 1.220E+10 N/C²

2) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 3a) is βkQ/a², where β equals

a) 3.38 x 10^-3 unit

b) 4.1 x 10^-3 unit

c) 4.96 x 10^-3 unit

d) 6.01 x 10^-3 unit

e) 7.28 x 10^-3 unit

3) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s − 9

b) 9 − s

c) 2

d) 2 − s

e) s − 2

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=5e$?

a) 5.569E+01 degrees

b) 6.125E+01 degrees

c) 6.738E+01 degrees

d) 7.412E+01 degrees

e) 8.153E+01 degrees

5) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−1

b) 5

c) 1−s

d) 5−s

e) s−4

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=5e$?

a) 2.248E-14 N

b) 2.473E-14 N

c) 2.721E-14 N

d) 2.993E-14 N

e) 3.292E-14 N

7) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 2² + (7-s)²

b) 9² + (2-s)²

c) 2² + (9-s)²

d) 7² + (2-s)²

e) 9² + (7-s)²

8) What is the magnitude of the electric field at the origin if a 2.5 nC charge is placed at x = 5.3 m, and a 1.9 nC charge is placed at y = 5.6 m?

a) 7.26 x 10^-1N/C

b) 8.38 x 10^-1N/C

c) 9.68 x 10^-1N/C

d) 1.12 x 10⁰N/C

e) 1.29 x 10⁰N/C

9) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

a) 1/2

b) 4

c) 8

d) 2

10) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 1/2

b) 2

c) 3

d) 3/2

e) 2/3

T1 Q0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-8e$, and $q_{3}=5e$?

a) 5.062E+01 degrees

b) 5.569E+01 degrees

c) 6.125E+01 degrees

d) 6.738E+01 degrees

e) 7.412E+01 degrees

2)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=4.3{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=2.4{\text{ m}}$.

a) 5.647E+00 V/m²

b) 6.212E+00 V/m²

c) 6.833E+00 V/m²

d) 7.517E+00 V/m²

e) 8.268E+00 V/m²

3)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.6 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.64 m, b=1.8 m. The total charge on the rod is 3 nC.

a) 2.955E+00 V/m²

b) 3.250E+00 V/m²

c) 3.575E+00 V/m²

d) 3.933E+00 V/m²

e) 4.326E+00 V/m²

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 4a) is βkQ/a², where β equals

a) 1.33 x 10^-3 unit

b) 1.61 x 10^-3 unit

c) 1.95 x 10^-3 unit

d) 2.37 x 10^-3 unit

e) 2.87 x 10^-3 unit

5) What angle does the electric field at the origin make with the x-axis if a 1.4 nC charge is placed at x = -8.7 m, and a 2.7 nC charge is placed at y = -8.3 m?

a) 4.85 x 10¹degrees

b) 5.61 x 10¹degrees

c) 6.47 x 10¹degrees

d) 7.48 x 10¹degrees

e) 8.63 x 10¹degrees

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

a) 3−s

b) s−7

c) 7−s

d) s−3

e) 3

7) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8−s

b) 4

c) 4−s

d) s−4

e) s−8

8) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 2 − s

b) 2

c) s − 9

d) 9 − s

e) s − 2

9) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) 2

b) −3

c) −3

d) −7

e) 3

10) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8−s

b) s−4

c) 4

d) 4−s

e) s−8

T1 Q1

1) What angle does the electric field at the origin make with the x-axis if a 2.8 nC charge is placed at x = -9.8 m, and a 2.8 nC charge is placed at y = -5.8 m?

a) 7.07 x 10¹degrees

b) 8.16 x 10¹degrees

c) 9.43 x 10¹degrees

d) 1.09 x 10²degrees

e) 1.26 x 10²degrees

2) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 2

b) s − 2

c) 2 − s

d) s − 9

e) 9 − s

3)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.6 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.64 m, b=1.8 m. The total charge on the rod is 3 nC.

a) 2.955E+00 V/m²

b) 3.250E+00 V/m²

c) 3.575E+00 V/m²

d) 3.933E+00 V/m²

e) 4.326E+00 V/m²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-7e$, and $q_{3}=3e$?

a) 4.743E+01 degrees

b) 5.217E+01 degrees

c) 5.739E+01 degrees

d) 6.313E+01 degrees

e) 6.944E+01 degrees

5) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−8

b) 4

c) s−4

d) 8−s

e) 4−s

6) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 2a) is βkQ/a², where β equals

a) 7.31 x 10^-3 unit

b) 8.86 x 10^-3 unit

c) 1.07 x 10^-2 unit

d) 1.3 x 10^-2 unit

e) 1.57 x 10^-2 unit

7) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8−s

b) 4

c) s−4

d) 4−s

e) s−8

8) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

a) 3−s

b) s−3

c) 7−s

d) 3

e) s−7

9)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.4{\text{ m}}$ and the surface charge density is $\sigma =6{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=0.56{\text{ m}}$.

a) 2.567E+01 V/m²

b) 2.824E+01 V/m²

c) 3.106E+01 V/m²

d) 3.417E+01 V/m²

e) 3.759E+01 V/m²

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) −3

b) 3

c) −7

d) −3

e) 2

T1 Q2

1) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−4

b) 4

c) 4−s

d) s−8

e) 8−s

2) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s − 9

b) 9 − s

c) 2

d) 2 − s

e) s − 2

3) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−4

b) 8−s

c) 4−s

d) 4

e) s−8

4)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m. Evaluate $f(x,y)$ at x=0.52 m if a=0.88 m, b=1.3 m. The total charge on the rod is 6 nC.

a) 6.804E+00 V/m²

b) 7.485E+00 V/m²

c) 8.233E+00 V/m²

d) 9.056E+00 V/m²

e) 9.962E+00 V/m²

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 3a) is βkQ/a², where β equals

a) 3.38 x 10^-3 unit

b) 4.1 x 10^-3 unit

c) 4.96 x 10^-3 unit

d) 6.01 x 10^-3 unit

e) 7.28 x 10^-3 unit

6)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.4{\text{ m}}$ and the surface charge density is $\sigma =6{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=0.56{\text{ m}}$.

a) 2.567E+01 V/m²

b) 2.824E+01 V/m²

c) 3.106E+01 V/m²

d) 3.417E+01 V/m²

e) 3.759E+01 V/m²

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

a) 3

b) s−7

c) 3−s

d) s−3

e) 7−s

8) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) −3

b) 2

c) −7

d) 3

e) −3

9) What angle does the electric field at the origin make with the x-axis if a 2.9 nC charge is placed at x = -6.3 m, and a 2.1 nC charge is placed at y = -8.8 m?

a) 1.32 x 10¹degrees

b) 1.53 x 10¹degrees

c) 1.76 x 10¹degrees

d) 2.04 x 10¹degrees

e) 2.35 x 10¹degrees

10)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-9e$, and $q_{3}=6e$?

a) 5.767E+01 degrees

b) 6.343E+01 degrees

c) 6.978E+01 degrees

d) 7.676E+01 degrees

e) 8.443E+01 degrees

T1 R0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-9e$, and $q_{3}=4e$?

a) 5.243E+01 degrees

b) 5.767E+01 degrees

c) 6.343E+01 degrees

d) 6.978E+01 degrees

e) 7.676E+01 degrees

2)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=4.3{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=2.4{\text{ m}}$.

a) 5.647E+00 V/m²

b) 6.212E+00 V/m²

c) 6.833E+00 V/m²

d) 7.517E+00 V/m²

e) 8.268E+00 V/m²

3) A large thin isolated square plate has an area of 3 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 1.694E+02 N/C

b) 1.864E+02 N/C

c) 2.050E+02 N/C

d) 2.255E+02 N/C

e) 2.480E+02 N/C

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

a) 1.33 x 10^-3 unit

b) 1.61 x 10^-3 unit

c) 1.95 x 10^-3 unit

d) 2.36 x 10^-3 unit

e) 2.86 x 10^-3 unit

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 1.95 x 10^-1 unit

b) 2.36 x 10^-1 unit

c) 2.86 x 10^-1 unit

d) 3.47 x 10^-1 unit

e) 4.2 x 10^-1 unit

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

a) s−3

b) 3−s

c) 7−s

d) 3

e) s−7

7) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 3/2

b) 3

c) 2

d) 1/2

e) 2/3

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 4

b) s−4

c) 4−s

d) s−8

e) 8−s

9) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

a) 2

b) 1/2

c) 4

d) 8

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) −3

b) 3

c) −3

d) 2

e) −7

T1 R1

1) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) 2

b) 3

c) −3

d) −7

e) −3

2) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 8.471E+01 N/C

b) 9.318E+01 N/C

c) 1.025E+02 N/C

d) 1.127E+02 N/C

e) 1.240E+02 N/C

3) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

a) 8

b) 1/2

c) 4

d) 2

4) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

a) 3−s

b) 7−s

c) 3

d) s−7

e) s−3

5) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 1/2

b) 3/2

c) 2/3

d) 3

e) 2

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=5e$?

a) 5.569E+01 degrees

b) 6.125E+01 degrees

c) 6.738E+01 degrees

d) 7.412E+01 degrees

e) 8.153E+01 degrees

7) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

a) 1.61 x 10^-3 unit

b) 1.95 x 10^-3 unit

c) 2.36 x 10^-3 unit

d) 2.86 x 10^-3 unit

e) 3.46 x 10^-3 unit

8)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.0{\text{ m}}$ and the surface charge density is $\sigma =8{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=2.0{\text{ m}}$.

a) 9.459E+00 V/m²

b) 1.040E+01 V/m²

c) 1.145E+01 V/m²

d) 1.259E+01 V/m²

e) 1.385E+01 V/m²

9) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 2.36 x 10^-1 unit

b) 2.86 x 10^-1 unit

c) 3.47 x 10^-1 unit

d) 4.2 x 10^-1 unit

e) 5.09 x 10^-1 unit

10) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8−s

b) 4−s

c) 4

d) s−8

e) s−4

T1 R2

1) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 2

b) 2/3

c) 3/2

d) 1/2

e) 3

2) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 2.86 x 10^-1 unit

b) 3.47 x 10^-1 unit

c) 4.2 x 10^-1 unit

d) 5.09 x 10^-1 unit

e) 6.17 x 10^-1 unit

3) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

a) 7.000E+01 N/C

b) 7.701E+01 N/C

c) 8.471E+01 N/C

d) 9.318E+01 N/C

e) 1.025E+02 N/C

4)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.8{\text{ m}}$ and the surface charge density is $\sigma =6{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=3.6{\text{ m}}$.

a) 1.258E+00 V/m²

b) 1.384E+00 V/m²

c) 1.522E+00 V/m²

d) 1.674E+00 V/m²

e) 1.842E+00 V/m²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-9e$, and $q_{3}=5e$?

a) 3.961E+01 degrees

b) 4.357E+01 degrees

c) 4.793E+01 degrees

d) 5.272E+01 degrees

e) 5.799E+01 degrees

6) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

a) 2

b) 4

c) 1/2

d) 8

7) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−8

b) 4−s

c) 8−s

d) 4

e) s−4

8) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 6a) is βkQ/a², where β equals

a) 1.52 x 10^-4 unit

b) 1.85 x 10^-4 unit

c) 2.24 x 10^-4 unit

d) 2.71 x 10^-4 unit

e) 3.28 x 10^-4 unit

9) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) −3

b) 3

c) −7

d) 2

e) −3

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

a) 7−s

b) 3−s

c) 3

d) s−7

e) s−3

T1 S0

1)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.4 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.69 m, b=2.2 m. The total charge on the rod is 6 nC.

a) 3.161E+00 V/m²

b) 3.477E+00 V/m²

c) 3.825E+00 V/m²

d) 4.208E+00 V/m²

e) 4.628E+00 V/m²

2)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.3 m (on axis) away from the loop's center?

a) 1.764E+09 N/C²

b) 1.941E+09 N/C²

c) 2.135E+09 N/C²

d) 2.348E+09 N/C²

e) 2.583E+09 N/C²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-7e$, and $q_{3}=3e$?

a) 4.171E-14 N

b) 4.588E-14 N

c) 5.047E-14 N

d) 5.551E-14 N

e) 6.107E-14 N

4) What is the magnitude of the electric field at the origin if a 2.5 nC charge is placed at x = 5.3 m, and a 1.9 nC charge is placed at y = 5.6 m?

a) 7.26 x 10^-1N/C

b) 8.38 x 10^-1N/C

c) 9.68 x 10^-1N/C

d) 1.12 x 10⁰N/C

e) 1.29 x 10⁰N/C

5) What angle does the electric field at the origin make with the x-axis if a 2 nC charge is placed at x = -8 m, and a 1.4 nC charge is placed at y = -9.3 m?

a) 2.37 x 10¹degrees

b) 2.74 x 10¹degrees

c) 3.16 x 10¹degrees

d) 3.65 x 10¹degrees

e) 4.22 x 10¹degrees

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) −3

b) 2

c) −3

d) 3

e) −7

7) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8

b) s−7

c) 7−s

d) s−3

e) 3−s

8) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 7² + 8²

b) 7² + (3−s)²

c) 3² + 8²

d) 7² + (8−s)²

e) (7-s)² + 8²

9) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 2

b) s − 9

c) 9 − s

d) 2 − s

e) s − 2

10) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−8

b) 4−s

c) 8−s

d) 4

e) s−4

T1 S1

1)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 8.336E+09 N/C²

b) 9.170E+09 N/C²

c) 1.009E+10 N/C²

d) 1.110E+10 N/C²

e) 1.220E+10 N/C²

2) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8

b) s−7

c) 3−s

d) 7−s

e) s−3

3)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m. Evaluate $f(x,y)$ at x=0.76 m if a=1.1 m, b=1.6 m. The total charge on the rod is 8 nC.

a) 5.267E+00 V/m²

b) 5.794E+00 V/m²

c) 6.374E+00 V/m²

d) 7.011E+00 V/m²

e) 7.712E+00 V/m²

4) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s − 2

b) 9 − s

c) s − 9

d) 2

e) 2 − s

5) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 3² + 8²

b) 7² + 8²

c) 7² + (3−s)²

d) (7-s)² + 8²

e) 7² + (8−s)²

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) −3

b) −3

c) 2

d) 3

e) −7

7)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=5e$?

a) 9.958E-15 N

b) 1.095E-14 N

c) 1.205E-14 N

d) 1.325E-14 N

e) 1.458E-14 N

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8−s

b) s−8

c) s−4

d) 4

e) 4−s

9) What is the magnitude of the electric field at the origin if a 2.1 nC charge is placed at x = 7 m, and a 2.1 nC charge is placed at y = 8.6 m?

a) 3 x 10^-1N/C

b) 3.47 x 10^-1N/C

c) 4 x 10^-1N/C

d) 4.62 x 10^-1N/C

e) 5.34 x 10^-1N/C

10) What angle does the electric field at the origin make with the x-axis if a 1.2 nC charge is placed at x = -6.7 m, and a 1.7 nC charge is placed at y = -6.1 m?

a) 4.47 x 10¹degrees

b) 5.17 x 10¹degrees

c) 5.97 x 10¹degrees

d) 6.89 x 10¹degrees

e) 7.96 x 10¹degrees

T1 S2

1) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 3² + 8²

b) 7² + (3−s)²

c) 7² + 8²

d) (7-s)² + 8²

e) 7² + (8−s)²

2)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.4 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.69 m, b=2.2 m. The total charge on the rod is 6 nC.

a) 3.161E+00 V/m²

b) 3.477E+00 V/m²

c) 3.825E+00 V/m²

d) 4.208E+00 V/m²

e) 4.628E+00 V/m²

3) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−8

b) 4

c) s−4

d) 8−s

e) 4−s

4)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.35 m (on axis) away from the loop's center?

a) 4.142E+09 N/C²

b) 4.556E+09 N/C²

c) 5.012E+09 N/C²

d) 5.513E+09 N/C²

e) 6.064E+09 N/C²

5) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 7−s

b) s−7

c) 8

d) 3−s

e) s−3

6) What angle does the electric field at the origin make with the x-axis if a 1.8 nC charge is placed at x = -6.9 m, and a 2.5 nC charge is placed at y = -7.5 m?

a) 2.79 x 10¹degrees

b) 3.22 x 10¹degrees

c) 3.72 x 10¹degrees

d) 4.3 x 10¹degrees

e) 4.96 x 10¹degrees

7) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 9 − s

b) s − 2

c) 2

d) 2 − s

e) s − 9

8)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-7e$, and $q_{3}=3e$?

a) 4.171E-14 N

b) 4.588E-14 N

c) 5.047E-14 N

d) 5.551E-14 N

e) 6.107E-14 N

9) What is the magnitude of the electric field at the origin if a 1.8 nC charge is placed at x = 9.6 m, and a 2 nC charge is placed at y = 8.7 m?

a) 2.95 x 10^-1N/C

b) 3.41 x 10^-1N/C

c) 3.94 x 10^-1N/C

d) 4.55 x 10^-1N/C

e) 5.25 x 10^-1N/C

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) 2

b) 3

c) −3

d) −3

e) −7

T1 T0

1)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

a) 2.013E+09 N/C²

b) 2.214E+09 N/C²

c) 2.435E+09 N/C²

d) 2.679E+09 N/C²

e) 2.947E+09 N/C²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-8e$, and $q_{3}=2e$?

a) 1.172E-14 N

b) 1.290E-14 N

c) 1.419E-14 N

d) 1.561E-14 N

e) 1.717E-14 N

3)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=1.0 m if a=1.1 m, b=1.4 m. The total charge on the rod is 5 nC.

a) 4.602E+00 V/m²

b) 5.062E+00 V/m²

c) 5.568E+00 V/m²

d) 6.125E+00 V/m²

e) 6.738E+00 V/m²

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 5a, 5a) is βkQ/a², where β equals

a) 6.46 x 10^-4 unit

b) 7.82 x 10^-4 unit

c) 9.48 x 10^-4 unit

d) 1.15 x 10^-3 unit

e) 1.39 x 10^-3 unit

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 1.61 x 10^-1 unit

b) 1.95 x 10^-1 unit

c) 2.36 x 10^-1 unit

d) 2.86 x 10^-1 unit

e) 3.47 x 10^-1 unit

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 3/2

b) 2

c) 1/2

d) 3

7) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−4

b) 8−s

c) 4−s

d) 4

e) s−8

8) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

a) 3−s

b) 7−s

c) 3

d) s−7

e) s−3

9) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 1−s

b) 5−s

c) 5

d) s−4

e) s−1

10) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s − 9

b) 9 − s

c) 2 − s

d) s − 2

e) 2

T1 T1

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-7e$, and $q_{3}=3e$?

a) 1.473E-14 N

b) 1.620E-14 N

c) 1.782E-14 N

d) 1.960E-14 N

e) 2.156E-14 N

2) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 2 − s

b) 2

c) s − 9

d) 9 − s

e) s − 2

3) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 3/2

b) 1/2

c) 2

d) 3

4) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

a) s−3

b) 7−s

c) s−7

d) 3−s

e) 3

5) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−4

b) 1−s

c) s−1

d) 5

e) 5−s

6) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 4

b) s−8

c) 8−s

d) 4−s

e) s−4

7)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.5 m if a=0.67 m, b=2.4 m. The total charge on the rod is 9 nC.

a) 5.465E+00 V/m²

b) 6.012E+00 V/m²

c) 6.613E+00 V/m²

d) 7.274E+00 V/m²

e) 8.002E+00 V/m²

8) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

a) 1.61 x 10^-3 unit

b) 1.95 x 10^-3 unit

c) 2.36 x 10^-3 unit

d) 2.86 x 10^-3 unit

e) 3.46 x 10^-3 unit

9)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 8.336E+09 N/C²

b) 9.170E+09 N/C²

c) 1.009E+10 N/C²

d) 1.110E+10 N/C²

e) 1.220E+10 N/C²

10) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 1.95 x 10^-1 unit

b) 2.36 x 10^-1 unit

c) 2.86 x 10^-1 unit

d) 3.47 x 10^-1 unit

e) 4.2 x 10^-1 unit

T1 T2

1) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 2

b) 9 − s

c) 2 − s

d) s − 2

e) s − 9

2) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−4

b) 1−s

c) 5−s

d) s−1

e) 5

3) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 3a, 5a) is βkQ/a², where β equals

a) 1.08 x 10^-3 unit

b) 1.31 x 10^-3 unit

c) 1.59 x 10^-3 unit

d) 1.93 x 10^-3 unit

e) 2.34 x 10^-3 unit

4) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

a) s−3

b) 3−s

c) 7−s

d) 3

e) s−7

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=6e$?

a) 2.544E-14 N

b) 2.798E-14 N

c) 3.078E-14 N

d) 3.385E-14 N

e) 3.724E-14 N

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 1/2

b) 3

c) 3/2

d) 2

7)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.62 m, b=1.3 m. The total charge on the rod is 7 nC.

a) 6.311E+00 V/m²

b) 6.943E+00 V/m²

c) 7.637E+00 V/m²

d) 8.401E+00 V/m²

e) 9.241E+00 V/m²

8)

A ring is uniformly charged with a net charge of 8 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.32 m (on axis) away from the loop's center?

a) 3.339E+09 N/C²

b) 3.673E+09 N/C²

c) 4.041E+09 N/C²

d) 4.445E+09 N/C²

e) 4.889E+09 N/C²

9) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 1.95 x 10^-1 unit

b) 2.36 x 10^-1 unit

c) 2.86 x 10^-1 unit

d) 3.47 x 10^-1 unit

e) 4.2 x 10^-1 unit

10) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 4−s

b) 4

c) 8−s

d) s−4

e) s−8

T1 U0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-9e$, and $q_{3}=6e$?

a) 1.308E-13 N

b) 1.439E-13 N

c) 1.583E-13 N

d) 1.741E-13 N

e) 1.915E-13 N

2)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.5 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.33 m (on axis) away from the loop's center?

a) 1.353E+09 N/C²

b) 1.488E+09 N/C²

c) 1.637E+09 N/C²

d) 1.801E+09 N/C²

e) 1.981E+09 N/C²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=4e$?

a) 5.377E+01 degrees

b) 5.914E+01 degrees

c) 6.506E+01 degrees

d) 7.157E+01 degrees

e) 7.872E+01 degrees

4) What is the magnitude of the electric field at the origin if a 3 nC charge is placed at x = 5.1 m, and a 2 nC charge is placed at y = 8.6 m?

a) 7.99 x 10^-1N/C

b) 9.22 x 10^-1N/C

c) 1.07 x 10⁰N/C

d) 1.23 x 10⁰N/C

e) 1.42 x 10⁰N/C

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 1.95 x 10^-1 unit

b) 2.36 x 10^-1 unit

c) 2.86 x 10^-1 unit

d) 3.47 x 10^-1 unit

e) 4.2 x 10^-1 unit

6) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

a) 2

b) 1/2

c) 4

d) 8

7) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 1/2

b) 2/3

c) 3/2

d) 2

e) 3

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8−s

b) s−8

c) 4−s

d) 4

e) s−4

9) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 9² + (2-s)²

b) 9² + (7-s)²

c) 2² + (9-s)²

d) 2² + (7-s)²

e) 7² + (2-s)²

10) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8

b) s−7

c) 3−s

d) 7−s

e) s−3

T1 U1

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=6e$?

a) 1.028E-14 N

b) 1.130E-14 N

c) 1.244E-14 N

d) 1.368E-14 N

e) 1.505E-14 N

2) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

a) 2

b) 1/2

c) 4

d) 8

3) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 3.47 x 10^-1 unit

b) 4.2 x 10^-1 unit

c) 5.09 x 10^-1 unit

d) 6.17 x 10^-1 unit

e) 7.47 x 10^-1 unit

4) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−4

b) 8−s

c) 4

d) s−8

e) 4−s

5) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 2

b) 3

c) 2/3

d) 1/2

e) 3/2

6) What is the magnitude of the electric field at the origin if a 1.8 nC charge is placed at x = 5.2 m, and a 3.1 nC charge is placed at y = 7.6 m?

a) 7.69 x 10^-1N/C

b) 8.88 x 10^-1N/C

c) 1.03 x 10⁰N/C

d) 1.18 x 10⁰N/C

e) 1.37 x 10⁰N/C

7) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 2² + (7-s)²

b) 2² + (9-s)²

c) 7² + (2-s)²

d) 9² + (2-s)²

e) 9² + (7-s)²

8)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=5e$?

a) 5.569E+01 degrees

b) 6.125E+01 degrees

c) 6.738E+01 degrees

d) 7.412E+01 degrees

e) 8.153E+01 degrees

9) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8

b) s−7

c) 3−s

d) s−3

e) 7−s

10)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.35 m (on axis) away from the loop's center?

a) 4.142E+09 N/C²

b) 4.556E+09 N/C²

c) 5.012E+09 N/C²

d) 5.513E+09 N/C²

e) 6.064E+09 N/C²

T1 U2

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=5e$?

a) 8.259E-15 N

b) 9.085E-15 N

c) 9.993E-15 N

d) 1.099E-14 N

e) 1.209E-14 N

2) What is the magnitude of the electric field at the origin if a 1.7 nC charge is placed at x = 6.4 m, and a 3 nC charge is placed at y = 8 m?

a) 4.22 x 10^-1N/C

b) 4.87 x 10^-1N/C

c) 5.63 x 10^-1N/C

d) 6.5 x 10^-1N/C

e) 7.51 x 10^-1N/C

3)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.99 m (on axis) away from the loop's center?

a) 2.429E+09 N/C²

b) 2.672E+09 N/C²

c) 2.939E+09 N/C²

d) 3.233E+09 N/C²

e) 3.556E+09 N/C²

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 1.61 x 10^-1 unit

b) 1.95 x 10^-1 unit

c) 2.36 x 10^-1 unit

d) 2.86 x 10^-1 unit

e) 3.47 x 10^-1 unit

5) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 9² + (2-s)²

b) 9² + (7-s)²

c) 7² + (2-s)²

d) 2² + (9-s)²

e) 2² + (7-s)²

6) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−4

b) 4−s

c) s−8

d) 8−s

e) 4

7) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 3

b) 2/3

c) 2

d) 1/2

e) 3/2

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

a) 4

b) 8

c) 1/2

d) 2

9) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 7−s

b) 3−s

c) s−3

d) 8

e) s−7

10)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=6e$?

a) 6.343E+01 degrees

b) 6.978E+01 degrees

c) 7.676E+01 degrees

d) 8.443E+01 degrees

e) 9.288E+01 degrees

T1 V0

1)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.99 m (on axis) away from the loop's center?

a) 2.429E+09 N/C²

b) 2.672E+09 N/C²

c) 2.939E+09 N/C²

d) 3.233E+09 N/C²

e) 3.556E+09 N/C²

2) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 2.652E+01 N/C

b) 2.917E+01 N/C

c) 3.209E+01 N/C

d) 3.529E+01 N/C

e) 3.882E+01 N/C

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=1e$, $q_{2}=-7e$, and $q_{3}=4e$?

a) 4.091E+01 degrees

b) 4.500E+01 degrees

c) 4.950E+01 degrees

d) 5.445E+01 degrees

e) 5.990E+01 degrees

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

a) 1.09 x 10^-3 unit

b) 1.33 x 10^-3 unit

c) 1.61 x 10^-3 unit

d) 1.95 x 10^-3 unit

e) 2.36 x 10^-3 unit

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 1.95 x 10^-1 unit

b) 2.36 x 10^-1 unit

c) 2.86 x 10^-1 unit

d) 3.47 x 10^-1 unit

e) 4.2 x 10^-1 unit

6) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 2² + (7-s)²

b) 2² + (9-s)²

c) 7² + (2-s)²

d) 9² + (7-s)²

e) 9² + (2-s)²

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 1/2

b) 2

c) 3

d) 3/2

8) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) 2

b) −3

c) 3

d) −7

e) −3

9) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

a) 3−s

b) 7−s

c) 3

d) s−7

e) s−3

10) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 3/2

b) 2

c) 1/2

d) 2/3

e) 3

T1 V1

1) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

a) 1.33 x 10^-3 unit

b) 1.61 x 10^-3 unit

c) 1.95 x 10^-3 unit

d) 2.36 x 10^-3 unit

e) 2.86 x 10^-3 unit

2) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) −3

b) −3

c) −7

d) 3

e) 2

3) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 1/2

b) 3/2

c) 3

d) 2

e) 2/3

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-7e$, and $q_{3}=5e$?

a) 4.357E+01 degrees

b) 4.793E+01 degrees

c) 5.272E+01 degrees

d) 5.799E+01 degrees

e) 6.379E+01 degrees

5)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 3.159E+09 N/C²

b) 3.475E+09 N/C²

c) 3.823E+09 N/C²

d) 4.205E+09 N/C²

e) 4.626E+09 N/C²

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 3

b) 1/2

c) 2

d) 3/2

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

a) s−7

b) 3−s

c) 7−s

d) 3

e) s−3

8) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 6.534E+01 N/C

b) 7.187E+01 N/C

c) 7.906E+01 N/C

d) 8.696E+01 N/C

e) 9.566E+01 N/C

9) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 9² + (2-s)²

b) 7² + (2-s)²

c) 2² + (9-s)²

d) 2² + (7-s)²

e) 9² + (7-s)²

10) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 1.95 x 10^-1 unit

b) 2.36 x 10^-1 unit

c) 2.86 x 10^-1 unit

d) 3.47 x 10^-1 unit

e) 4.2 x 10^-1 unit

T1 V2

1) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 1.95 x 10^-1 unit

b) 2.36 x 10^-1 unit

c) 2.86 x 10^-1 unit

d) 3.47 x 10^-1 unit

e) 4.2 x 10^-1 unit

2)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.99 m (on axis) away from the loop's center?

a) 2.429E+09 N/C²

b) 2.672E+09 N/C²

c) 2.939E+09 N/C²

d) 3.233E+09 N/C²

e) 3.556E+09 N/C²

3) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 2.357E+01 N/C

b) 2.593E+01 N/C

c) 2.852E+01 N/C

d) 3.137E+01 N/C

e) 3.451E+01 N/C

4) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 2² + (9-s)²

b) 7² + (2-s)²

c) 9² + (2-s)²

d) 2² + (7-s)²

e) 9² + (7-s)²

5) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

a) s−7

b) s−3

c) 7−s

d) 3−s

e) 3

6) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

a) 1.61 x 10^-3 unit

b) 1.95 x 10^-3 unit

c) 2.36 x 10^-3 unit

d) 2.86 x 10^-3 unit

e) 3.46 x 10^-3 unit

7) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 3

b) 2/3

c) 3/2

d) 2

e) 1/2

8)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-9e$, and $q_{3}=5e$?

a) 5.272E+01 degrees

b) 5.799E+01 degrees

c) 6.379E+01 degrees

d) 7.017E+01 degrees

e) 7.719E+01 degrees

9) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

a) 3/2

b) 2

c) 3

d) 1/2

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) −7

b) 2

c) −3

d) 3

e) −3

T1 W0

1)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 8.336E+09 N/C²

b) 9.170E+09 N/C²

c) 1.009E+10 N/C²

d) 1.110E+10 N/C²

e) 1.220E+10 N/C²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-9e$, and $q_{3}=4e$?

a) 5.243E+01 degrees

b) 5.767E+01 degrees

c) 6.343E+01 degrees

d) 6.978E+01 degrees

e) 7.676E+01 degrees

3) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 3.500E+01 N/C

b) 3.850E+01 N/C

c) 4.235E+01 N/C

d) 4.659E+01 N/C

e) 5.125E+01 N/C

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

a) 1.09 x 10^-3 unit

b) 1.33 x 10^-3 unit

c) 1.61 x 10^-3 unit

d) 1.95 x 10^-3 unit

e) 2.36 x 10^-3 unit

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 3.47 x 10^-1 unit

b) 4.2 x 10^-1 unit

c) 5.09 x 10^-1 unit

d) 6.17 x 10^-1 unit

e) 7.47 x 10^-1 unit

6) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 4−s

b) s−4

c) 4

d) s−8

e) 8−s

7) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 3

b) 2/3

c) 3/2

d) 2

e) 1/2

8) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−3

b) 3−s

c) 8

d) s−7

e) 7−s

9) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 4−s

b) s−4

c) 4

d) s−8

e) 8−s

10) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 9² + (7-s)²

b) 2² + (9-s)²

c) 2² + (7-s)²

d) 9² + (2-s)²

e) 7² + (2-s)²

T1 W1

1) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8−s

b) s−8

c) 4−s

d) s−4

e) 4

2) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 7² + (2-s)²

b) 9² + (2-s)²

c) 2² + (9-s)²

d) 9² + (7-s)²

e) 2² + (7-s)²

3) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−8

b) s−4

c) 4−s

d) 4

e) 8−s

4) A large thin isolated square plate has an area of 3 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 9.412E+01 N/C

b) 1.035E+02 N/C

c) 1.139E+02 N/C

d) 1.253E+02 N/C

e) 1.378E+02 N/C

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

a) 1.33 x 10^-3 unit

b) 1.61 x 10^-3 unit

c) 1.95 x 10^-3 unit

d) 2.36 x 10^-3 unit

e) 2.86 x 10^-3 unit

6) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 1.95 x 10^-1 unit

b) 2.36 x 10^-1 unit

c) 2.86 x 10^-1 unit

d) 3.47 x 10^-1 unit

e) 4.2 x 10^-1 unit

7) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8

b) s−7

c) s−3

d) 7−s

e) 3−s

8)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 5.581E+09 N/C²

b) 6.139E+09 N/C²

c) 6.753E+09 N/C²

d) 7.428E+09 N/C²

e) 8.171E+09 N/C²

9)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-9e$, and $q_{3}=6e$?

a) 5.767E+01 degrees

b) 6.343E+01 degrees

c) 6.978E+01 degrees

d) 7.676E+01 degrees

e) 8.443E+01 degrees

10) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 3

b) 1/2

c) 2

d) 3/2

e) 2/3

T1 W2

1) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 1.61 x 10^-1 unit

b) 1.95 x 10^-1 unit

c) 2.36 x 10^-1 unit

d) 2.86 x 10^-1 unit

e) 3.47 x 10^-1 unit

2) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 2² + (9-s)²

b) 9² + (2-s)²

c) 2² + (7-s)²

d) 9² + (7-s)²

e) 7² + (2-s)²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-8e$, and $q_{3}=6e$?

a) 5.243E+01 degrees

b) 5.767E+01 degrees

c) 6.343E+01 degrees

d) 6.978E+01 degrees

e) 7.676E+01 degrees

4) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 4.821E+01 N/C

b) 5.303E+01 N/C

c) 5.834E+01 N/C

d) 6.417E+01 N/C

e) 7.059E+01 N/C

5) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 2

b) 3

c) 2/3

d) 1/2

e) 3/2

6) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 3a) is βkQ/a², where β equals

a) 3.38 x 10^-3 unit

b) 4.1 x 10^-3 unit

c) 4.96 x 10^-3 unit

d) 6.01 x 10^-3 unit

e) 7.28 x 10^-3 unit

7)

A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.4 m (on axis) away from the loop's center?

a) 7.119E+09 N/C²

b) 7.831E+09 N/C²

c) 8.614E+09 N/C²

d) 9.476E+09 N/C²

e) 1.042E+10 N/C²

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 4

b) 8−s

c) s−4

d) 4−s

e) s−8

9) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−4

b) 4−s

c) 8−s

d) s−8

e) 4

10) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 3−s

b) s−3

c) s−7

d) 7−s

e) 8

T1 X0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-9e$, and $q_{3}=5e$?

a) 5.272E+01 degrees

b) 5.799E+01 degrees

c) 6.379E+01 degrees

d) 7.017E+01 degrees

e) 7.719E+01 degrees

2)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.0{\text{ m}}$ and the surface charge density is $\sigma =8{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=2.0{\text{ m}}$.

a) 9.459E+00 V/m²

b) 1.040E+01 V/m²

c) 1.145E+01 V/m²

d) 1.259E+01 V/m²

e) 1.385E+01 V/m²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=6e$?

a) 1.028E-14 N

b) 1.130E-14 N

c) 1.244E-14 N

d) 1.368E-14 N

e) 1.505E-14 N

4) What is the magnitude of the electric field at the origin if a 1.9 nC charge is placed at x = 9.7 m, and a 3.1 nC charge is placed at y = 5.5 m?

a) 5.28 x 10^-1N/C

b) 6.1 x 10^-1N/C

c) 7.04 x 10^-1N/C

d) 8.13 x 10^-1N/C

e) 9.39 x 10^-1N/C

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 2.36 x 10^-1 unit

b) 2.86 x 10^-1 unit

c) 3.47 x 10^-1 unit

d) 4.2 x 10^-1 unit

e) 5.09 x 10^-1 unit

6) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−4

b) 5−s

c) 5

d) s−1

e) 1−s

7) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

a) 1/2

b) 8

c) 4

d) 2

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−8

b) 8−s

c) 4

d) s−4

e) 4−s

9) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s − 2

b) 2

c) s − 9

d) 9 − s

e) 2 − s

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

a) 7−s

b) 3−s

c) s−7

d) s−3

e) 3

T1 X1

1) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

a) 1/2

b) 8

c) 2

d) 4

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=6e$?

a) 2.544E-14 N

b) 2.798E-14 N

c) 3.078E-14 N

d) 3.385E-14 N

e) 3.724E-14 N

3) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

a) 7−s

b) 3−s

c) s−7

d) s−3

e) 3

4) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 9 − s

b) 2 − s

c) s − 2

d) 2

e) s − 9

5)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.8{\text{ m}}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=1.1{\text{ m}}$.

a) 7.517E+00 V/m²

b) 8.269E+00 V/m²

c) 9.096E+00 V/m²

d) 1.001E+01 V/m²

e) 1.101E+01 V/m²

6) What is the magnitude of the electric field at the origin if a 1.8 nC charge is placed at x = 5.2 m, and a 3.1 nC charge is placed at y = 7.6 m?

a) 7.69 x 10^-1N/C

b) 8.88 x 10^-1N/C

c) 1.03 x 10⁰N/C

d) 1.18 x 10⁰N/C

e) 1.37 x 10⁰N/C

7)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=4e$?

a) 5.377E+01 degrees

b) 5.914E+01 degrees

c) 6.506E+01 degrees

d) 7.157E+01 degrees

e) 7.872E+01 degrees

8) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−1

b) 5

c) 5−s

d) 1−s

e) s−4

9) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 4−s

b) 4

c) s−4

d) 8−s

e) s−8

10) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 1.95 x 10^-1 unit

b) 2.36 x 10^-1 unit

c) 2.86 x 10^-1 unit

d) 3.47 x 10^-1 unit

e) 4.2 x 10^-1 unit

T1 X2

1) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 1.61 x 10^-1 unit

b) 1.95 x 10^-1 unit

c) 2.36 x 10^-1 unit

d) 2.86 x 10^-1 unit

e) 3.47 x 10^-1 unit

2) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

a) 7−s

b) s−3

c) 3−s

d) 3

e) s−7

3) What is the magnitude of the electric field at the origin if a 1.8 nC charge is placed at x = 9.6 m, and a 2 nC charge is placed at y = 8.7 m?

a) 2.95 x 10^-1N/C

b) 3.41 x 10^-1N/C

c) 3.94 x 10^-1N/C

d) 4.55 x 10^-1N/C

e) 5.25 x 10^-1N/C

4) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 4

b) s−8

c) 4−s

d) s−4

e) 8−s

5)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.9{\text{ m}}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=4.3{\text{ m}}$.

a) 8.924E-01 V/m²

b) 9.816E-01 V/m²

c) 1.080E+00 V/m²

d) 1.188E+00 V/m²

e) 1.307E+00 V/m²

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=1e$, $q_{2}=-7e$, and $q_{3}=4e$?

a) 4.091E+01 degrees

b) 4.500E+01 degrees

c) 4.950E+01 degrees

d) 5.445E+01 degrees

e) 5.990E+01 degrees

7) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 2 − s

b) 2

c) s − 9

d) s − 2

e) 9 − s

8) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 1−s

b) s−1

c) 5−s

d) 5

e) s−4

9)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=6e$?

a) 1.028E-14 N

b) 1.130E-14 N

c) 1.244E-14 N

d) 1.368E-14 N

e) 1.505E-14 N

10) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

a) 2

b) 8

c) 4

d) 1/2

T1 Y0

1)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.2{\text{ m}}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=3.6{\text{ m}}$.

a) 1.606E+00 V/m²

b) 1.767E+00 V/m²

c) 1.943E+00 V/m²

d) 2.138E+00 V/m²

e) 2.351E+00 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-9e$, and $q_{3}=4e$?

a) 5.014E-14 N

b) 5.515E-14 N

c) 6.067E-14 N

d) 6.674E-14 N

e) 7.341E-14 N

3)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.4 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.69 m, b=2.2 m. The total charge on the rod is 6 nC.

a) 3.161E+00 V/m²

b) 3.477E+00 V/m²

c) 3.825E+00 V/m²

d) 4.208E+00 V/m²

e) 4.628E+00 V/m²

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

a) 1.09 x 10^-3 unit

b) 1.33 x 10^-3 unit

c) 1.61 x 10^-3 unit

d) 1.95 x 10^-3 unit

e) 2.36 x 10^-3 unit

5) What is the magnitude of the electric field at the origin if a 3 nC charge is placed at x = 5.1 m, and a 2 nC charge is placed at y = 8.6 m?

a) 7.99 x 10^-1N/C

b) 9.22 x 10^-1N/C

c) 1.07 x 10⁰N/C

d) 1.23 x 10⁰N/C

e) 1.42 x 10⁰N/C

6) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8−s

b) s−4

c) 4−s

d) 4

e) s−8

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) −3

b) −3

c) 3

d) 2

e) −7

8) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−3

b) s−7

c) 3−s

d) 8

e) 7−s

9) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 9 − s

b) 2

c) s − 9

d) 2 − s

e) s − 2

10) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 9² + (2-s)²

b) 9² + (7-s)²

c) 7² + (2-s)²

d) 2² + (9-s)²

e) 2² + (7-s)²

T1 Y1

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-9e$, and $q_{3}=6e$?

a) 1.308E-13 N

b) 1.439E-13 N

c) 1.583E-13 N

d) 1.741E-13 N

e) 1.915E-13 N

2)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.2 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.52 m, b=1.6 m. The total charge on the rod is 7 nC.

a) 9.655E+00 V/m²

b) 1.062E+01 V/m²

c) 1.168E+01 V/m²

d) 1.285E+01 V/m²

e) 1.414E+01 V/m²

3) What is the magnitude of the electric field at the origin if a 1.4 nC charge is placed at x = 8.2 m, and a 2.3 nC charge is placed at y = 5.9 m?

a) 5.39 x 10^-1N/C

b) 6.23 x 10^-1N/C

c) 7.19 x 10^-1N/C

d) 8.31 x 10^-1N/C

e) 9.59 x 10^-1N/C

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 4a) is βkQ/a², where β equals

a) 1.33 x 10^-3 unit

b) 1.61 x 10^-3 unit

c) 1.95 x 10^-3 unit

d) 2.37 x 10^-3 unit

e) 2.87 x 10^-3 unit

5)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.9{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=5.1{\text{ m}}$.

a) 8.253E-01 V/m²

b) 9.079E-01 V/m²

c) 9.987E-01 V/m²

d) 1.099E+00 V/m²

e) 1.208E+00 V/m²

6) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s − 2

b) 9 − s

c) 2

d) 2 − s

e) s − 9

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) 2

b) −7

c) 3

d) −3

e) −3

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8−s

b) 4

c) 4−s

d) s−4

e) s−8

9) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 9² + (2-s)²

b) 2² + (9-s)²

c) 7² + (2-s)²

d) 2² + (7-s)²

e) 9² + (7-s)²

10) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−3

b) s−7

c) 8

d) 7−s

e) 3−s

T1 Y2

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=5e$?

a) 2.248E-14 N

b) 2.473E-14 N

c) 2.721E-14 N

d) 2.993E-14 N

e) 3.292E-14 N

2) What is the magnitude of the electric field at the origin if a 2.7 nC charge is placed at x = 9.1 m, and a 2.5 nC charge is placed at y = 5.9 m?

a) 3.99 x 10^-1N/C

b) 4.6 x 10^-1N/C

c) 5.32 x 10^-1N/C

d) 6.14 x 10^-1N/C

e) 7.09 x 10^-1N/C

3) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 3−s

b) 7−s

c) 8

d) s−7

e) s−3

4) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

a) 2² + (9-s)²

b) 9² + (2-s)²

c) 7² + (2-s)²

d) 9² + (7-s)²

e) 2² + (7-s)²

5)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m. Evaluate $f(x,y)$ at x=0.83 m if a=0.82 m, b=1.3 m. The total charge on the rod is 7 nC.

a) 8.690E+00 V/m²

b) 9.559E+00 V/m²

c) 1.051E+01 V/m²

d) 1.157E+01 V/m²

e) 1.272E+01 V/m²

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

a) 3

b) −3

c) 2

d) −3

e) −7

7) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−4

b) 4−s

c) 4

d) 8−s

e) s−8

8) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 2

b) s − 9

c) s − 2

d) 9 − s

e) 2 − s

9)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.9{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=5.1{\text{ m}}$.

a) 8.253E-01 V/m²

b) 9.079E-01 V/m²

c) 9.987E-01 V/m²

d) 1.099E+00 V/m²

e) 1.208E+00 V/m²

10) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

a) 1.61 x 10^-3 unit

b) 1.95 x 10^-3 unit

c) 2.36 x 10^-3 unit

d) 2.86 x 10^-3 unit

e) 3.46 x 10^-3 unit

T1 Z0

1)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

a) 2.013E+09 N/C²

b) 2.214E+09 N/C²

c) 2.435E+09 N/C²

d) 2.679E+09 N/C²

e) 2.947E+09 N/C²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-9e$, and $q_{3}=4e$?

a) 5.014E-14 N

b) 5.515E-14 N

c) 6.067E-14 N

d) 6.674E-14 N

e) 7.341E-14 N

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-9e$, and $q_{3}=4e$?

a) 4.766E+01 degrees

b) 5.243E+01 degrees

c) 5.767E+01 degrees

d) 6.343E+01 degrees

e) 6.978E+01 degrees

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 2.36 x 10^-1 unit

b) 2.86 x 10^-1 unit

c) 3.47 x 10^-1 unit

d) 4.2 x 10^-1 unit

e) 5.09 x 10^-1 unit

5) What is the magnitude of the electric field at the origin if a 2.7 nC charge is placed at x = 9.1 m, and a 2.5 nC charge is placed at y = 5.9 m?

a) 3.99 x 10^-1N/C

b) 4.6 x 10^-1N/C

c) 5.32 x 10^-1N/C

d) 6.14 x 10^-1N/C

e) 7.09 x 10^-1N/C

6) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−4

b) 1−s

c) s−1

d) 5−s

e) 5

7) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 4

b) 8−s

c) s−4

d) 4−s

e) s−8

8) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 3/2

b) 2

c) 1/2

d) 2/3

e) 3

9) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 4

b) s−4

c) 4−s

d) s−8

e) 8−s

10) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 3−s

b) 7−s

c) s−3

d) 8

e) s−7

T1 Z1

1) What is the magnitude of the electric field at the origin if a 3 nC charge is placed at x = 5.1 m, and a 2 nC charge is placed at y = 8.6 m?

a) 7.99 x 10^-1N/C

b) 9.22 x 10^-1N/C

c) 1.07 x 10⁰N/C

d) 1.23 x 10⁰N/C

e) 1.42 x 10⁰N/C

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=4e$?

a) 8.613E-15 N

b) 9.474E-15 N

c) 1.042E-14 N

d) 1.146E-14 N

e) 1.261E-14 N

3) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 2.36 x 10^-1 unit

b) 2.86 x 10^-1 unit

c) 3.47 x 10^-1 unit

d) 4.2 x 10^-1 unit

e) 5.09 x 10^-1 unit

4) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 5

b) s−4

c) 1−s

d) 5−s

e) s−1

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-7e$, and $q_{3}=3e$?

a) 4.743E+01 degrees

b) 5.217E+01 degrees

c) 5.739E+01 degrees

d) 6.313E+01 degrees

e) 6.944E+01 degrees

6) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−8

b) 4−s

c) 4

d) 8−s

e) s−4

7)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

a) 2.013E+09 N/C²

b) 2.214E+09 N/C²

c) 2.435E+09 N/C²

d) 2.679E+09 N/C²

e) 2.947E+09 N/C²

8) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 3−s

b) s−3

c) s−7

d) 8

e) 7−s

9) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−4

b) 8−s

c) 4

d) s−8

e) 4−s

10) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 1/2

b) 3

c) 3/2

d) 2

e) 2/3

T1 Z2

1) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 2.86 x 10^-1 unit

b) 3.47 x 10^-1 unit

c) 4.2 x 10^-1 unit

d) 5.09 x 10^-1 unit

e) 6.17 x 10^-1 unit

2) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 1/2

b) 2/3

c) 2

d) 3/2

e) 3

3) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 4−s

b) 8−s

c) s−4

d) 4

e) s−8

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-9e$, and $q_{3}=4e$?

a) 5.243E+01 degrees

b) 5.767E+01 degrees

c) 6.343E+01 degrees

d) 6.978E+01 degrees

e) 7.676E+01 degrees

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=3e$?

a) 2.036E-14 N

b) 2.240E-14 N

c) 2.464E-14 N

d) 2.710E-14 N

e) 2.981E-14 N

6) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 5

b) s−1

c) s−4

d) 1−s

e) 5−s

7)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.5 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.33 m (on axis) away from the loop's center?

a) 1.353E+09 N/C²

b) 1.488E+09 N/C²

c) 1.637E+09 N/C²

d) 1.801E+09 N/C²

e) 1.981E+09 N/C²

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 4

b) 8−s

c) s−4

d) s−8

e) 4−s

9) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 3−s

b) 7−s

c) s−3

d) s−7

e) 8

10) What is the magnitude of the electric field at the origin if a 2.1 nC charge is placed at x = 7 m, and a 2.1 nC charge is placed at y = 8.6 m?

a) 3 x 10^-1N/C

b) 3.47 x 10^-1N/C

c) 4 x 10^-1N/C

d) 4.62 x 10^-1N/C

e) 5.34 x 10^-1N/C

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Key: A0

1)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.4{\text{ m}}$ and the surface charge density is $\sigma =6{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=0.56{\text{ m}}$.

-a) 2.567E+01 V/m²

-b) 2.824E+01 V/m²

-c) 3.106E+01 V/m²

-d) 3.417E+01 V/m²

+e) 3.759E+01 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-8e$, and $q_{3}=2e$?

-a) 3.876E-14 N

-b) 4.263E-14 N

-c) 4.690E-14 N

+d) 5.159E-14 N

-e) 5.675E-14 N

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-7e$, and $q_{3}=5e$?

-a) 4.357E+01 degrees

-b) 4.793E+01 degrees

-c) 5.272E+01 degrees

+d) 5.799E+01 degrees

-e) 6.379E+01 degrees

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 2.86 x 10^-1

+b) 3.47 x 10^-1

-c) 4.2 x 10^-1

-d) 5.09 x 10^-1

-e) 6.17 x 10^-1

5) What angle does the electric field at the origin make with the x-axis if a 2 nC charge is placed at x = -8 m, and a 1.4 nC charge is placed at y = -9.3 m?

-a) 2.37 x 10¹degrees

+b) 2.74 x 10¹degrees

-c) 3.16 x 10¹degrees

-d) 3.65 x 10¹degrees

-e) 4.22 x 10¹degrees

6) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−7

-b) 3−s

+c) 7−s

-d) s−3

-e) 8

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) −3

-b) −7

-c) −3

+d) 2

-e) 3

8) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 5−s

+b) 5

-c) s−1

-d) 1−s

-e) s−4

9) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

+a) 4

-b) 2

-c) 8

-d) 1/2

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

+a) 3/2

-b) 3

-c) 1/2

-d) 2

Key: A1

1) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) −7

-b) −3

-c) 3

-d) −3

+e) 2

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-9e$, and $q_{3}=5e$?

-a) 5.272E+01 degrees

+b) 5.799E+01 degrees

-c) 6.379E+01 degrees

-d) 7.017E+01 degrees

-e) 7.719E+01 degrees

3) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 8

-b) s−3

-c) 3−s

+d) 7−s

-e) s−7

4) What angle does the electric field at the origin make with the x-axis if a 1.9 nC charge is placed at x = -5.4 m, and a 1.5 nC charge is placed at y = -7.1 m?

-a) 1.38 x 10¹degrees

-b) 1.59 x 10¹degrees

-c) 1.84 x 10¹degrees

-d) 2.13 x 10¹degrees

+e) 2.45 x 10¹degrees

5) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

-a) 2

-b) 1/2

-c) 8

+d) 4

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

+a) 3/2

-b) 1/2

-c) 2

-d) 3

7) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 5

-b) 1−s

-c) s−4

-d) 5−s

-e) s−1

8)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.8{\text{ m}}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=1.9{\text{ m}}$.

-a) 4.295E+00 V/m²

+b) 4.724E+00 V/m²

-c) 5.196E+00 V/m²

-d) 5.716E+00 V/m²

-e) 6.288E+00 V/m²

9) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 1.95 x 10^-1 unit

-b) 2.36 x 10^-1 unit

-c) 2.86 x 10^-1 unit

+d) 3.47 x 10^-1 unit

-e) 4.2 x 10^-1 unit

10)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-8e$, and $q_{3}=2e$?

-a) 3.876E-14 N

-b) 4.263E-14 N

-c) 4.690E-14 N

+d) 5.159E-14 N

-e) 5.675E-14 N

Key: A2

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=5e$?

-a) 9.958E-15 N

-b) 1.095E-14 N

-c) 1.205E-14 N

-d) 1.325E-14 N

+e) 1.458E-14 N

2) What angle does the electric field at the origin make with the x-axis if a 1.8 nC charge is placed at x = -6.9 m, and a 2.5 nC charge is placed at y = -7.5 m?

-a) 2.79 x 10¹degrees

-b) 3.22 x 10¹degrees

-c) 3.72 x 10¹degrees

-d) 4.3 x 10¹degrees

+e) 4.96 x 10¹degrees

3) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 2.36 x 10^-1 unit

-b) 2.86 x 10^-1 unit

+c) 3.47 x 10^-1 unit

-d) 4.2 x 10^-1 unit

-e) 5.09 x 10^-1 unit

4) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) 3

-b) −3

+c) 2

-d) −7

-e) −3

5) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

-a) 2

-b) 1/2

-c) 3

+d) 3/2

6) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−4

-b) 1−s

-c) s−1

-d) 5−s

+e) 5

7) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 3−s

-b) s−7

-c) 8

-d) s−3

+e) 7−s

8)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-8e$, and $q_{3}=6e$?

-a) 5.243E+01 degrees

-b) 5.767E+01 degrees

+c) 6.343E+01 degrees

-d) 6.978E+01 degrees

-e) 7.676E+01 degrees

9) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

+a) 4

-b) 1/2

-c) 2

-d) 8

10)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.3{\text{ m}}$ and the surface charge density is $\sigma =5{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=5.3{\text{ m}}$.

+a) 1.022E+00 V/m²

-b) 1.125E+00 V/m²

-c) 1.237E+00 V/m²

-d) 1.361E+00 V/m²

-e) 1.497E+00 V/m²

Key: B0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-9e$, and $q_{3}=6e$?

-a) 1.308E-13 N

-b) 1.439E-13 N

-c) 1.583E-13 N

+d) 1.741E-13 N

-e) 1.915E-13 N

2)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.9{\text{ m}}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=4.3{\text{ m}}$.

-a) 8.924E-01 V/m²

-b) 9.816E-01 V/m²

+c) 1.080E+00 V/m²

-d) 1.188E+00 V/m²

-e) 1.307E+00 V/m²

3) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 2.357E+01 N/C

-b) 2.593E+01 N/C

-c) 2.852E+01 N/C

+d) 3.137E+01 N/C

-e) 3.451E+01 N/C

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 3a) is βkQ/a², where β equals

-a) 3.38 x 10^-3 unit

-b) 4.1 x 10^-3 unit

-c) 4.96 x 10^-3 unit

-d) 6.01 x 10^-3 unit

+e) 7.28 x 10^-3 unit

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

+a) 3.47 x 10^-1 unit

-b) 4.2 x 10^-1 unit

-c) 5.09 x 10^-1 unit

-d) 6.17 x 10^-1 unit

-e) 7.47 x 10^-1 unit

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

-a) 3

-b) 1/2

+c) 3/2

-d) 2

7) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 7² + (2-s)²

-b) 2² + (7-s)²

+c) 2² + (9-s)²

-d) 9² + (7-s)²

-e) 9² + (2-s)²

8) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) −3

+b) 2

-c) −7

-d) −3

-e) 3

9) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s − 2

+b) 9 − s

-c) 2 − s

-d) s − 9

-e) 2

10) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−4

-b) s−8

-c) 8−s

-d) 4−s

+e) 4

Key: B1

1) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) −3

-b) −7

+c) 2

-d) 3

-e) −3

2) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

+a) 3.47 x 10^-1 unit

-b) 4.2 x 10^-1 unit

-c) 5.09 x 10^-1 unit

-d) 6.17 x 10^-1 unit

-e) 7.47 x 10^-1 unit

3) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

-a) 2

+b) 3/2

-c) 3

-d) 1/2

4) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−4

-b) 8−s

-c) 4−s

-d) s−8

+e) 4

5) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

+a) 2² + (9-s)²

-b) 7² + (2-s)²

-c) 9² + (7-s)²

-d) 2² + (7-s)²

-e) 9² + (2-s)²

6) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 6.171E+01 N/C

-b) 6.788E+01 N/C

-c) 7.467E+01 N/C

-d) 8.214E+01 N/C

+e) 9.035E+01 N/C

7) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 6a) is βkQ/a², where β equals

-a) 1.52 x 10^-4 unit

-b) 1.85 x 10^-4 unit

+c) 2.24 x 10^-4 unit

-d) 2.71 x 10^-4 unit

-e) 3.28 x 10^-4 unit

8)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=6e$?

-a) 2.544E-14 N

-b) 2.798E-14 N

-c) 3.078E-14 N

+d) 3.385E-14 N

-e) 3.724E-14 N

9)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.0{\text{ m}}$ and the surface charge density is $\sigma =8{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=2.0{\text{ m}}$.

-a) 9.459E+00 V/m²

+b) 1.040E+01 V/m²

-c) 1.145E+01 V/m²

-d) 1.259E+01 V/m²

-e) 1.385E+01 V/m²

10) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s − 2

+b) 9 − s

-c) s − 9

-d) 2 − s

-e) 2

Key: B2

1) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) −3

+b) 2

-c) −3

-d) 3

-e) −7

2) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 5a, 4a) is βkQ/a², where β equals

-a) 1.76 x 10^-3 unit

-b) 2.13 x 10^-3 unit

-c) 2.59 x 10^-3 unit

+d) 3.13 x 10^-3 unit

-e) 3.79 x 10^-3 unit

3) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 2

-b) 2 − s

-c) s − 2

-d) s − 9

+e) 9 − s

4)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=9.1{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=6.2{\text{ m}}$.

-a) 4.961E-01 V/m²

-b) 5.457E-01 V/m²

-c) 6.002E-01 V/m²

-d) 6.603E-01 V/m²

+e) 7.263E-01 V/m²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=6e$?

-a) 1.028E-14 N

-b) 1.130E-14 N

-c) 1.244E-14 N

-d) 1.368E-14 N

+e) 1.505E-14 N

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

-a) 3

-b) 2

-c) 1/2

+d) 3/2

7) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 2.36 x 10^-1 unit

-b) 2.86 x 10^-1 unit

+c) 3.47 x 10^-1 unit

-d) 4.2 x 10^-1 unit

-e) 5.09 x 10^-1 unit

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−8

+b) 4

-c) 4−s

-d) 8−s

-e) s−4

9) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

+a) 5.647E+01 N/C

-b) 6.212E+01 N/C

-c) 6.833E+01 N/C

-d) 7.516E+01 N/C

-e) 8.268E+01 N/C

10) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 9² + (7-s)²

-b) 7² + (2-s)²

-c) 9² + (2-s)²

+d) 2² + (9-s)²

-e) 2² + (7-s)²

Key: C0

1) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 3.214E+01 N/C

-b) 3.536E+01 N/C

-c) 3.889E+01 N/C

-d) 4.278E+01 N/C

+e) 4.706E+01 N/C

2)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.3 m (on axis) away from the loop's center?

+a) 4.788E+09 N/C²

-b) 5.267E+09 N/C²

-c) 5.793E+09 N/C²

-d) 6.373E+09 N/C²

-e) 7.010E+09 N/C²

3)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.3{\text{ m}}$ and the surface charge density is $\sigma =4{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=2.0{\text{ m}}$.

-a) 6.877E+00 V/m²

-b) 7.565E+00 V/m²

+c) 8.321E+00 V/m²

-d) 9.153E+00 V/m²

-e) 1.007E+01 V/m²

4) What is the magnitude of the electric field at the origin if a 1.4 nC charge is placed at x = 8.2 m, and a 2.3 nC charge is placed at y = 5.9 m?

-a) 5.39 x 10^-1N/C

+b) 6.23 x 10^-1N/C

-c) 7.19 x 10^-1N/C

-d) 8.31 x 10^-1N/C

-e) 9.59 x 10^-1N/C

5) What angle does the electric field at the origin make with the x-axis if a 2 nC charge is placed at x = -8 m, and a 1.4 nC charge is placed at y = -9.3 m?

-a) 2.37 x 10¹degrees

+b) 2.74 x 10¹degrees

-c) 3.16 x 10¹degrees

-d) 3.65 x 10¹degrees

-e) 4.22 x 10¹degrees

6) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−8

+b) 4

-c) s−4

-d) 8−s

-e) 4−s

7) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 3−s

+b) 7−s

-c) s−7

-d) 8

-e) s−3

8) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 2/3

-b) 2

+c) 3/2

-d) 3

-e) 1/2

9) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

-a) 1/2

-b) 2

-c) 8

+d) 4

10) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 8−s

-b) 4−s

-c) 4

-d) s−4

-e) s−8

Key: C1

1)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=9.1{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=6.2{\text{ m}}$.

-a) 4.961E-01 V/m²

-b) 5.457E-01 V/m²

-c) 6.002E-01 V/m²

-d) 6.603E-01 V/m²

+e) 7.263E-01 V/m²

2) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−8

-b) 4−s

-c) 8−s

-d) s−4

+e) 4

3) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

-a) 1/2

-b) 8

+c) 4

-d) 2

4) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 3

-b) 1/2

-c) 2

+d) 3/2

-e) 2/3

5)

A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.73 m (on axis) away from the loop's center?

-a) 7.415E+09 N/C²

-b) 8.156E+09 N/C²

-c) 8.972E+09 N/C²

-d) 9.869E+09 N/C²

+e) 1.086E+10 N/C²

6) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 6.534E+01 N/C

-b) 7.187E+01 N/C

+c) 7.906E+01 N/C

-d) 8.696E+01 N/C

-e) 9.566E+01 N/C

7) What angle does the electric field at the origin make with the x-axis if a 2.8 nC charge is placed at x = -9.8 m, and a 2.8 nC charge is placed at y = -5.8 m?

+a) 7.07 x 10¹degrees

-b) 8.16 x 10¹degrees

-c) 9.43 x 10¹degrees

-d) 1.09 x 10²degrees

-e) 1.26 x 10²degrees

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 8−s

-b) s−8

-c) 4−s

-d) 4

-e) s−4

9) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−7

+b) 7−s

-c) 8

-d) 3−s

-e) s−3

10) What is the magnitude of the electric field at the origin if a 1.8 nC charge is placed at x = 9.6 m, and a 2 nC charge is placed at y = 8.7 m?

+a) 2.95 x 10^-1N/C

-b) 3.41 x 10^-1N/C

-c) 3.94 x 10^-1N/C

-d) 4.55 x 10^-1N/C

-e) 5.25 x 10^-1N/C

Key: C2

1)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=4.3{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=2.4{\text{ m}}$.

+a) 5.647E+00 V/m²

-b) 6.212E+00 V/m²

-c) 6.833E+00 V/m²

-d) 7.517E+00 V/m²

-e) 8.268E+00 V/m²

2) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 8−s

-b) s−8

-c) s−4

-d) 4−s

+e) 4

3) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−3

+b) 7−s

-c) 3−s

-d) s−7

-e) 8

4) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 3

-b) 1/2

+c) 3/2

-d) 2/3

-e) 2

5) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 4

-b) s−4

+c) 8−s

-d) s−8

-e) 4−s

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

+a) 5.647E+01 N/C

-b) 6.212E+01 N/C

-c) 6.833E+01 N/C

-d) 7.516E+01 N/C

-e) 8.268E+01 N/C

7) What is the magnitude of the electric field at the origin if a 3.1 nC charge is placed at x = 6.2 m, and a 2.6 nC charge is placed at y = 6 m?

-a) 5.47 x 10^-1N/C

-b) 6.32 x 10^-1N/C

-c) 7.3 x 10^-1N/C

-d) 8.43 x 10^-1N/C

+e) 9.73 x 10^-1N/C

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

+a) 4

-b) 2

-c) 8

-d) 1/2

9)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

-a) 2.013E+09 N/C²

-b) 2.214E+09 N/C²

-c) 2.435E+09 N/C²

-d) 2.679E+09 N/C²

+e) 2.947E+09 N/C²

10) What angle does the electric field at the origin make with the x-axis if a 2.6 nC charge is placed at x = -8.3 m, and a 2.5 nC charge is placed at y = -9.6 m?

-a) 2.32 x 10¹degrees

-b) 2.68 x 10¹degrees

-c) 3.09 x 10¹degrees

+d) 3.57 x 10¹degrees

-e) 4.12 x 10¹degrees

Key: D0

1)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

-a) 2.013E+09 N/C²

-b) 2.214E+09 N/C²

-c) 2.435E+09 N/C²

-d) 2.679E+09 N/C²

+e) 2.947E+09 N/C²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=3e$?

-a) 2.036E-14 N

-b) 2.240E-14 N

+c) 2.464E-14 N

-d) 2.710E-14 N

-e) 2.981E-14 N

3)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m. Evaluate $f(x,y)$ at x=0.52 m if a=0.88 m, b=1.3 m. The total charge on the rod is 6 nC.

-a) 6.804E+00 V/m²

+b) 7.485E+00 V/m²

-c) 8.233E+00 V/m²

-d) 9.056E+00 V/m²

-e) 9.962E+00 V/m²

4) What is the magnitude of the electric field at the origin if a 2.1 nC charge is placed at x = 7 m, and a 2.1 nC charge is placed at y = 8.6 m?

-a) 3 x 10^-1N/C

-b) 3.47 x 10^-1N/C

-c) 4 x 10^-1N/C

+d) 4.62 x 10^-1N/C

-e) 5.34 x 10^-1N/C

5) What angle does the electric field at the origin make with the x-axis if a 2.9 nC charge is placed at x = -7.3 m, and a 1.7 nC charge is placed at y = -8.1 m?

+a) 2.55 x 10¹degrees

-b) 2.94 x 10¹degrees

-c) 3.4 x 10¹degrees

-d) 3.92 x 10¹degrees

-e) 4.53 x 10¹degrees

6) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 4

-b) s−4

-c) 8−s

-d) 4−s

-e) s−8

7) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 7² + (3−s)²

+b) (7-s)² + 8²

-c) 7² + 8²

-d) 7² + (8−s)²

-e) 3² + 8²

8) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 8

-b) s−7

-c) 3−s

+d) 7−s

-e) s−3

9) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 2

-b) s − 2

-c) s − 9

+d) 9 − s

-e) 2 − s

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) −3

-b) −3

-c) −7

-d) 3

+e) 2

Key: D1

1)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.3 m (on axis) away from the loop's center?

+a) 4.788E+09 N/C²

-b) 5.267E+09 N/C²

-c) 5.793E+09 N/C²

-d) 6.373E+09 N/C²

-e) 7.010E+09 N/C²

2) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−3

-b) s−7

-c) 8

-d) 3−s

+e) 7−s

3) What angle does the electric field at the origin make with the x-axis if a 2.6 nC charge is placed at x = -8.3 m, and a 2.5 nC charge is placed at y = -9.6 m?

-a) 2.32 x 10¹degrees

-b) 2.68 x 10¹degrees

-c) 3.09 x 10¹degrees

+d) 3.57 x 10¹degrees

-e) 4.12 x 10¹degrees

4) What is the magnitude of the electric field at the origin if a 1.9 nC charge is placed at x = 9.7 m, and a 3.1 nC charge is placed at y = 5.5 m?

-a) 5.28 x 10^-1N/C

-b) 6.1 x 10^-1N/C

-c) 7.04 x 10^-1N/C

-d) 8.13 x 10^-1N/C

+e) 9.39 x 10^-1N/C

5) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) 3

-b) −7

-c) −3

+d) 2

-e) −3

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-9e$, and $q_{3}=4e$?

-a) 5.014E-14 N

-b) 5.515E-14 N

-c) 6.067E-14 N

-d) 6.674E-14 N

+e) 7.341E-14 N

7) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 3² + 8²

-b) 7² + (8−s)²

-c) 7² + (3−s)²

+d) (7-s)² + 8²

-e) 7² + 8²

8)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=1.0 m if a=1.0 m, b=1.8 m. The total charge on the rod is 6 nC.

-a) 3.610E+00 V/m²

+b) 3.971E+00 V/m²

-c) 4.368E+00 V/m²

-d) 4.804E+00 V/m²

-e) 5.285E+00 V/m²

9) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 8−s

-b) s−8

-c) 4−s

-d) s−4

+e) 4

10) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 9 − s

-b) 2

-c) s − 2

-d) s − 9

-e) 2 − s

Key: D2

1) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s − 2

+b) 9 − s

-c) 2

-d) 2 − s

-e) s − 9

2) What angle does the electric field at the origin make with the x-axis if a 1.4 nC charge is placed at x = -8.7 m, and a 2.7 nC charge is placed at y = -8.3 m?

-a) 4.85 x 10¹degrees

-b) 5.61 x 10¹degrees

+c) 6.47 x 10¹degrees

-d) 7.48 x 10¹degrees

-e) 8.63 x 10¹degrees

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-8e$, and $q_{3}=2e$?

-a) 3.876E-14 N

-b) 4.263E-14 N

-c) 4.690E-14 N

+d) 5.159E-14 N

-e) 5.675E-14 N

4) What is the magnitude of the electric field at the origin if a 1.9 nC charge is placed at x = 9.7 m, and a 3.1 nC charge is placed at y = 5.5 m?

-a) 5.28 x 10^-1N/C

-b) 6.1 x 10^-1N/C

-c) 7.04 x 10^-1N/C

-d) 8.13 x 10^-1N/C

+e) 9.39 x 10^-1N/C

5) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−3

-b) 8

+c) 7−s

-d) s−7

-e) 3−s

6) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 7² + 8²

+b) (7-s)² + 8²

-c) 3² + 8²

-d) 7² + (8−s)²

-e) 7² + (3−s)²

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

+a) 2

-b) −3

-c) −7

-d) 3

-e) −3

8)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.6 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.64 m, b=1.8 m. The total charge on the rod is 3 nC.

-a) 2.955E+00 V/m²

+b) 3.250E+00 V/m²

-c) 3.575E+00 V/m²

-d) 3.933E+00 V/m²

-e) 4.326E+00 V/m²

9) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 4−s

+b) 4

-c) 8−s

-d) s−4

-e) s−8

10)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.3 m (on axis) away from the loop's center?

+a) 4.788E+09 N/C²

-b) 5.267E+09 N/C²

-c) 5.793E+09 N/C²

-d) 6.373E+09 N/C²

-e) 7.010E+09 N/C²

Key: E0

1)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.8{\text{ m}}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=1.9{\text{ m}}$.

-a) 4.295E+00 V/m²

+b) 4.724E+00 V/m²

-c) 5.196E+00 V/m²

-d) 5.716E+00 V/m²

-e) 6.288E+00 V/m²

2) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 3.428E+01 N/C

-b) 3.771E+01 N/C

-c) 4.148E+01 N/C

-d) 4.563E+01 N/C

+e) 5.020E+01 N/C

3)

A ring is uniformly charged with a net charge of 8 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.32 m (on axis) away from the loop's center?

-a) 3.339E+09 N/C²

-b) 3.673E+09 N/C²

-c) 4.041E+09 N/C²

+d) 4.445E+09 N/C²

-e) 4.889E+09 N/C²

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

+a) 3.47 x 10^-1 unit

-b) 4.2 x 10^-1 unit

-c) 5.09 x 10^-1 unit

-d) 6.17 x 10^-1 unit

-e) 7.47 x 10^-1 unit

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 5a) is βkQ/a², where β equals

+a) 6.11 x 10^-4

-b) 7.4 x 10^-4

-c) 8.97 x 10^-4

-d) 1.09 x 10^-3

-e) 1.32 x 10^-3

6) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 2² + (7-s)²

-b) 9² + (7-s)²

-c) 9² + (2-s)²

-d) 7² + (2-s)²

+e) 2² + (9-s)²

7) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s − 2

-b) 2 − s

-c) s − 9

-d) 2

+e) 9 − s

8) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 7² + 8²

-b) 3² + 8²

-c) 7² + (3−s)²

-d) 7² + (8−s)²

+e) (7-s)² + 8²

9) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 5−s

+b) 1−s

-c) s−1

-d) s−4

-e) 5

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

-a) 1/2

-b) 3

-c) 2

+d) 3/2

Key: E1

1) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

+a) 3/2

-b) 3

-c) 1/2

-d) 2

2)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.9{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=5.1{\text{ m}}$.

-a) 8.253E-01 V/m²

-b) 9.079E-01 V/m²

+c) 9.987E-01 V/m²

-d) 1.099E+00 V/m²

-e) 1.208E+00 V/m²

3) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 6a) is βkQ/a², where β equals

-a) 1.52 x 10^-4 unit

-b) 1.85 x 10^-4 unit

+c) 2.24 x 10^-4 unit

-d) 2.71 x 10^-4 unit

-e) 3.28 x 10^-4 unit

4) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 9² + (7-s)²

-b) 7² + (2-s)²

-c) 9² + (2-s)²

+d) 2² + (9-s)²

-e) 2² + (7-s)²

5) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−4

+b) 1−s

-c) 5−s

-d) 5

-e) s−1

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 7.701E+01 N/C

+b) 8.471E+01 N/C

-c) 9.318E+01 N/C

-d) 1.025E+02 N/C

-e) 1.127E+02 N/C

7) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s − 9

-b) 2 − s

-c) s − 2

+d) 9 − s

-e) 2

8) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 1.95 x 10^-1 unit

-b) 2.36 x 10^-1 unit

-c) 2.86 x 10^-1 unit

+d) 3.47 x 10^-1 unit

-e) 4.2 x 10^-1 unit

9)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.99 m (on axis) away from the loop's center?

-a) 2.429E+09 N/C²

+b) 2.672E+09 N/C²

-c) 2.939E+09 N/C²

-d) 3.233E+09 N/C²

-e) 3.556E+09 N/C²

10) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 7² + (3−s)²

-b) 7² + (8−s)²

-c) 7² + 8²

+d) (7-s)² + 8²

-e) 3² + 8²

Key: E2

1) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 2² + (7-s)²

-b) 9² + (7-s)²

+c) 2² + (9-s)²

-d) 7² + (2-s)²

-e) 9² + (2-s)²

2) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 5−s

+b) 1−s

-c) 5

-d) s−4

-e) s−1

3) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 1.95 x 10^-1 unit

-b) 2.36 x 10^-1 unit

-c) 2.86 x 10^-1 unit

+d) 3.47 x 10^-1 unit

-e) 4.2 x 10^-1 unit

4) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 2.357E+01 N/C

-b) 2.593E+01 N/C

-c) 2.852E+01 N/C

+d) 3.137E+01 N/C

-e) 3.451E+01 N/C

5) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 7² + (8−s)²

-b) 7² + 8²

-c) 3² + 8²

+d) (7-s)² + 8²

-e) 7² + (3−s)²

6) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

-a) 1.09 x 10^-3 unit

-b) 1.33 x 10^-3 unit

+c) 1.61 x 10^-3 unit

-d) 1.95 x 10^-3 unit

-e) 2.36 x 10^-3 unit

7)

A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.73 m (on axis) away from the loop's center?

-a) 7.415E+09 N/C²

-b) 8.156E+09 N/C²

-c) 8.972E+09 N/C²

-d) 9.869E+09 N/C²

+e) 1.086E+10 N/C²

8) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s − 9

+b) 9 − s

-c) 2 − s

-d) s − 2

-e) 2

9) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

+a) 3/2

-b) 3

-c) 2

-d) 1/2

10)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=4.3{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=2.4{\text{ m}}$.

+a) 5.647E+00 V/m²

-b) 6.212E+00 V/m²

-c) 6.833E+00 V/m²

-d) 7.517E+00 V/m²

-e) 8.268E+00 V/m²

Key: F0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=1e$, $q_{2}=-8e$, and $q_{3}=3e$?

-a) 3.629E+01 degrees

-b) 3.992E+01 degrees

-c) 4.391E+01 degrees

-d) 4.830E+01 degrees

+e) 5.313E+01 degrees

2)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.2{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=2.2{\text{ m}}$.

-a) 3.228E+00 V/m²

-b) 3.551E+00 V/m²

-c) 3.906E+00 V/m²

-d) 4.297E+00 V/m²

+e) 4.727E+00 V/m²

3) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 4.492E+01 N/C

+b) 4.941E+01 N/C

-c) 5.435E+01 N/C

-d) 5.979E+01 N/C

-e) 6.577E+01 N/C

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 2a) is βkQ/a², where β equals

-a) 7.31 x 10^-3 unit

-b) 8.86 x 10^-3 unit

-c) 1.07 x 10^-2 unit

-d) 1.3 x 10^-2 unit

+e) 1.57 x 10^-2 unit

5) What is the magnitude of the electric field at the origin if a 1.9 nC charge is placed at x = 9.7 m, and a 3.1 nC charge is placed at y = 5.5 m?

-a) 5.28 x 10^-1N/C

-b) 6.1 x 10^-1N/C

-c) 7.04 x 10^-1N/C

-d) 8.13 x 10^-1N/C

+e) 9.39 x 10^-1N/C

6) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

+a) 3/2

-b) 1/2

-c) 3

-d) 2/3

-e) 2

7) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

+a) 2² + (9-s)²

-b) 2² + (7-s)²

-c) 9² + (2-s)²

-d) 9² + (7-s)²

-e) 7² + (2-s)²

8) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) 3

-b) −3

-c) −3

+d) 2

-e) −7

9) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 7² + (3−s)²

-b) 7² + (8−s)²

-c) 7² + 8²

+d) (7-s)² + 8²

-e) 3² + 8²

10) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

-a) 8

-b) 1/2

-c) 2

+d) 4

Key: F1

1) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 2² + (7-s)²

+b) 2² + (9-s)²

-c) 9² + (2-s)²

-d) 7² + (2-s)²

-e) 9² + (7-s)²

2) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

-a) 1/2

-b) 8

+c) 4

-d) 2

3)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.8{\text{ m}}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=1.1{\text{ m}}$.

-a) 7.517E+00 V/m²

-b) 8.269E+00 V/m²

-c) 9.096E+00 V/m²

-d) 1.001E+01 V/m²

+e) 1.101E+01 V/m²

4) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

+a) 8.471E+01 N/C

-b) 9.318E+01 N/C

-c) 1.025E+02 N/C

-d) 1.127E+02 N/C

-e) 1.240E+02 N/C

5) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 3

-b) 2/3

+c) 3/2

-d) 2

-e) 1/2

6) What is the magnitude of the electric field at the origin if a 1.9 nC charge is placed at x = 9.7 m, and a 3.1 nC charge is placed at y = 5.5 m?

-a) 5.28 x 10^-1N/C

-b) 6.1 x 10^-1N/C

-c) 7.04 x 10^-1N/C

-d) 8.13 x 10^-1N/C

+e) 9.39 x 10^-1N/C

7) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 5a) is βkQ/a², where β equals

+a) 6.11 x 10^-4

-b) 7.4 x 10^-4

-c) 8.97 x 10^-4

-d) 1.09 x 10^-3

-e) 1.32 x 10^-3

8) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) 3

+b) 2

-c) −7

-d) −3

-e) −3

9)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-9e$, and $q_{3}=5e$?

-a) 5.272E+01 degrees

+b) 5.799E+01 degrees

-c) 6.379E+01 degrees

-d) 7.017E+01 degrees

-e) 7.719E+01 degrees

10) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 7² + (3−s)²

-b) 7² + (8−s)²

-c) 7² + 8²

-d) 3² + 8²

+e) (7-s)² + 8²

Key: F2

1) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

-a) 2

-b) 8

+c) 4

-d) 1/2

2)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.8{\text{ m}}$ and the surface charge density is $\sigma =6{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=3.6{\text{ m}}$.

-a) 1.258E+00 V/m²

-b) 1.384E+00 V/m²

-c) 1.522E+00 V/m²

+d) 1.674E+00 V/m²

-e) 1.842E+00 V/m²

3) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 4a) is βkQ/a², where β equals

-a) 2.22 x 10^-3 unit

+b) 2.69 x 10^-3 unit

-c) 3.26 x 10^-3 unit

-d) 3.95 x 10^-3 unit

-e) 4.79 x 10^-3 unit

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=5e$?

-a) 5.569E+01 degrees

-b) 6.125E+01 degrees

+c) 6.738E+01 degrees

-d) 7.412E+01 degrees

-e) 8.153E+01 degrees

5) What is the magnitude of the electric field at the origin if a 1.8 nC charge is placed at x = 5.2 m, and a 3.1 nC charge is placed at y = 7.6 m?

+a) 7.69 x 10^-1N/C

-b) 8.88 x 10^-1N/C

-c) 1.03 x 10⁰N/C

-d) 1.18 x 10⁰N/C

-e) 1.37 x 10⁰N/C

6) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

+a) (7-s)² + 8²

-b) 7² + (3−s)²

-c) 7² + (8−s)²

-d) 3² + 8²

-e) 7² + 8²

7) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

-a) 3.214E+01 N/C

-b) 3.536E+01 N/C

-c) 3.889E+01 N/C

-d) 4.278E+01 N/C

+e) 4.706E+01 N/C

8) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 2

-b) 3

-c) 1/2

-d) 2/3

+e) 3/2

9) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) 3

-b) −7

-c) −3

+d) 2

-e) −3

10) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 9² + (7-s)²

-b) 2² + (7-s)²

-c) 7² + (2-s)²

-d) 9² + (2-s)²

+e) 2² + (9-s)²

Key: G0

1)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.65 m if a=0.85 m, b=1.8 m. The total charge on the rod is 5 nC.

-a) 3.959E+00 V/m²

+b) 4.355E+00 V/m²

-c) 4.790E+00 V/m²

-d) 5.269E+00 V/m²

-e) 5.796E+00 V/m²

2) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 4.821E+01 N/C

-b) 5.303E+01 N/C

-c) 5.834E+01 N/C

-d) 6.417E+01 N/C

+e) 7.059E+01 N/C

3)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.35 m (on axis) away from the loop's center?

-a) 4.142E+09 N/C²

-b) 4.556E+09 N/C²

+c) 5.012E+09 N/C²

-d) 5.513E+09 N/C²

-e) 6.064E+09 N/C²

4) What is the magnitude of the electric field at the origin if a 3 nC charge is placed at x = 8.8 m, and a 2.9 nC charge is placed at y = 6.9 m?

-a) 4.87 x 10^-1N/C

-b) 5.62 x 10^-1N/C

+c) 6.49 x 10^-1N/C

-d) 7.49 x 10^-1N/C

-e) 8.65 x 10^-1N/C

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 1.95 x 10^-1 unit

-b) 2.36 x 10^-1 unit

-c) 2.86 x 10^-1 unit

+d) 3.47 x 10^-1 unit

-e) 4.2 x 10^-1 unit

6) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 7−s

-b) 8

-c) 3−s

-d) s−3

-e) s−7

7) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 1/2

-b) 2

-c) 3

-d) 2/3

+e) 3/2

8) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−4

-b) 5−s

+c) 5

-d) 1−s

-e) s−1

9) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 4

-b) s−8

+c) 8−s

-d) s−4

-e) 4−s

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

-a) 2

-b) 1/2

+c) 3/2

-d) 3

Key: G1

1) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

+a) 3.47 x 10^-1 unit

-b) 4.2 x 10^-1 unit

-c) 5.09 x 10^-1 unit

-d) 6.17 x 10^-1 unit

-e) 7.47 x 10^-1 unit

2)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.99 m (on axis) away from the loop's center?

-a) 2.429E+09 N/C²

+b) 2.672E+09 N/C²

-c) 2.939E+09 N/C²

-d) 3.233E+09 N/C²

-e) 3.556E+09 N/C²

3) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 3−s

+b) 7−s

-c) 8

-d) s−7

-e) s−3

4) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

-a) 2

+b) 3/2

-c) 1/2

-d) 3

5) What is the magnitude of the electric field at the origin if a 1.8 nC charge is placed at x = 9.6 m, and a 2 nC charge is placed at y = 8.7 m?

+a) 2.95 x 10^-1N/C

-b) 3.41 x 10^-1N/C

-c) 3.94 x 10^-1N/C

-d) 4.55 x 10^-1N/C

-e) 5.25 x 10^-1N/C

6) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 6.171E+01 N/C

-b) 6.788E+01 N/C

-c) 7.467E+01 N/C

-d) 8.214E+01 N/C

+e) 9.035E+01 N/C

7) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−4

+b) 8−s

-c) 4

-d) s−8

-e) 4−s

8) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 3

-b) 1/2

-c) 2/3

+d) 3/2

-e) 2

9) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 5

-b) 1−s

-c) 5−s

-d) s−4

-e) s−1

10)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.6 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.64 m, b=1.8 m. The total charge on the rod is 3 nC.

-a) 2.955E+00 V/m²

+b) 3.250E+00 V/m²

-c) 3.575E+00 V/m²

-d) 3.933E+00 V/m²

-e) 4.326E+00 V/m²

Key: G2

1) What is the magnitude of the electric field at the origin if a 3.1 nC charge is placed at x = 6.2 m, and a 2.6 nC charge is placed at y = 6 m?

-a) 5.47 x 10^-1N/C

-b) 6.32 x 10^-1N/C

-c) 7.3 x 10^-1N/C

-d) 8.43 x 10^-1N/C

+e) 9.73 x 10^-1N/C

2) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 4

-b) s−8

+c) 8−s

-d) s−4

-e) 4−s

3)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m. Evaluate $f(x,y)$ at x=0.76 m if a=1.1 m, b=1.6 m. The total charge on the rod is 8 nC.

-a) 5.267E+00 V/m²

-b) 5.794E+00 V/m²

-c) 6.374E+00 V/m²

+d) 7.011E+00 V/m²

-e) 7.712E+00 V/m²

4) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 3−s

-b) s−3

+c) 7−s

-d) 8

-e) s−7

5)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.2 m (on axis) away from the loop's center?

-a) 6.925E+09 N/C²

-b) 7.617E+09 N/C²

+c) 8.379E+09 N/C²

-d) 9.217E+09 N/C²

-e) 1.014E+10 N/C²

6) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 2.36 x 10^-1 unit

-b) 2.86 x 10^-1 unit

+c) 3.47 x 10^-1 unit

-d) 4.2 x 10^-1 unit

-e) 5.09 x 10^-1 unit

7) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 2

-b) 3

+c) 3/2

-d) 1/2

-e) 2/3

8) A large thin isolated square plate has an area of 3 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

+a) 1.694E+02 N/C

-b) 1.864E+02 N/C

-c) 2.050E+02 N/C

-d) 2.255E+02 N/C

-e) 2.480E+02 N/C

9) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 5−s

-b) s−1

-c) s−4

+d) 5

-e) 1−s

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

-a) 2

+b) 3/2

-c) 1/2

-d) 3

Key: H0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=1e$, $q_{2}=-8e$, and $q_{3}=4e$?

-a) 3.719E+01 degrees

-b) 4.091E+01 degrees

+c) 4.500E+01 degrees

-d) 4.950E+01 degrees

-e) 5.445E+01 degrees

2)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.3 m (on axis) away from the loop's center?

-a) 1.764E+09 N/C²

-b) 1.941E+09 N/C²

+c) 2.135E+09 N/C²

-d) 2.348E+09 N/C²

-e) 2.583E+09 N/C²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-9e$, and $q_{3}=4e$?

-a) 5.014E-14 N

-b) 5.515E-14 N

-c) 6.067E-14 N

-d) 6.674E-14 N

+e) 7.341E-14 N

4) What is the magnitude of the electric field at the origin if a 1.2 nC charge is placed at x = 5.9 m, and a 3.1 nC charge is placed at y = 6.1 m?

-a) 7.02 x 10^-1N/C

+b) 8.11 x 10^-1N/C

-c) 9.36 x 10^-1N/C

-d) 1.08 x 10⁰N/C

-e) 1.25 x 10⁰N/C

5) What angle does the electric field at the origin make with the x-axis if a 1.9 nC charge is placed at x = -5.4 m, and a 1.5 nC charge is placed at y = -7.1 m?

-a) 1.38 x 10¹degrees

-b) 1.59 x 10¹degrees

-c) 1.84 x 10¹degrees

-d) 2.13 x 10¹degrees

+e) 2.45 x 10¹degrees

6) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 7² + 8²

-b) 3² + 8²

-c) 7² + (8−s)²

+d) (7-s)² + 8²

-e) 7² + (3−s)²

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

-a) 3

-b) 2

-c) 1/2

+d) 3/2

8) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 9² + (2-s)²

+b) 2² + (9-s)²

-c) 7² + (2-s)²

-d) 9² + (7-s)²

-e) 2² + (7-s)²

9) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 8

+b) 7−s

-c) s−7

-d) 3−s

-e) s−3

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) 3

-b) −3

+c) 2

-d) −3

-e) −7

Key: H1

1) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 7² + 8²

-b) 7² + (3−s)²

+c) (7-s)² + 8²

-d) 3² + 8²

-e) 7² + (8−s)²

2) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) −7

-b) 3

-c) −3

+d) 2

-e) −3

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=1e$, $q_{2}=-8e$, and $q_{3}=3e$?

-a) 3.629E+01 degrees

-b) 3.992E+01 degrees

-c) 4.391E+01 degrees

-d) 4.830E+01 degrees

+e) 5.313E+01 degrees

4) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 7−s

-b) s−3

-c) 3−s

-d) 8

-e) s−7

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=6e$?

-a) 2.544E-14 N

-b) 2.798E-14 N

-c) 3.078E-14 N

+d) 3.385E-14 N

-e) 3.724E-14 N

6) What angle does the electric field at the origin make with the x-axis if a 1.2 nC charge is placed at x = -6.7 m, and a 1.7 nC charge is placed at y = -6.1 m?

-a) 4.47 x 10¹degrees

-b) 5.17 x 10¹degrees

+c) 5.97 x 10¹degrees

-d) 6.89 x 10¹degrees

-e) 7.96 x 10¹degrees

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

-a) 1/2

+b) 3/2

-c) 2

-d) 3

8) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 7² + (2-s)²

-b) 9² + (7-s)²

-c) 9² + (2-s)²

+d) 2² + (9-s)²

-e) 2² + (7-s)²

9)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 3.159E+09 N/C²

-b) 3.475E+09 N/C²

-c) 3.823E+09 N/C²

-d) 4.205E+09 N/C²

-e) 4.626E+09 N/C²

10) What is the magnitude of the electric field at the origin if a 1.4 nC charge is placed at x = 8.2 m, and a 2.3 nC charge is placed at y = 5.9 m?

-a) 5.39 x 10^-1N/C

+b) 6.23 x 10^-1N/C

-c) 7.19 x 10^-1N/C

-d) 8.31 x 10^-1N/C

-e) 9.59 x 10^-1N/C

Key: H2

1) What is the magnitude of the electric field at the origin if a 2.5 nC charge is placed at x = 5.3 m, and a 1.9 nC charge is placed at y = 5.6 m?

-a) 7.26 x 10^-1N/C

-b) 8.38 x 10^-1N/C

+c) 9.68 x 10^-1N/C

-d) 1.12 x 10⁰N/C

-e) 1.29 x 10⁰N/C

2) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 2² + (7-s)²

+b) 2² + (9-s)²

-c) 9² + (7-s)²

-d) 7² + (2-s)²

-e) 9² + (2-s)²

3)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 3.159E+09 N/C²

-b) 3.475E+09 N/C²

-c) 3.823E+09 N/C²

-d) 4.205E+09 N/C²

-e) 4.626E+09 N/C²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-7e$, and $q_{3}=3e$?

-a) 4.743E+01 degrees

-b) 5.217E+01 degrees

-c) 5.739E+01 degrees

-d) 6.313E+01 degrees

+e) 6.944E+01 degrees

5) What angle does the electric field at the origin make with the x-axis if a 2.9 nC charge is placed at x = -7.3 m, and a 1.7 nC charge is placed at y = -8.1 m?

+a) 2.55 x 10¹degrees

-b) 2.94 x 10¹degrees

-c) 3.4 x 10¹degrees

-d) 3.92 x 10¹degrees

-e) 4.53 x 10¹degrees

6) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 7² + (8−s)²

-b) 7² + (3−s)²

-c) 3² + 8²

+d) (7-s)² + 8²

-e) 7² + 8²

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

-a) 1/2

+b) 3/2

-c) 2

-d) 3

8) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 8

-b) s−3

-c) 3−s

+d) 7−s

-e) s−7

9)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=5e$?

-a) 8.259E-15 N

-b) 9.085E-15 N

-c) 9.993E-15 N

-d) 1.099E-14 N

+e) 1.209E-14 N

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) −7

-b) 3

+c) 2

-d) −3

-e) −3

Key: I0

1) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 7.701E+01 N/C

+b) 8.471E+01 N/C

-c) 9.318E+01 N/C

-d) 1.025E+02 N/C

-e) 1.127E+02 N/C

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=5e$?

-a) 8.259E-15 N

-b) 9.085E-15 N

-c) 9.993E-15 N

-d) 1.099E-14 N

+e) 1.209E-14 N

3)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.3 m (on axis) away from the loop's center?

+a) 4.788E+09 N/C²

-b) 5.267E+09 N/C²

-c) 5.793E+09 N/C²

-d) 6.373E+09 N/C²

-e) 7.010E+09 N/C²

4) What is the magnitude of the electric field at the origin if a 3 nC charge is placed at x = 5.1 m, and a 2 nC charge is placed at y = 8.6 m?

-a) 7.99 x 10^-1N/C

-b) 9.22 x 10^-1N/C

+c) 1.07 x 10⁰N/C

-d) 1.23 x 10⁰N/C

-e) 1.42 x 10⁰N/C

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 1.95 x 10^-1 unit

-b) 2.36 x 10^-1 unit

-c) 2.86 x 10^-1 unit

+d) 3.47 x 10^-1 unit

-e) 4.2 x 10^-1 unit

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

-a) s−3

-b) s−7

-c) 3

+d) 7−s

-e) 3−s

7) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s − 9

-b) 2

+c) 9 − s

-d) 2 − s

-e) s − 2

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−4

+b) 8−s

-c) 4−s

-d) s−8

-e) 4

9) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−1

-b) 5

-c) s−4

-d) 5−s

+e) 1−s

10) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 2/3

-b) 1/2

-c) 3

+d) 3/2

-e) 2

Key: I1

1) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

+a) 7−s

-b) 3−s

-c) 3

-d) s−3

-e) s−7

2) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 2/3

+b) 3/2

-c) 1/2

-d) 3

-e) 2

3) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

+a) 3.47 x 10^-1 unit

-b) 4.2 x 10^-1 unit

-c) 5.09 x 10^-1 unit

-d) 6.17 x 10^-1 unit

-e) 7.47 x 10^-1 unit

4) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 2.571E+01 N/C

-b) 2.828E+01 N/C

-c) 3.111E+01 N/C

-d) 3.422E+01 N/C

+e) 3.765E+01 N/C

5) What is the magnitude of the electric field at the origin if a 1.8 nC charge is placed at x = 9.6 m, and a 2 nC charge is placed at y = 8.7 m?

+a) 2.95 x 10^-1N/C

-b) 3.41 x 10^-1N/C

-c) 3.94 x 10^-1N/C

-d) 4.55 x 10^-1N/C

-e) 5.25 x 10^-1N/C

6) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 2

+b) 9 − s

-c) 2 − s

-d) s − 9

-e) s − 2

7) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−8

+b) 8−s

-c) 4−s

-d) 4

-e) s−4

8)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=5e$?

-a) 2.248E-14 N

-b) 2.473E-14 N

+c) 2.721E-14 N

-d) 2.993E-14 N

-e) 3.292E-14 N

9) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−1

-b) s−4

+c) 1−s

-d) 5−s

-e) 5

10)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

-a) 5.581E+09 N/C²

-b) 6.139E+09 N/C²

+c) 6.753E+09 N/C²

-d) 7.428E+09 N/C²

-e) 8.171E+09 N/C²

Key: I2

1) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 7.701E+01 N/C

+b) 8.471E+01 N/C

-c) 9.318E+01 N/C

-d) 1.025E+02 N/C

-e) 1.127E+02 N/C

2) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s − 9

-b) 2

-c) 2 − s

-d) s − 2

+e) 9 − s

3) What is the magnitude of the electric field at the origin if a 3 nC charge is placed at x = 8.8 m, and a 2.9 nC charge is placed at y = 6.9 m?

-a) 4.87 x 10^-1N/C

-b) 5.62 x 10^-1N/C

+c) 6.49 x 10^-1N/C

-d) 7.49 x 10^-1N/C

-e) 8.65 x 10^-1N/C

4) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

-a) s−7

+b) 7−s

-c) s−3

-d) 3

-e) 3−s

5) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−8

+b) 8−s

-c) 4−s

-d) 4

-e) s−4

6)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.99 m (on axis) away from the loop's center?

-a) 2.429E+09 N/C²

+b) 2.672E+09 N/C²

-c) 2.939E+09 N/C²

-d) 3.233E+09 N/C²

-e) 3.556E+09 N/C²

7) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

+a) 3/2

-b) 2

-c) 3

-d) 1/2

-e) 2/3

8) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 1.95 x 10^-1 unit

-b) 2.36 x 10^-1 unit

-c) 2.86 x 10^-1 unit

+d) 3.47 x 10^-1 unit

-e) 4.2 x 10^-1 unit

9) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−1

-b) s−4

-c) 5−s

+d) 1−s

-e) 5

10)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-7e$, and $q_{3}=2e$?

-a) 3.391E-14 N

-b) 3.731E-14 N

-c) 4.104E-14 N

+d) 4.514E-14 N

-e) 4.965E-14 N

Key: J0

1)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.54 m if a=1.0 m, b=2.0 m. The total charge on the rod is 3 nC.

-a) 1.665E+00 V/m²

-b) 1.831E+00 V/m²

-c) 2.014E+00 V/m²

+d) 2.216E+00 V/m²

-e) 2.437E+00 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=4e$?

-a) 5.914E+01 degrees

-b) 6.506E+01 degrees

+c) 7.157E+01 degrees

-d) 7.872E+01 degrees

-e) 8.659E+01 degrees

3)

A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.4 m (on axis) away from the loop's center?

-a) 7.119E+09 N/C²

-b) 7.831E+09 N/C²

+c) 8.614E+09 N/C²

-d) 9.476E+09 N/C²

-e) 1.042E+10 N/C²

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 1.61 x 10^-1 unit

-b) 1.95 x 10^-1 unit

-c) 2.36 x 10^-1 unit

-d) 2.86 x 10^-1 unit

+e) 3.47 x 10^-1 unit

5) What angle does the electric field at the origin make with the x-axis if a 2 nC charge is placed at x = -8.7 m, and a 2.7 nC charge is placed at y = -5.2 m?

-a) 4.23 x 10¹degrees

-b) 4.88 x 10¹degrees

-c) 5.64 x 10¹degrees

-d) 6.51 x 10¹degrees

+e) 7.52 x 10¹degrees

6) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

-a) 8

-b) 1/2

+c) 4

-d) 2

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) −3

-b) 3

+c) 2

-d) −7

-e) −3

8) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 7² + (3−s)²

-b) 7² + (8−s)²

-c) 7² + 8²

+d) (7-s)² + 8²

-e) 3² + 8²

9) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 5

-b) 1−s

-c) s−4

-d) s−1

-e) 5−s

10) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s − 2

+b) 9 − s

-c) s − 9

-d) 2

-e) 2 − s

Key: J1

1) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) −7

-b) −3

+c) 2

-d) −3

-e) 3

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-7e$, and $q_{3}=3e$?

-a) 4.743E+01 degrees

-b) 5.217E+01 degrees

-c) 5.739E+01 degrees

-d) 6.313E+01 degrees

+e) 6.944E+01 degrees

3)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.4 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.69 m, b=2.2 m. The total charge on the rod is 6 nC.

-a) 3.161E+00 V/m²

-b) 3.477E+00 V/m²

-c) 3.825E+00 V/m²

-d) 4.208E+00 V/m²

+e) 4.628E+00 V/m²

4) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 2 − s

-b) s − 9

+c) 9 − s

-d) s − 2

-e) 2

5) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 7² + (8−s)²

+b) (7-s)² + 8²

-c) 7² + 8²

-d) 3² + 8²

-e) 7² + (3−s)²

6) What angle does the electric field at the origin make with the x-axis if a 2.6 nC charge is placed at x = -8.3 m, and a 2.5 nC charge is placed at y = -9.6 m?

-a) 2.32 x 10¹degrees

-b) 2.68 x 10¹degrees

-c) 3.09 x 10¹degrees

+d) 3.57 x 10¹degrees

-e) 4.12 x 10¹degrees

7) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 2.86 x 10^-1

+b) 3.47 x 10^-1

-c) 4.2 x 10^-1

-d) 5.09 x 10^-1

-e) 6.17 x 10^-1

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

-a) 8

-b) 1/2

-c) 2

+d) 4

9)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

-a) 5.581E+09 N/C²

-b) 6.139E+09 N/C²

+c) 6.753E+09 N/C²

-d) 7.428E+09 N/C²

-e) 8.171E+09 N/C²

10) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−4

+b) 5

-c) 5−s

-d) 1−s

-e) s−1

Key: J2

1) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 1.95 x 10^-1 unit

-b) 2.36 x 10^-1 unit

-c) 2.86 x 10^-1 unit

+d) 3.47 x 10^-1 unit

-e) 4.2 x 10^-1 unit

2)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.96 m if a=0.95 m, b=1.8 m. The total charge on the rod is 7 nC.

-a) 3.385E+00 V/m²

-b) 3.724E+00 V/m²

-c) 4.096E+00 V/m²

+d) 4.506E+00 V/m²

-e) 4.957E+00 V/m²

3)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

-a) 2.013E+09 N/C²

-b) 2.214E+09 N/C²

-c) 2.435E+09 N/C²

-d) 2.679E+09 N/C²

+e) 2.947E+09 N/C²

4) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s − 2

-b) 2 − s

-c) 2

-d) s − 9

+e) 9 − s

5) What angle does the electric field at the origin make with the x-axis if a 1.8 nC charge is placed at x = -6.9 m, and a 2.5 nC charge is placed at y = -7.5 m?

-a) 2.79 x 10¹degrees

-b) 3.22 x 10¹degrees

-c) 3.72 x 10¹degrees

-d) 4.3 x 10¹degrees

+e) 4.96 x 10¹degrees

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) −7

-b) −3

+c) 2

-d) 3

-e) −3

7)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-9e$, and $q_{3}=6e$?

-a) 5.767E+01 degrees

+b) 6.343E+01 degrees

-c) 6.978E+01 degrees

-d) 7.676E+01 degrees

-e) 8.443E+01 degrees

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

-a) 8

-b) 2

-c) 1/2

+d) 4

9) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 7² + (8−s)²

+b) (7-s)² + 8²

-c) 7² + 8²

-d) 3² + 8²

-e) 7² + (3−s)²

10) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−1

-b) 1−s

-c) s−4

-d) 5−s

+e) 5

Key: K0

1)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.7{\text{ m}}$ and the surface charge density is $\sigma =7{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=5.8{\text{ m}}$.

-a) 3.722E-01 V/m²

-b) 4.094E-01 V/m²

-c) 4.504E-01 V/m²

+d) 4.954E-01 V/m²

-e) 5.450E-01 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-9e$, and $q_{3}=5e$?

-a) 3.961E+01 degrees

-b) 4.357E+01 degrees

-c) 4.793E+01 degrees

-d) 5.272E+01 degrees

+e) 5.799E+01 degrees

3)

A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 5.402E+09 N/C²

-b) 5.943E+09 N/C²

-c) 6.537E+09 N/C²

-d) 7.191E+09 N/C²

-e) 7.910E+09 N/C²

4) What is the magnitude of the electric field at the origin if a 3 nC charge is placed at x = 5.1 m, and a 2 nC charge is placed at y = 8.6 m?

-a) 7.99 x 10^-1N/C

-b) 9.22 x 10^-1N/C

+c) 1.07 x 10⁰N/C

-d) 1.23 x 10⁰N/C

-e) 1.42 x 10⁰N/C

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 4a) is βkQ/a², where β equals

-a) 1.33 x 10^-3 unit

-b) 1.61 x 10^-3 unit

-c) 1.95 x 10^-3 unit

-d) 2.37 x 10^-3 unit

+e) 2.87 x 10^-3 unit

6) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 7² + (2-s)²

-b) 9² + (7-s)²

+c) 2² + (9-s)²

-d) 2² + (7-s)²

-e) 9² + (2-s)²

7) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 5

-b) 1−s

-c) s−4

-d) s−1

-e) 5−s

8) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 5−s

-b) 5

+c) 1−s

-d) s−4

-e) s−1

9) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) 3

-b) −3

+c) 2

-d) −3

-e) −7

10) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 3−s

+b) 7−s

-c) s−7

-d) 8

-e) s−3

Key: K1

1) What is the magnitude of the electric field at the origin if a 2.7 nC charge is placed at x = 9.1 m, and a 2.5 nC charge is placed at y = 5.9 m?

-a) 3.99 x 10^-1N/C

-b) 4.6 x 10^-1N/C

-c) 5.32 x 10^-1N/C

-d) 6.14 x 10^-1N/C

+e) 7.09 x 10^-1N/C

2) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−1

-b) 5

+c) 1−s

-d) 5−s

-e) s−4

3) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−3

+b) 7−s

-c) 3−s

-d) 8

-e) s−7

4) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 5−s

+b) 5

-c) s−4

-d) s−1

-e) 1−s

5) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 7² + (2-s)²

+b) 2² + (9-s)²

-c) 2² + (7-s)²

-d) 9² + (7-s)²

-e) 9² + (2-s)²

6) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 2a) is βkQ/a², where β equals

-a) 7.31 x 10^-3 unit

-b) 8.86 x 10^-3 unit

-c) 1.07 x 10^-2 unit

-d) 1.3 x 10^-2 unit

+e) 1.57 x 10^-2 unit

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

+a) 2

-b) −7

-c) 3

-d) −3

-e) −3

8)

A ring is uniformly charged with a net charge of 8 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.32 m (on axis) away from the loop's center?

-a) 3.339E+09 N/C²

-b) 3.673E+09 N/C²

-c) 4.041E+09 N/C²

+d) 4.445E+09 N/C²

-e) 4.889E+09 N/C²

9)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.9{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=5.1{\text{ m}}$.

-a) 8.253E-01 V/m²

-b) 9.079E-01 V/m²

+c) 9.987E-01 V/m²

-d) 1.099E+00 V/m²

-e) 1.208E+00 V/m²

10)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=4e$?

-a) 5.377E+01 degrees

-b) 5.914E+01 degrees

-c) 6.506E+01 degrees

+d) 7.157E+01 degrees

-e) 7.872E+01 degrees

Key: K2

1) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−4

+b) 5

-c) 1−s

-d) s−1

-e) 5−s

2)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.0{\text{ m}}$ and the surface charge density is $\sigma =8{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=2.0{\text{ m}}$.

-a) 9.459E+00 V/m²

+b) 1.040E+01 V/m²

-c) 1.145E+01 V/m²

-d) 1.259E+01 V/m²

-e) 1.385E+01 V/m²

3) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 9² + (2-s)²

-b) 9² + (7-s)²

-c) 7² + (2-s)²

-d) 2² + (7-s)²

+e) 2² + (9-s)²

4)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.2 m (on axis) away from the loop's center?

-a) 6.925E+09 N/C²

-b) 7.617E+09 N/C²

+c) 8.379E+09 N/C²

-d) 9.217E+09 N/C²

-e) 1.014E+10 N/C²

5) What is the magnitude of the electric field at the origin if a 2.7 nC charge is placed at x = 9.1 m, and a 2.5 nC charge is placed at y = 5.9 m?

-a) 3.99 x 10^-1N/C

-b) 4.6 x 10^-1N/C

-c) 5.32 x 10^-1N/C

-d) 6.14 x 10^-1N/C

+e) 7.09 x 10^-1N/C

6) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−3

-b) 8

+c) 7−s

-d) s−7

-e) 3−s

7) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 4a) is βkQ/a², where β equals

-a) 2.22 x 10^-3 unit

+b) 2.69 x 10^-3 unit

-c) 3.26 x 10^-3 unit

-d) 3.95 x 10^-3 unit

-e) 4.79 x 10^-3 unit

8) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) −3

-b) 3

+c) 2

-d) −3

-e) −7

9) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 5

-b) s−4

-c) s−1

+d) 1−s

-e) 5−s

10)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-7e$, and $q_{3}=5e$?

-a) 4.357E+01 degrees

-b) 4.793E+01 degrees

-c) 5.272E+01 degrees

+d) 5.799E+01 degrees

-e) 6.379E+01 degrees

Key: L0

1)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.0{\text{ m}}$ and the surface charge density is $\sigma =8{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=2.0{\text{ m}}$.

-a) 9.459E+00 V/m²

+b) 1.040E+01 V/m²

-c) 1.145E+01 V/m²

-d) 1.259E+01 V/m²

-e) 1.385E+01 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=5e$?

-a) 2.248E-14 N

-b) 2.473E-14 N

+c) 2.721E-14 N

-d) 2.993E-14 N

-e) 3.292E-14 N

3) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 3.428E+01 N/C

-b) 3.771E+01 N/C

-c) 4.148E+01 N/C

-d) 4.563E+01 N/C

+e) 5.020E+01 N/C

4) What angle does the electric field at the origin make with the x-axis if a 2.8 nC charge is placed at x = -9.8 m, and a 2.8 nC charge is placed at y = -5.8 m?

+a) 7.07 x 10¹degrees

-b) 8.16 x 10¹degrees

-c) 9.43 x 10¹degrees

-d) 1.09 x 10²degrees

-e) 1.26 x 10²degrees

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

-a) 1.09 x 10^-3 unit

-b) 1.33 x 10^-3 unit

+c) 1.61 x 10^-3 unit

-d) 1.95 x 10^-3 unit

-e) 2.36 x 10^-3 unit

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) −3

+b) 2

-c) −3

-d) 3

-e) −7

7) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 4

-b) 4−s

-c) 8−s

-d) s−4

-e) s−8

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−8

-b) s−4

-c) 4

+d) 8−s

-e) 4−s

9) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

-a) 3

+b) 7−s

-c) s−7

-d) s−3

-e) 3−s

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

+a) 3/2

-b) 1/2

-c) 3

-d) 2

Key: L1

1) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 4a) is βkQ/a², where β equals

-a) 2.22 x 10^-3 unit

+b) 2.69 x 10^-3 unit

-c) 3.26 x 10^-3 unit

-d) 3.95 x 10^-3 unit

-e) 4.79 x 10^-3 unit

2) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 4.821E+01 N/C

-b) 5.303E+01 N/C

-c) 5.834E+01 N/C

-d) 6.417E+01 N/C

+e) 7.059E+01 N/C

3)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=4.3{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=2.4{\text{ m}}$.

+a) 5.647E+00 V/m²

-b) 6.212E+00 V/m²

-c) 6.833E+00 V/m²

-d) 7.517E+00 V/m²

-e) 8.268E+00 V/m²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=5e$?

-a) 9.958E-15 N

-b) 1.095E-14 N

-c) 1.205E-14 N

-d) 1.325E-14 N

+e) 1.458E-14 N

5) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 8−s

-b) s−4

-c) 4−s

-d) 4

-e) s−8

6) What angle does the electric field at the origin make with the x-axis if a 2.8 nC charge is placed at x = -9.8 m, and a 2.8 nC charge is placed at y = -5.8 m?

+a) 7.07 x 10¹degrees

-b) 8.16 x 10¹degrees

-c) 9.43 x 10¹degrees

-d) 1.09 x 10²degrees

-e) 1.26 x 10²degrees

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

-a) 3

+b) 7−s

-c) s−3

-d) s−7

-e) 3−s

8) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) −3

-b) −3

-c) −7

+d) 2

-e) 3

9) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

-a) 2

-b) 3

-c) 1/2

+d) 3/2

10) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 4−s

-b) s−8

-c) 8−s

-d) s−4

+e) 4

Key: L2

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=5e$?

-a) 8.259E-15 N

-b) 9.085E-15 N

-c) 9.993E-15 N

-d) 1.099E-14 N

+e) 1.209E-14 N

2) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 8−s

+b) 4

-c) s−8

-d) 4−s

-e) s−4

3) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 4

-b) s−4

-c) s−8

-d) 4−s

+e) 8−s

4) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

+a) 2

-b) −3

-c) −3

-d) 3

-e) −7

5) What angle does the electric field at the origin make with the x-axis if a 1.4 nC charge is placed at x = -5.5 m, and a 2.8 nC charge is placed at y = -6.8 m?

-a) 3.95 x 10¹degrees

-b) 4.56 x 10¹degrees

+c) 5.26 x 10¹degrees

-d) 6.08 x 10¹degrees

-e) 7.02 x 10¹degrees

6)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.8{\text{ m}}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=0.83{\text{ m}}$.

+a) 2.898E+01 V/m²

-b) 3.188E+01 V/m²

-c) 3.507E+01 V/m²

-d) 3.857E+01 V/m²

-e) 4.243E+01 V/m²

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

-a) s−3

-b) 3−s

+c) 7−s

-d) s−7

-e) 3

8) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 3a, 5a) is βkQ/a², where β equals

+a) 1.08 x 10^-3 unit

-b) 1.31 x 10^-3 unit

-c) 1.59 x 10^-3 unit

-d) 1.93 x 10^-3 unit

-e) 2.34 x 10^-3 unit

9) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

-a) 1/2

-b) 3

+c) 3/2

-d) 2

10) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 6.534E+01 N/C

-b) 7.187E+01 N/C

+c) 7.906E+01 N/C

-d) 8.696E+01 N/C

-e) 9.566E+01 N/C

Key: M0

1)

A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.73 m (on axis) away from the loop's center?

-a) 7.415E+09 N/C²

-b) 8.156E+09 N/C²

-c) 8.972E+09 N/C²

-d) 9.869E+09 N/C²

+e) 1.086E+10 N/C²

2) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

-a) 9.546E+01 N/C

-b) 1.050E+02 N/C

-c) 1.155E+02 N/C

+d) 1.271E+02 N/C

-e) 1.398E+02 N/C

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-8e$, and $q_{3}=2e$?

-a) 1.172E-14 N

+b) 1.290E-14 N

-c) 1.419E-14 N

-d) 1.561E-14 N

-e) 1.717E-14 N

4) What is the magnitude of the electric field at the origin if a 2.5 nC charge is placed at x = 5.3 m, and a 1.9 nC charge is placed at y = 5.6 m?

-a) 7.26 x 10^-1N/C

-b) 8.38 x 10^-1N/C

+c) 9.68 x 10^-1N/C

-d) 1.12 x 10⁰N/C

-e) 1.29 x 10⁰N/C

5) What angle does the electric field at the origin make with the x-axis if a 1.4 nC charge is placed at x = -5.5 m, and a 2.8 nC charge is placed at y = -6.8 m?

-a) 3.95 x 10¹degrees

-b) 4.56 x 10¹degrees

+c) 5.26 x 10¹degrees

-d) 6.08 x 10¹degrees

-e) 7.02 x 10¹degrees

6) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−3

+b) 7−s

-c) s−7

-d) 3−s

-e) 8

7) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 2

-b) 3

+c) 3/2

-d) 2/3

-e) 1/2

8) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 2

-b) s − 9

-c) 2 − s

+d) 9 − s

-e) s − 2

9) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 9² + (2-s)²

-b) 9² + (7-s)²

+c) 2² + (9-s)²

-d) 2² + (7-s)²

-e) 7² + (2-s)²

10) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−8

-b) s−4

-c) 4

+d) 8−s

-e) 4−s

Key: M1

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=6e$?

-a) 1.028E-14 N

-b) 1.130E-14 N

-c) 1.244E-14 N

-d) 1.368E-14 N

+e) 1.505E-14 N

2) What is the magnitude of the electric field at the origin if a 3.1 nC charge is placed at x = 6.2 m, and a 2.6 nC charge is placed at y = 6 m?

-a) 5.47 x 10^-1N/C

-b) 6.32 x 10^-1N/C

-c) 7.3 x 10^-1N/C

-d) 8.43 x 10^-1N/C

+e) 9.73 x 10^-1N/C

3) What angle does the electric field at the origin make with the x-axis if a 2.8 nC charge is placed at x = -9.8 m, and a 2.8 nC charge is placed at y = -5.8 m?

+a) 7.07 x 10¹degrees

-b) 8.16 x 10¹degrees

-c) 9.43 x 10¹degrees

-d) 1.09 x 10²degrees

-e) 1.26 x 10²degrees

4) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 2/3

-b) 1/2

+c) 3/2

-d) 2

-e) 3

5) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 4.492E+01 N/C

+b) 4.941E+01 N/C

-c) 5.435E+01 N/C

-d) 5.979E+01 N/C

-e) 6.577E+01 N/C

6) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 9 − s

-b) s − 9

-c) 2

-d) s − 2

-e) 2 − s

7) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 8

+b) 7−s

-c) 3−s

-d) s−3

-e) s−7

8) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 7² + (2-s)²

+b) 2² + (9-s)²

-c) 9² + (2-s)²

-d) 2² + (7-s)²

-e) 9² + (7-s)²

9)

A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.73 m (on axis) away from the loop's center?

-a) 7.415E+09 N/C²

-b) 8.156E+09 N/C²

-c) 8.972E+09 N/C²

-d) 9.869E+09 N/C²

+e) 1.086E+10 N/C²

10) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 4−s

+b) 8−s

-c) s−4

-d) 4

-e) s−8

Key: M2

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-7e$, and $q_{3}=2e$?

-a) 3.426E-15 N

-b) 3.768E-15 N

-c) 4.145E-15 N

-d) 4.560E-15 N

+e) 5.015E-15 N

2) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 2/3

-b) 3

-c) 2

+d) 3/2

-e) 1/2

3) What angle does the electric field at the origin make with the x-axis if a 2.9 nC charge is placed at x = -6.3 m, and a 2.1 nC charge is placed at y = -8.8 m?

-a) 1.32 x 10¹degrees

-b) 1.53 x 10¹degrees

-c) 1.76 x 10¹degrees

+d) 2.04 x 10¹degrees

-e) 2.35 x 10¹degrees

4) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 8−s

-b) 4

-c) s−4

-d) 4−s

-e) s−8

5) What is the magnitude of the electric field at the origin if a 1.7 nC charge is placed at x = 6.4 m, and a 3 nC charge is placed at y = 8 m?

-a) 4.22 x 10^-1N/C

-b) 4.87 x 10^-1N/C

+c) 5.63 x 10^-1N/C

-d) 6.5 x 10^-1N/C

-e) 7.51 x 10^-1N/C

6) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

+a) 2² + (9-s)²

-b) 9² + (7-s)²

-c) 2² + (7-s)²

-d) 7² + (2-s)²

-e) 9² + (2-s)²

7) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

+a) 8.471E+01 N/C

-b) 9.318E+01 N/C

-c) 1.025E+02 N/C

-d) 1.127E+02 N/C

-e) 1.240E+02 N/C

8) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 9 − s

-b) s − 2

-c) s − 9

-d) 2

-e) 2 − s

9)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.35 m (on axis) away from the loop's center?

-a) 4.142E+09 N/C²

-b) 4.556E+09 N/C²

+c) 5.012E+09 N/C²

-d) 5.513E+09 N/C²

-e) 6.064E+09 N/C²

10) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 7−s

-b) s−7

-c) 3−s

-d) 8

-e) s−3

Key: N0

1)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

-a) 5.581E+09 N/C²

-b) 6.139E+09 N/C²

+c) 6.753E+09 N/C²

-d) 7.428E+09 N/C²

-e) 8.171E+09 N/C²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=3e$?

-a) 2.036E-14 N

-b) 2.240E-14 N

+c) 2.464E-14 N

-d) 2.710E-14 N

-e) 2.981E-14 N

3)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.0{\text{ m}}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=1.2{\text{ m}}$.

-a) 8.933E+00 V/m²

-b) 9.826E+00 V/m²

+c) 1.081E+01 V/m²

-d) 1.189E+01 V/m²

-e) 1.308E+01 V/m²

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 2.86 x 10^-1

+b) 3.47 x 10^-1

-c) 4.2 x 10^-1

-d) 5.09 x 10^-1

-e) 6.17 x 10^-1

5) What angle does the electric field at the origin make with the x-axis if a 2.9 nC charge is placed at x = -7.3 m, and a 1.7 nC charge is placed at y = -8.1 m?

+a) 2.55 x 10¹degrees

-b) 2.94 x 10¹degrees

-c) 3.4 x 10¹degrees

-d) 3.92 x 10¹degrees

-e) 4.53 x 10¹degrees

6) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 2

+b) 3/2

-c) 3

-d) 1/2

-e) 2/3

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

-a) 1/2

+b) 3/2

-c) 2

-d) 3

8) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−1

+b) 1−s

-c) 5−s

-d) s−4

-e) 5

9) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 3−s

-b) 8

+c) 7−s

-d) s−3

-e) s−7

10) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−8

+b) 8−s

-c) 4−s

-d) s−4

-e) 4

Key: N1

1) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

-a) 3

+b) 3/2

-c) 2

-d) 1/2

2) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−3

+b) 7−s

-c) s−7

-d) 3−s

-e) 8

3) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 1−s

-b) s−1

-c) s−4

-d) 5−s

-e) 5

4)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=4.3{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=2.4{\text{ m}}$.

+a) 5.647E+00 V/m²

-b) 6.212E+00 V/m²

-c) 6.833E+00 V/m²

-d) 7.517E+00 V/m²

-e) 8.268E+00 V/m²

5) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 8−s

-b) 4−s

-c) s−4

-d) 4

-e) s−8

6) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 1.95 x 10^-1 unit

-b) 2.36 x 10^-1 unit

-c) 2.86 x 10^-1 unit

+d) 3.47 x 10^-1 unit

-e) 4.2 x 10^-1 unit

7)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-8e$, and $q_{3}=3e$?

-a) 5.243E-14 N

+b) 5.768E-14 N

-c) 6.344E-14 N

-d) 6.979E-14 N

-e) 7.677E-14 N

8)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.5 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.33 m (on axis) away from the loop's center?

-a) 1.353E+09 N/C²

-b) 1.488E+09 N/C²

+c) 1.637E+09 N/C²

-d) 1.801E+09 N/C²

-e) 1.981E+09 N/C²

9) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 3

+b) 3/2

-c) 2/3

-d) 2

-e) 1/2

10) What angle does the electric field at the origin make with the x-axis if a 1.4 nC charge is placed at x = -5.5 m, and a 2.8 nC charge is placed at y = -6.8 m?

-a) 3.95 x 10¹degrees

-b) 4.56 x 10¹degrees

+c) 5.26 x 10¹degrees

-d) 6.08 x 10¹degrees

-e) 7.02 x 10¹degrees

Key: N2

1) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

-a) 1/2

-b) 3

-c) 2

+d) 3/2

2) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 2

-b) 3

-c) 1/2

+d) 3/2

-e) 2/3

3) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 5

+b) 1−s

-c) s−1

-d) s−4

-e) 5−s

4)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.4{\text{ m}}$ and the surface charge density is $\sigma =6{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=0.56{\text{ m}}$.

-a) 2.567E+01 V/m²

-b) 2.824E+01 V/m²

-c) 3.106E+01 V/m²

-d) 3.417E+01 V/m²

+e) 3.759E+01 V/m²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-7e$, and $q_{3}=3e$?

-a) 4.171E-14 N

-b) 4.588E-14 N

+c) 5.047E-14 N

-d) 5.551E-14 N

-e) 6.107E-14 N

6) What angle does the electric field at the origin make with the x-axis if a 2.8 nC charge is placed at x = -8 m, and a 1.5 nC charge is placed at y = -8.7 m?

+a) 2.44 x 10¹degrees

-b) 2.81 x 10¹degrees

-c) 3.25 x 10¹degrees

-d) 3.75 x 10¹degrees

-e) 4.33 x 10¹degrees

7) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 8−s

-b) 4−s

-c) 4

-d) s−4

-e) s−8

8) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

+a) 3.47 x 10^-1 unit

-b) 4.2 x 10^-1 unit

-c) 5.09 x 10^-1 unit

-d) 6.17 x 10^-1 unit

-e) 7.47 x 10^-1 unit

9)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 8.336E+09 N/C²

-b) 9.170E+09 N/C²

-c) 1.009E+10 N/C²

-d) 1.110E+10 N/C²

-e) 1.220E+10 N/C²

10) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 8

-b) s−7

-c) 3−s

+d) 7−s

-e) s−3

Key: O0

1) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 3.500E+01 N/C

-b) 3.850E+01 N/C

+c) 4.235E+01 N/C

-d) 4.659E+01 N/C

-e) 5.125E+01 N/C

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=6e$?

-a) 2.544E-14 N

-b) 2.798E-14 N

-c) 3.078E-14 N

+d) 3.385E-14 N

-e) 3.724E-14 N

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-9e$, and $q_{3}=5e$?

-a) 5.272E+01 degrees

+b) 5.799E+01 degrees

-c) 6.379E+01 degrees

-d) 7.017E+01 degrees

-e) 7.719E+01 degrees

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 1.95 x 10^-1 unit

-b) 2.36 x 10^-1 unit

-c) 2.86 x 10^-1 unit

+d) 3.47 x 10^-1 unit

-e) 4.2 x 10^-1 unit

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 2a) is βkQ/a², where β equals

-a) 7.31 x 10^-3 unit

-b) 8.86 x 10^-3 unit

-c) 1.07 x 10^-2 unit

-d) 1.3 x 10^-2 unit

+e) 1.57 x 10^-2 unit

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) −3

-b) −7

-c) 3

+d) 2

-e) −3

7) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 5−s

-b) 5

+c) 1−s

-d) s−1

-e) s−4

8) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 1−s

-b) 5−s

+c) 5

-d) s−4

-e) s−1

9) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 1/2

-b) 2/3

+c) 3/2

-d) 3

-e) 2

10) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−7

+b) 7−s

-c) 3−s

-d) 8

-e) s−3

Key: O1

1) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 1.61 x 10^-1 unit

-b) 1.95 x 10^-1 unit

-c) 2.36 x 10^-1 unit

-d) 2.86 x 10^-1 unit

+e) 3.47 x 10^-1 unit

2) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 3a, 5a) is βkQ/a², where β equals

+a) 1.08 x 10^-3 unit

-b) 1.31 x 10^-3 unit

-c) 1.59 x 10^-3 unit

-d) 1.93 x 10^-3 unit

-e) 2.34 x 10^-3 unit

3) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 7−s

-b) 8

-c) 3−s

-d) s−7

-e) s−3

4) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 6.534E+01 N/C

-b) 7.187E+01 N/C

+c) 7.906E+01 N/C

-d) 8.696E+01 N/C

-e) 9.566E+01 N/C

5) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 5

-b) s−4

-c) s−1

+d) 1−s

-e) 5−s

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

+a) 2

-b) −3

-c) 3

-d) −3

-e) −7

7)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-9e$, and $q_{3}=5e$?

-a) 6.125E+01 degrees

+b) 6.738E+01 degrees

-c) 7.412E+01 degrees

-d) 8.153E+01 degrees

-e) 8.968E+01 degrees

8) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 2

+b) 3/2

-c) 1/2

-d) 2/3

-e) 3

9) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 5

-b) s−4

-c) s−1

-d) 5−s

-e) 1−s

10)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=5e$?

-a) 8.259E-15 N

-b) 9.085E-15 N

-c) 9.993E-15 N

-d) 1.099E-14 N

+e) 1.209E-14 N

Key: O2

1) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

+a) 2

-b) −3

-c) −7

-d) −3

-e) 3

2) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 2/3

-b) 1/2

+c) 3/2

-d) 2

-e) 3

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-7e$, and $q_{3}=3e$?

-a) 4.743E+01 degrees

-b) 5.217E+01 degrees

-c) 5.739E+01 degrees

-d) 6.313E+01 degrees

+e) 6.944E+01 degrees

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=4e$?

-a) 8.613E-15 N

-b) 9.474E-15 N

-c) 1.042E-14 N

+d) 1.146E-14 N

-e) 1.261E-14 N

5) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

+a) 5.647E+01 N/C

-b) 6.212E+01 N/C

-c) 6.833E+01 N/C

-d) 7.516E+01 N/C

-e) 8.268E+01 N/C

6) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 5−s

-b) s−1

-c) 5

-d) s−4

+e) 1−s

7) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−3

+b) 7−s

-c) s−7

-d) 8

-e) 3−s

8) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

-a) 1.09 x 10^-3 unit

-b) 1.33 x 10^-3 unit

+c) 1.61 x 10^-3 unit

-d) 1.95 x 10^-3 unit

-e) 2.36 x 10^-3 unit

9) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 5

-b) 5−s

-c) 1−s

-d) s−1

-e) s−4

10) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 1.95 x 10^-1 unit

-b) 2.36 x 10^-1 unit

-c) 2.86 x 10^-1 unit

+d) 3.47 x 10^-1 unit

-e) 4.2 x 10^-1 unit

Key: P0

1)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.5 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.33 m (on axis) away from the loop's center?

-a) 1.353E+09 N/C²

-b) 1.488E+09 N/C²

+c) 1.637E+09 N/C²

-d) 1.801E+09 N/C²

-e) 1.981E+09 N/C²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-8e$, and $q_{3}=6e$?

-a) 5.243E+01 degrees

-b) 5.767E+01 degrees

+c) 6.343E+01 degrees

-d) 6.978E+01 degrees

-e) 7.676E+01 degrees

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-7e$, and $q_{3}=3e$?

-a) 1.473E-14 N

-b) 1.620E-14 N

-c) 1.782E-14 N

-d) 1.960E-14 N

+e) 2.156E-14 N

4) What is the magnitude of the electric field at the origin if a 1.8 nC charge is placed at x = 9.6 m, and a 2 nC charge is placed at y = 8.7 m?

+a) 2.95 x 10^-1N/C

-b) 3.41 x 10^-1N/C

-c) 3.94 x 10^-1N/C

-d) 4.55 x 10^-1N/C

-e) 5.25 x 10^-1N/C

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 6a) is βkQ/a², where β equals

-a) 1.52 x 10^-4 unit

-b) 1.85 x 10^-4 unit

+c) 2.24 x 10^-4 unit

-d) 2.71 x 10^-4 unit

-e) 3.28 x 10^-4 unit

6) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−1

-b) 1−s

-c) s−4

-d) 5−s

+e) 5

7) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

-a) 8

-b) 1/2

-c) 2

+d) 4

8) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 9² + (7-s)²

-b) 9² + (2-s)²

+c) 2² + (9-s)²

-d) 2² + (7-s)²

-e) 7² + (2-s)²

9) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 2

-b) s − 2

-c) 2 − s

-d) s − 9

+e) 9 − s

10) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 3

-b) 2/3

-c) 2

-d) 1/2

+e) 3/2

Key: P1

1) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

-a) 8

+b) 4

-c) 2

-d) 1/2

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=4e$?

-a) 5.914E+01 degrees

-b) 6.506E+01 degrees

+c) 7.157E+01 degrees

-d) 7.872E+01 degrees

-e) 8.659E+01 degrees

3)

A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 5.402E+09 N/C²

-b) 5.943E+09 N/C²

-c) 6.537E+09 N/C²

-d) 7.191E+09 N/C²

-e) 7.910E+09 N/C²

4) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 5−s

+b) 5

-c) s−4

-d) s−1

-e) 1−s

5) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 2

-b) 3

-c) 2/3

+d) 3/2

-e) 1/2

6) What is the magnitude of the electric field at the origin if a 2.1 nC charge is placed at x = 7 m, and a 2.1 nC charge is placed at y = 8.6 m?

-a) 3 x 10^-1N/C

-b) 3.47 x 10^-1N/C

-c) 4 x 10^-1N/C

+d) 4.62 x 10^-1N/C

-e) 5.34 x 10^-1N/C

7) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

+a) 1.61 x 10^-3 unit

-b) 1.95 x 10^-3 unit

-c) 2.36 x 10^-3 unit

-d) 2.86 x 10^-3 unit

-e) 3.46 x 10^-3 unit

8)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-7e$, and $q_{3}=3e$?

-a) 1.473E-14 N

-b) 1.620E-14 N

-c) 1.782E-14 N

-d) 1.960E-14 N

+e) 2.156E-14 N

9) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 9 − s

-b) s − 9

-c) 2

-d) 2 − s

-e) s − 2

10) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 9² + (2-s)²

-b) 2² + (7-s)²

+c) 2² + (9-s)²

-d) 7² + (2-s)²

-e) 9² + (7-s)²

Key: P2

1)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 8.336E+09 N/C²

-b) 9.170E+09 N/C²

-c) 1.009E+10 N/C²

-d) 1.110E+10 N/C²

-e) 1.220E+10 N/C²

2) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 3a) is βkQ/a², where β equals

-a) 3.38 x 10^-3 unit

-b) 4.1 x 10^-3 unit

-c) 4.96 x 10^-3 unit

-d) 6.01 x 10^-3 unit

+e) 7.28 x 10^-3 unit

3) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s − 9

+b) 9 − s

-c) 2

-d) 2 − s

-e) s − 2

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=5e$?

-a) 5.569E+01 degrees

-b) 6.125E+01 degrees

+c) 6.738E+01 degrees

-d) 7.412E+01 degrees

-e) 8.153E+01 degrees

5) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−1

+b) 5

-c) 1−s

-d) 5−s

-e) s−4

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=5e$?

-a) 2.248E-14 N

-b) 2.473E-14 N

+c) 2.721E-14 N

-d) 2.993E-14 N

-e) 3.292E-14 N

7) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 2² + (7-s)²

-b) 9² + (2-s)²

+c) 2² + (9-s)²

-d) 7² + (2-s)²

-e) 9² + (7-s)²

8) What is the magnitude of the electric field at the origin if a 2.5 nC charge is placed at x = 5.3 m, and a 1.9 nC charge is placed at y = 5.6 m?

-a) 7.26 x 10^-1N/C

-b) 8.38 x 10^-1N/C

+c) 9.68 x 10^-1N/C

-d) 1.12 x 10⁰N/C

-e) 1.29 x 10⁰N/C

9) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

-a) 1/2

+b) 4

-c) 8

-d) 2

10) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 1/2

-b) 2

-c) 3

+d) 3/2

-e) 2/3

Key: Q0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-8e$, and $q_{3}=5e$?

-a) 5.062E+01 degrees

-b) 5.569E+01 degrees

-c) 6.125E+01 degrees

+d) 6.738E+01 degrees

-e) 7.412E+01 degrees

2)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=4.3{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=2.4{\text{ m}}$.

+a) 5.647E+00 V/m²

-b) 6.212E+00 V/m²

-c) 6.833E+00 V/m²

-d) 7.517E+00 V/m²

-e) 8.268E+00 V/m²

3)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.6 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.64 m, b=1.8 m. The total charge on the rod is 3 nC.

-a) 2.955E+00 V/m²

+b) 3.250E+00 V/m²

-c) 3.575E+00 V/m²

-d) 3.933E+00 V/m²

-e) 4.326E+00 V/m²

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 4a) is βkQ/a², where β equals

-a) 1.33 x 10^-3 unit

-b) 1.61 x 10^-3 unit

-c) 1.95 x 10^-3 unit

-d) 2.37 x 10^-3 unit

+e) 2.87 x 10^-3 unit

5) What angle does the electric field at the origin make with the x-axis if a 1.4 nC charge is placed at x = -8.7 m, and a 2.7 nC charge is placed at y = -8.3 m?

-a) 4.85 x 10¹degrees

-b) 5.61 x 10¹degrees

+c) 6.47 x 10¹degrees

-d) 7.48 x 10¹degrees

-e) 8.63 x 10¹degrees

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

-a) 3−s

-b) s−7

+c) 7−s

-d) s−3

-e) 3

7) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 8−s

-b) 4

-c) 4−s

-d) s−4

-e) s−8

8) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 2 − s

-b) 2

-c) s − 9

+d) 9 − s

-e) s − 2

9) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

+a) 2

-b) −3

-c) −3

-d) −7

-e) 3

10) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 8−s

-b) s−4

+c) 4

-d) 4−s

-e) s−8

Key: Q1

1) What angle does the electric field at the origin make with the x-axis if a 2.8 nC charge is placed at x = -9.8 m, and a 2.8 nC charge is placed at y = -5.8 m?

+a) 7.07 x 10¹degrees

-b) 8.16 x 10¹degrees

-c) 9.43 x 10¹degrees

-d) 1.09 x 10²degrees

-e) 1.26 x 10²degrees

2) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 2

-b) s − 2

-c) 2 − s

-d) s − 9

+e) 9 − s

3)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.6 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.64 m, b=1.8 m. The total charge on the rod is 3 nC.

-a) 2.955E+00 V/m²

+b) 3.250E+00 V/m²

-c) 3.575E+00 V/m²

-d) 3.933E+00 V/m²

-e) 4.326E+00 V/m²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-7e$, and $q_{3}=3e$?

-a) 4.743E+01 degrees

-b) 5.217E+01 degrees

-c) 5.739E+01 degrees

-d) 6.313E+01 degrees

+e) 6.944E+01 degrees

5) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−8

-b) 4

-c) s−4

+d) 8−s

-e) 4−s

6) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 2a) is βkQ/a², where β equals

-a) 7.31 x 10^-3 unit

-b) 8.86 x 10^-3 unit

-c) 1.07 x 10^-2 unit

-d) 1.3 x 10^-2 unit

+e) 1.57 x 10^-2 unit

7) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 8−s

+b) 4

-c) s−4

-d) 4−s

-e) s−8

8) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

-a) 3−s

-b) s−3

+c) 7−s

-d) 3

-e) s−7

9)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.4{\text{ m}}$ and the surface charge density is $\sigma =6{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=0.56{\text{ m}}$.

-a) 2.567E+01 V/m²

-b) 2.824E+01 V/m²

-c) 3.106E+01 V/m²

-d) 3.417E+01 V/m²

+e) 3.759E+01 V/m²

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) −3

-b) 3

-c) −7

-d) −3

+e) 2

Key: Q2

1) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−4

-b) 4

-c) 4−s

-d) s−8

+e) 8−s

2) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s − 9

+b) 9 − s

-c) 2

-d) 2 − s

-e) s − 2

3) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−4

-b) 8−s

-c) 4−s

+d) 4

-e) s−8

4)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m. Evaluate $f(x,y)$ at x=0.52 m if a=0.88 m, b=1.3 m. The total charge on the rod is 6 nC.

-a) 6.804E+00 V/m²

+b) 7.485E+00 V/m²

-c) 8.233E+00 V/m²

-d) 9.056E+00 V/m²

-e) 9.962E+00 V/m²

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 3a) is βkQ/a², where β equals

-a) 3.38 x 10^-3 unit

-b) 4.1 x 10^-3 unit

-c) 4.96 x 10^-3 unit

-d) 6.01 x 10^-3 unit

+e) 7.28 x 10^-3 unit

6)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.4{\text{ m}}$ and the surface charge density is $\sigma =6{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=0.56{\text{ m}}$.

-a) 2.567E+01 V/m²

-b) 2.824E+01 V/m²

-c) 3.106E+01 V/m²

-d) 3.417E+01 V/m²

+e) 3.759E+01 V/m²

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

-a) 3

-b) s−7

-c) 3−s

-d) s−3

+e) 7−s

8) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) −3

+b) 2

-c) −7

-d) 3

-e) −3

9) What angle does the electric field at the origin make with the x-axis if a 2.9 nC charge is placed at x = -6.3 m, and a 2.1 nC charge is placed at y = -8.8 m?

-a) 1.32 x 10¹degrees

-b) 1.53 x 10¹degrees

-c) 1.76 x 10¹degrees

+d) 2.04 x 10¹degrees

-e) 2.35 x 10¹degrees

10)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-9e$, and $q_{3}=6e$?

-a) 5.767E+01 degrees

+b) 6.343E+01 degrees

-c) 6.978E+01 degrees

-d) 7.676E+01 degrees

-e) 8.443E+01 degrees

Key: R0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-9e$, and $q_{3}=4e$?

-a) 5.243E+01 degrees

-b) 5.767E+01 degrees

+c) 6.343E+01 degrees

-d) 6.978E+01 degrees

-e) 7.676E+01 degrees

2)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=4.3{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=2.4{\text{ m}}$.

+a) 5.647E+00 V/m²

-b) 6.212E+00 V/m²

-c) 6.833E+00 V/m²

-d) 7.517E+00 V/m²

-e) 8.268E+00 V/m²

3) A large thin isolated square plate has an area of 3 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

+a) 1.694E+02 N/C

-b) 1.864E+02 N/C

-c) 2.050E+02 N/C

-d) 2.255E+02 N/C

-e) 2.480E+02 N/C

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

-a) 1.33 x 10^-3 unit

+b) 1.61 x 10^-3 unit

-c) 1.95 x 10^-3 unit

-d) 2.36 x 10^-3 unit

-e) 2.86 x 10^-3 unit

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 1.95 x 10^-1 unit

-b) 2.36 x 10^-1 unit

-c) 2.86 x 10^-1 unit

+d) 3.47 x 10^-1 unit

-e) 4.2 x 10^-1 unit

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

-a) s−3

-b) 3−s

+c) 7−s

-d) 3

-e) s−7

7) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

+a) 3/2

-b) 3

-c) 2

-d) 1/2

-e) 2/3

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 4

-b) s−4

-c) 4−s

-d) s−8

-e) 8−s

9) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

-a) 2

-b) 1/2

+c) 4

-d) 8

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) −3

-b) 3

-c) −3

+d) 2

-e) −7

Key: R1

1) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

+a) 2

-b) 3

-c) −3

-d) −7

-e) −3

2) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

+a) 8.471E+01 N/C

-b) 9.318E+01 N/C

-c) 1.025E+02 N/C

-d) 1.127E+02 N/C

-e) 1.240E+02 N/C

3) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

-a) 8

-b) 1/2

+c) 4

-d) 2

4) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

-a) 3−s

+b) 7−s

-c) 3

-d) s−7

-e) s−3

5) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 1/2

+b) 3/2

-c) 2/3

-d) 3

-e) 2

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=5e$?

-a) 5.569E+01 degrees

-b) 6.125E+01 degrees

+c) 6.738E+01 degrees

-d) 7.412E+01 degrees

-e) 8.153E+01 degrees

7) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

+a) 1.61 x 10^-3 unit

-b) 1.95 x 10^-3 unit

-c) 2.36 x 10^-3 unit

-d) 2.86 x 10^-3 unit

-e) 3.46 x 10^-3 unit

8)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.0{\text{ m}}$ and the surface charge density is $\sigma =8{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=2.0{\text{ m}}$.

-a) 9.459E+00 V/m²

+b) 1.040E+01 V/m²

-c) 1.145E+01 V/m²

-d) 1.259E+01 V/m²

-e) 1.385E+01 V/m²

9) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 2.36 x 10^-1 unit

-b) 2.86 x 10^-1 unit

+c) 3.47 x 10^-1 unit

-d) 4.2 x 10^-1 unit

-e) 5.09 x 10^-1 unit

10) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 8−s

-b) 4−s

+c) 4

-d) s−8

-e) s−4

Key: R2

1) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 2

-b) 2/3

+c) 3/2

-d) 1/2

-e) 3

2) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 2.86 x 10^-1 unit

+b) 3.47 x 10^-1 unit

-c) 4.2 x 10^-1 unit

-d) 5.09 x 10^-1 unit

-e) 6.17 x 10^-1 unit

3) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

-a) 7.000E+01 N/C

-b) 7.701E+01 N/C

+c) 8.471E+01 N/C

-d) 9.318E+01 N/C

-e) 1.025E+02 N/C

4)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.8{\text{ m}}$ and the surface charge density is $\sigma =6{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=3.6{\text{ m}}$.

-a) 1.258E+00 V/m²

-b) 1.384E+00 V/m²

-c) 1.522E+00 V/m²

+d) 1.674E+00 V/m²

-e) 1.842E+00 V/m²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-9e$, and $q_{3}=5e$?

-a) 3.961E+01 degrees

-b) 4.357E+01 degrees

-c) 4.793E+01 degrees

-d) 5.272E+01 degrees

+e) 5.799E+01 degrees

6) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

-a) 2

+b) 4

-c) 1/2

-d) 8

7) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−8

-b) 4−s

-c) 8−s

+d) 4

-e) s−4

8) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 6a) is βkQ/a², where β equals

-a) 1.52 x 10^-4 unit

-b) 1.85 x 10^-4 unit

+c) 2.24 x 10^-4 unit

-d) 2.71 x 10^-4 unit

-e) 3.28 x 10^-4 unit

9) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) −3

-b) 3

-c) −7

+d) 2

-e) −3

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

+a) 7−s

-b) 3−s

-c) 3

-d) s−7

-e) s−3

Key: S0

1)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.4 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.69 m, b=2.2 m. The total charge on the rod is 6 nC.

-a) 3.161E+00 V/m²

-b) 3.477E+00 V/m²

-c) 3.825E+00 V/m²

-d) 4.208E+00 V/m²

+e) 4.628E+00 V/m²

2)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.3 m (on axis) away from the loop's center?

-a) 1.764E+09 N/C²

-b) 1.941E+09 N/C²

+c) 2.135E+09 N/C²

-d) 2.348E+09 N/C²

-e) 2.583E+09 N/C²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-7e$, and $q_{3}=3e$?

-a) 4.171E-14 N

-b) 4.588E-14 N

+c) 5.047E-14 N

-d) 5.551E-14 N

-e) 6.107E-14 N

4) What is the magnitude of the electric field at the origin if a 2.5 nC charge is placed at x = 5.3 m, and a 1.9 nC charge is placed at y = 5.6 m?

-a) 7.26 x 10^-1N/C

-b) 8.38 x 10^-1N/C

+c) 9.68 x 10^-1N/C

-d) 1.12 x 10⁰N/C

-e) 1.29 x 10⁰N/C

5) What angle does the electric field at the origin make with the x-axis if a 2 nC charge is placed at x = -8 m, and a 1.4 nC charge is placed at y = -9.3 m?

-a) 2.37 x 10¹degrees

+b) 2.74 x 10¹degrees

-c) 3.16 x 10¹degrees

-d) 3.65 x 10¹degrees

-e) 4.22 x 10¹degrees

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) −3

+b) 2

-c) −3

-d) 3

-e) −7

7) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 8

-b) s−7

+c) 7−s

-d) s−3

-e) 3−s

8) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 7² + 8²

-b) 7² + (3−s)²

-c) 3² + 8²

-d) 7² + (8−s)²

+e) (7-s)² + 8²

9) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 2

-b) s − 9

+c) 9 − s

-d) 2 − s

-e) s − 2

10) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−8

-b) 4−s

-c) 8−s

+d) 4

-e) s−4

Key: S1

1)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 8.336E+09 N/C²

-b) 9.170E+09 N/C²

-c) 1.009E+10 N/C²

-d) 1.110E+10 N/C²

-e) 1.220E+10 N/C²

2) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 8

-b) s−7

-c) 3−s

+d) 7−s

-e) s−3

3)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m. Evaluate $f(x,y)$ at x=0.76 m if a=1.1 m, b=1.6 m. The total charge on the rod is 8 nC.

-a) 5.267E+00 V/m²

-b) 5.794E+00 V/m²

-c) 6.374E+00 V/m²

+d) 7.011E+00 V/m²

-e) 7.712E+00 V/m²

4) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s − 2

+b) 9 − s

-c) s − 9

-d) 2

-e) 2 − s

5) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 3² + 8²

-b) 7² + 8²

-c) 7² + (3−s)²

+d) (7-s)² + 8²

-e) 7² + (8−s)²

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) −3

-b) −3

+c) 2

-d) 3

-e) −7

7)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=5e$?

-a) 9.958E-15 N

-b) 1.095E-14 N

-c) 1.205E-14 N

-d) 1.325E-14 N

+e) 1.458E-14 N

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 8−s

-b) s−8

-c) s−4

+d) 4

-e) 4−s

9) What is the magnitude of the electric field at the origin if a 2.1 nC charge is placed at x = 7 m, and a 2.1 nC charge is placed at y = 8.6 m?

-a) 3 x 10^-1N/C

-b) 3.47 x 10^-1N/C

-c) 4 x 10^-1N/C

+d) 4.62 x 10^-1N/C

-e) 5.34 x 10^-1N/C

10) What angle does the electric field at the origin make with the x-axis if a 1.2 nC charge is placed at x = -6.7 m, and a 1.7 nC charge is placed at y = -6.1 m?

-a) 4.47 x 10¹degrees

-b) 5.17 x 10¹degrees

+c) 5.97 x 10¹degrees

-d) 6.89 x 10¹degrees

-e) 7.96 x 10¹degrees

Key: S2

1) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 3² + 8²

-b) 7² + (3−s)²

-c) 7² + 8²

+d) (7-s)² + 8²

-e) 7² + (8−s)²

2)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.4 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.69 m, b=2.2 m. The total charge on the rod is 6 nC.

-a) 3.161E+00 V/m²

-b) 3.477E+00 V/m²

-c) 3.825E+00 V/m²

-d) 4.208E+00 V/m²

+e) 4.628E+00 V/m²

3) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−8

+b) 4

-c) s−4

-d) 8−s

-e) 4−s

4)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.35 m (on axis) away from the loop's center?

-a) 4.142E+09 N/C²

-b) 4.556E+09 N/C²

+c) 5.012E+09 N/C²

-d) 5.513E+09 N/C²

-e) 6.064E+09 N/C²

5) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 7−s

-b) s−7

-c) 8

-d) 3−s

-e) s−3

6) What angle does the electric field at the origin make with the x-axis if a 1.8 nC charge is placed at x = -6.9 m, and a 2.5 nC charge is placed at y = -7.5 m?

-a) 2.79 x 10¹degrees

-b) 3.22 x 10¹degrees

-c) 3.72 x 10¹degrees

-d) 4.3 x 10¹degrees

+e) 4.96 x 10¹degrees

7) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 9 − s

-b) s − 2

-c) 2

-d) 2 − s

-e) s − 9

8)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-7e$, and $q_{3}=3e$?

-a) 4.171E-14 N

-b) 4.588E-14 N

+c) 5.047E-14 N

-d) 5.551E-14 N

-e) 6.107E-14 N

9) What is the magnitude of the electric field at the origin if a 1.8 nC charge is placed at x = 9.6 m, and a 2 nC charge is placed at y = 8.7 m?

+a) 2.95 x 10^-1N/C

-b) 3.41 x 10^-1N/C

-c) 3.94 x 10^-1N/C

-d) 4.55 x 10^-1N/C

-e) 5.25 x 10^-1N/C

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

+a) 2

-b) 3

-c) −3

-d) −3

-e) −7

Key: T0

1)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

-a) 2.013E+09 N/C²

-b) 2.214E+09 N/C²

-c) 2.435E+09 N/C²

-d) 2.679E+09 N/C²

+e) 2.947E+09 N/C²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-8e$, and $q_{3}=2e$?

-a) 1.172E-14 N

+b) 1.290E-14 N

-c) 1.419E-14 N

-d) 1.561E-14 N

-e) 1.717E-14 N

3)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=1.0 m if a=1.1 m, b=1.4 m. The total charge on the rod is 5 nC.

+a) 4.602E+00 V/m²

-b) 5.062E+00 V/m²

-c) 5.568E+00 V/m²

-d) 6.125E+00 V/m²

-e) 6.738E+00 V/m²

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 5a, 5a) is βkQ/a², where β equals

-a) 6.46 x 10^-4 unit

-b) 7.82 x 10^-4 unit

-c) 9.48 x 10^-4 unit

-d) 1.15 x 10^-3 unit

+e) 1.39 x 10^-3 unit

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 1.61 x 10^-1 unit

-b) 1.95 x 10^-1 unit

-c) 2.36 x 10^-1 unit

-d) 2.86 x 10^-1 unit

+e) 3.47 x 10^-1 unit

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

+a) 3/2

-b) 2

-c) 1/2

-d) 3

7) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−4

+b) 8−s

-c) 4−s

-d) 4

-e) s−8

8) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

-a) 3−s

+b) 7−s

-c) 3

-d) s−7

-e) s−3

9) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 1−s

-b) 5−s

-c) 5

-d) s−4

-e) s−1

10) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s − 9

+b) 9 − s

-c) 2 − s

-d) s − 2

-e) 2

Key: T1

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-7e$, and $q_{3}=3e$?

-a) 1.473E-14 N

-b) 1.620E-14 N

-c) 1.782E-14 N

-d) 1.960E-14 N

+e) 2.156E-14 N

2) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 2 − s

-b) 2

-c) s − 9

+d) 9 − s

-e) s − 2

3) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

+a) 3/2

-b) 1/2

-c) 2

-d) 3

4) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

-a) s−3

+b) 7−s

-c) s−7

-d) 3−s

-e) 3

5) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−4

+b) 1−s

-c) s−1

-d) 5

-e) 5−s

6) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 4

-b) s−8

+c) 8−s

-d) 4−s

-e) s−4

7)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.5 m if a=0.67 m, b=2.4 m. The total charge on the rod is 9 nC.

-a) 5.465E+00 V/m²

-b) 6.012E+00 V/m²

-c) 6.613E+00 V/m²

+d) 7.274E+00 V/m²

-e) 8.002E+00 V/m²

8) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

+a) 1.61 x 10^-3 unit

-b) 1.95 x 10^-3 unit

-c) 2.36 x 10^-3 unit

-d) 2.86 x 10^-3 unit

-e) 3.46 x 10^-3 unit

9)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 8.336E+09 N/C²

-b) 9.170E+09 N/C²

-c) 1.009E+10 N/C²

-d) 1.110E+10 N/C²

-e) 1.220E+10 N/C²

10) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 1.95 x 10^-1 unit

-b) 2.36 x 10^-1 unit

-c) 2.86 x 10^-1 unit

+d) 3.47 x 10^-1 unit

-e) 4.2 x 10^-1 unit

Key: T2

1) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 2

+b) 9 − s

-c) 2 − s

-d) s − 2

-e) s − 9

2) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−4

+b) 1−s

-c) 5−s

-d) s−1

-e) 5

3) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 3a, 5a) is βkQ/a², where β equals

+a) 1.08 x 10^-3 unit

-b) 1.31 x 10^-3 unit

-c) 1.59 x 10^-3 unit

-d) 1.93 x 10^-3 unit

-e) 2.34 x 10^-3 unit

4) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

-a) s−3

-b) 3−s

+c) 7−s

-d) 3

-e) s−7

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=6e$?

-a) 2.544E-14 N

-b) 2.798E-14 N

-c) 3.078E-14 N

+d) 3.385E-14 N

-e) 3.724E-14 N

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

-a) 1/2

-b) 3

+c) 3/2

-d) 2

7)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.62 m, b=1.3 m. The total charge on the rod is 7 nC.

-a) 6.311E+00 V/m²

-b) 6.943E+00 V/m²

+c) 7.637E+00 V/m²

-d) 8.401E+00 V/m²

-e) 9.241E+00 V/m²

8)

A ring is uniformly charged with a net charge of 8 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.32 m (on axis) away from the loop's center?

-a) 3.339E+09 N/C²

-b) 3.673E+09 N/C²

-c) 4.041E+09 N/C²

+d) 4.445E+09 N/C²

-e) 4.889E+09 N/C²

9) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 1.95 x 10^-1 unit

-b) 2.36 x 10^-1 unit

-c) 2.86 x 10^-1 unit

+d) 3.47 x 10^-1 unit

-e) 4.2 x 10^-1 unit

10) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 4−s

-b) 4

+c) 8−s

-d) s−4

-e) s−8

Key: U0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-9e$, and $q_{3}=6e$?

-a) 1.308E-13 N

-b) 1.439E-13 N

-c) 1.583E-13 N

+d) 1.741E-13 N

-e) 1.915E-13 N

2)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.5 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.33 m (on axis) away from the loop's center?

-a) 1.353E+09 N/C²

-b) 1.488E+09 N/C²

+c) 1.637E+09 N/C²

-d) 1.801E+09 N/C²

-e) 1.981E+09 N/C²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=4e$?

-a) 5.377E+01 degrees

-b) 5.914E+01 degrees

-c) 6.506E+01 degrees

+d) 7.157E+01 degrees

-e) 7.872E+01 degrees

4) What is the magnitude of the electric field at the origin if a 3 nC charge is placed at x = 5.1 m, and a 2 nC charge is placed at y = 8.6 m?

-a) 7.99 x 10^-1N/C

-b) 9.22 x 10^-1N/C

+c) 1.07 x 10⁰N/C

-d) 1.23 x 10⁰N/C

-e) 1.42 x 10⁰N/C

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 1.95 x 10^-1 unit

-b) 2.36 x 10^-1 unit

-c) 2.86 x 10^-1 unit

+d) 3.47 x 10^-1 unit

-e) 4.2 x 10^-1 unit

6) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

-a) 2

-b) 1/2

+c) 4

-d) 8

7) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 1/2

-b) 2/3

+c) 3/2

-d) 2

-e) 3

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 8−s

-b) s−8

-c) 4−s

-d) 4

-e) s−4

9) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 9² + (2-s)²

-b) 9² + (7-s)²

+c) 2² + (9-s)²

-d) 2² + (7-s)²

-e) 7² + (2-s)²

10) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 8

-b) s−7

-c) 3−s

+d) 7−s

-e) s−3

Key: U1

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=6e$?

-a) 1.028E-14 N

-b) 1.130E-14 N

-c) 1.244E-14 N

-d) 1.368E-14 N

+e) 1.505E-14 N

2) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

-a) 2

-b) 1/2

+c) 4

-d) 8

3) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

+a) 3.47 x 10^-1 unit

-b) 4.2 x 10^-1 unit

-c) 5.09 x 10^-1 unit

-d) 6.17 x 10^-1 unit

-e) 7.47 x 10^-1 unit

4) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−4

+b) 8−s

-c) 4

-d) s−8

-e) 4−s

5) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 2

-b) 3

-c) 2/3

-d) 1/2

+e) 3/2

6) What is the magnitude of the electric field at the origin if a 1.8 nC charge is placed at x = 5.2 m, and a 3.1 nC charge is placed at y = 7.6 m?

+a) 7.69 x 10^-1N/C

-b) 8.88 x 10^-1N/C

-c) 1.03 x 10⁰N/C

-d) 1.18 x 10⁰N/C

-e) 1.37 x 10⁰N/C

7) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 2² + (7-s)²

+b) 2² + (9-s)²

-c) 7² + (2-s)²

-d) 9² + (2-s)²

-e) 9² + (7-s)²

8)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=5e$?

-a) 5.569E+01 degrees

-b) 6.125E+01 degrees

+c) 6.738E+01 degrees

-d) 7.412E+01 degrees

-e) 8.153E+01 degrees

9) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 8

-b) s−7

-c) 3−s

-d) s−3

+e) 7−s

10)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.35 m (on axis) away from the loop's center?

-a) 4.142E+09 N/C²

-b) 4.556E+09 N/C²

+c) 5.012E+09 N/C²

-d) 5.513E+09 N/C²

-e) 6.064E+09 N/C²

Key: U2

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=5e$?

-a) 8.259E-15 N

-b) 9.085E-15 N

-c) 9.993E-15 N

-d) 1.099E-14 N

+e) 1.209E-14 N

2) What is the magnitude of the electric field at the origin if a 1.7 nC charge is placed at x = 6.4 m, and a 3 nC charge is placed at y = 8 m?

-a) 4.22 x 10^-1N/C

-b) 4.87 x 10^-1N/C

+c) 5.63 x 10^-1N/C

-d) 6.5 x 10^-1N/C

-e) 7.51 x 10^-1N/C

3)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.99 m (on axis) away from the loop's center?

-a) 2.429E+09 N/C²

+b) 2.672E+09 N/C²

-c) 2.939E+09 N/C²

-d) 3.233E+09 N/C²

-e) 3.556E+09 N/C²

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 1.61 x 10^-1 unit

-b) 1.95 x 10^-1 unit

-c) 2.36 x 10^-1 unit

-d) 2.86 x 10^-1 unit

+e) 3.47 x 10^-1 unit

5) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 9² + (2-s)²

-b) 9² + (7-s)²

-c) 7² + (2-s)²

+d) 2² + (9-s)²

-e) 2² + (7-s)²

6) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−4

-b) 4−s

-c) s−8

+d) 8−s

-e) 4

7) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 3

-b) 2/3

-c) 2

-d) 1/2

+e) 3/2

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

+a) 4

-b) 8

-c) 1/2

-d) 2

9) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 7−s

-b) 3−s

-c) s−3

-d) 8

-e) s−7

10)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=6e$?

+a) 6.343E+01 degrees

-b) 6.978E+01 degrees

-c) 7.676E+01 degrees

-d) 8.443E+01 degrees

-e) 9.288E+01 degrees

Key: V0

1)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.99 m (on axis) away from the loop's center?

-a) 2.429E+09 N/C²

+b) 2.672E+09 N/C²

-c) 2.939E+09 N/C²

-d) 3.233E+09 N/C²

-e) 3.556E+09 N/C²

2) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 2.652E+01 N/C

-b) 2.917E+01 N/C

-c) 3.209E+01 N/C

+d) 3.529E+01 N/C

-e) 3.882E+01 N/C

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=1e$, $q_{2}=-7e$, and $q_{3}=4e$?

-a) 4.091E+01 degrees

+b) 4.500E+01 degrees

-c) 4.950E+01 degrees

-d) 5.445E+01 degrees

-e) 5.990E+01 degrees

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

-a) 1.09 x 10^-3 unit

-b) 1.33 x 10^-3 unit

+c) 1.61 x 10^-3 unit

-d) 1.95 x 10^-3 unit

-e) 2.36 x 10^-3 unit

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 1.95 x 10^-1 unit

-b) 2.36 x 10^-1 unit

-c) 2.86 x 10^-1 unit

+d) 3.47 x 10^-1 unit

-e) 4.2 x 10^-1 unit

6) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 2² + (7-s)²

+b) 2² + (9-s)²

-c) 7² + (2-s)²

-d) 9² + (7-s)²

-e) 9² + (2-s)²

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

-a) 1/2

-b) 2

-c) 3

+d) 3/2

8) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

+a) 2

-b) −3

-c) 3

-d) −7

-e) −3

9) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

-a) 3−s

+b) 7−s

-c) 3

-d) s−7

-e) s−3

10) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

+a) 3/2

-b) 2

-c) 1/2

-d) 2/3

-e) 3

Key: V1

1) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

-a) 1.33 x 10^-3 unit

+b) 1.61 x 10^-3 unit

-c) 1.95 x 10^-3 unit

-d) 2.36 x 10^-3 unit

-e) 2.86 x 10^-3 unit

2) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) −3

-b) −3

-c) −7

-d) 3

+e) 2

3) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 1/2

+b) 3/2

-c) 3

-d) 2

-e) 2/3

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-7e$, and $q_{3}=5e$?

-a) 4.357E+01 degrees

-b) 4.793E+01 degrees

-c) 5.272E+01 degrees

+d) 5.799E+01 degrees

-e) 6.379E+01 degrees

5)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 3.159E+09 N/C²

-b) 3.475E+09 N/C²

-c) 3.823E+09 N/C²

-d) 4.205E+09 N/C²

-e) 4.626E+09 N/C²

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

-a) 3

-b) 1/2

-c) 2

+d) 3/2

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

-a) s−7

-b) 3−s

+c) 7−s

-d) 3

-e) s−3

8) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 6.534E+01 N/C

-b) 7.187E+01 N/C

+c) 7.906E+01 N/C

-d) 8.696E+01 N/C

-e) 9.566E+01 N/C

9) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 9² + (2-s)²

-b) 7² + (2-s)²

+c) 2² + (9-s)²

-d) 2² + (7-s)²

-e) 9² + (7-s)²

10) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 1.95 x 10^-1 unit

-b) 2.36 x 10^-1 unit

-c) 2.86 x 10^-1 unit

+d) 3.47 x 10^-1 unit

-e) 4.2 x 10^-1 unit

Key: V2

1) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 1.95 x 10^-1 unit

-b) 2.36 x 10^-1 unit

-c) 2.86 x 10^-1 unit

+d) 3.47 x 10^-1 unit

-e) 4.2 x 10^-1 unit

2)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.99 m (on axis) away from the loop's center?

-a) 2.429E+09 N/C²

+b) 2.672E+09 N/C²

-c) 2.939E+09 N/C²

-d) 3.233E+09 N/C²

-e) 3.556E+09 N/C²

3) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 2.357E+01 N/C

-b) 2.593E+01 N/C

-c) 2.852E+01 N/C

+d) 3.137E+01 N/C

-e) 3.451E+01 N/C

4) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

+a) 2² + (9-s)²

-b) 7² + (2-s)²

-c) 9² + (2-s)²

-d) 2² + (7-s)²

-e) 9² + (7-s)²

5) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

-a) s−7

-b) s−3

+c) 7−s

-d) 3−s

-e) 3

6) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

+a) 1.61 x 10^-3 unit

-b) 1.95 x 10^-3 unit

-c) 2.36 x 10^-3 unit

-d) 2.86 x 10^-3 unit

-e) 3.46 x 10^-3 unit

7) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 3

-b) 2/3

+c) 3/2

-d) 2

-e) 1/2

8)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-9e$, and $q_{3}=5e$?

-a) 5.272E+01 degrees

+b) 5.799E+01 degrees

-c) 6.379E+01 degrees

-d) 7.017E+01 degrees

-e) 7.719E+01 degrees

9) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

+a) 3/2

-b) 2

-c) 3

-d) 1/2

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) −7

+b) 2

-c) −3

-d) 3

-e) −3

Key: W0

1)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 8.336E+09 N/C²

-b) 9.170E+09 N/C²

-c) 1.009E+10 N/C²

-d) 1.110E+10 N/C²

-e) 1.220E+10 N/C²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-9e$, and $q_{3}=4e$?

-a) 5.243E+01 degrees

-b) 5.767E+01 degrees

+c) 6.343E+01 degrees

-d) 6.978E+01 degrees

-e) 7.676E+01 degrees

3) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 3.500E+01 N/C

-b) 3.850E+01 N/C

+c) 4.235E+01 N/C

-d) 4.659E+01 N/C

-e) 5.125E+01 N/C

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

-a) 1.09 x 10^-3 unit

-b) 1.33 x 10^-3 unit

+c) 1.61 x 10^-3 unit

-d) 1.95 x 10^-3 unit

-e) 2.36 x 10^-3 unit

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

+a) 3.47 x 10^-1 unit

-b) 4.2 x 10^-1 unit

-c) 5.09 x 10^-1 unit

-d) 6.17 x 10^-1 unit

-e) 7.47 x 10^-1 unit

6) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 4−s

-b) s−4

+c) 4

-d) s−8

-e) 8−s

7) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 3

-b) 2/3

+c) 3/2

-d) 2

-e) 1/2

8) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−3

-b) 3−s

-c) 8

-d) s−7

+e) 7−s

9) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 4−s

-b) s−4

-c) 4

-d) s−8

+e) 8−s

10) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 9² + (7-s)²

+b) 2² + (9-s)²

-c) 2² + (7-s)²

-d) 9² + (2-s)²

-e) 7² + (2-s)²

Key: W1

1) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 8−s

-b) s−8

-c) 4−s

-d) s−4

-e) 4

2) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 7² + (2-s)²

-b) 9² + (2-s)²

+c) 2² + (9-s)²

-d) 9² + (7-s)²

-e) 2² + (7-s)²

3) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−8

-b) s−4

-c) 4−s

+d) 4

-e) 8−s

4) A large thin isolated square plate has an area of 3 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

+a) 9.412E+01 N/C

-b) 1.035E+02 N/C

-c) 1.139E+02 N/C

-d) 1.253E+02 N/C

-e) 1.378E+02 N/C

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

-a) 1.33 x 10^-3 unit

+b) 1.61 x 10^-3 unit

-c) 1.95 x 10^-3 unit

-d) 2.36 x 10^-3 unit

-e) 2.86 x 10^-3 unit

6) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 1.95 x 10^-1 unit

-b) 2.36 x 10^-1 unit

-c) 2.86 x 10^-1 unit

+d) 3.47 x 10^-1 unit

-e) 4.2 x 10^-1 unit

7) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 8

-b) s−7

-c) s−3

+d) 7−s

-e) 3−s

8)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

-a) 5.581E+09 N/C²

-b) 6.139E+09 N/C²

+c) 6.753E+09 N/C²

-d) 7.428E+09 N/C²

-e) 8.171E+09 N/C²

9)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-9e$, and $q_{3}=6e$?

-a) 5.767E+01 degrees

+b) 6.343E+01 degrees

-c) 6.978E+01 degrees

-d) 7.676E+01 degrees

-e) 8.443E+01 degrees

10) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 3

-b) 1/2

-c) 2

+d) 3/2

-e) 2/3

Key: W2

1) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 1.61 x 10^-1 unit

-b) 1.95 x 10^-1 unit

-c) 2.36 x 10^-1 unit

-d) 2.86 x 10^-1 unit

+e) 3.47 x 10^-1 unit

2) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

+a) 2² + (9-s)²

-b) 9² + (2-s)²

-c) 2² + (7-s)²

-d) 9² + (7-s)²

-e) 7² + (2-s)²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-8e$, and $q_{3}=6e$?

-a) 5.243E+01 degrees

-b) 5.767E+01 degrees

+c) 6.343E+01 degrees

-d) 6.978E+01 degrees

-e) 7.676E+01 degrees

4) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 4.821E+01 N/C

-b) 5.303E+01 N/C

-c) 5.834E+01 N/C

-d) 6.417E+01 N/C

+e) 7.059E+01 N/C

5) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 2

-b) 3

-c) 2/3

-d) 1/2

+e) 3/2

6) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 3a) is βkQ/a², where β equals

-a) 3.38 x 10^-3 unit

-b) 4.1 x 10^-3 unit

-c) 4.96 x 10^-3 unit

-d) 6.01 x 10^-3 unit

+e) 7.28 x 10^-3 unit

7)

A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.4 m (on axis) away from the loop's center?

-a) 7.119E+09 N/C²

-b) 7.831E+09 N/C²

+c) 8.614E+09 N/C²

-d) 9.476E+09 N/C²

-e) 1.042E+10 N/C²

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 4

+b) 8−s

-c) s−4

-d) 4−s

-e) s−8

9) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−4

-b) 4−s

-c) 8−s

-d) s−8

+e) 4

10) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 3−s

-b) s−3

-c) s−7

+d) 7−s

-e) 8

Key: X0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-9e$, and $q_{3}=5e$?

-a) 5.272E+01 degrees

+b) 5.799E+01 degrees

-c) 6.379E+01 degrees

-d) 7.017E+01 degrees

-e) 7.719E+01 degrees

2)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.0{\text{ m}}$ and the surface charge density is $\sigma =8{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=2.0{\text{ m}}$.

-a) 9.459E+00 V/m²

+b) 1.040E+01 V/m²

-c) 1.145E+01 V/m²

-d) 1.259E+01 V/m²

-e) 1.385E+01 V/m²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=6e$?

-a) 1.028E-14 N

-b) 1.130E-14 N

-c) 1.244E-14 N

-d) 1.368E-14 N

+e) 1.505E-14 N

4) What is the magnitude of the electric field at the origin if a 1.9 nC charge is placed at x = 9.7 m, and a 3.1 nC charge is placed at y = 5.5 m?

-a) 5.28 x 10^-1N/C

-b) 6.1 x 10^-1N/C

-c) 7.04 x 10^-1N/C

-d) 8.13 x 10^-1N/C

+e) 9.39 x 10^-1N/C

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 2.36 x 10^-1 unit

-b) 2.86 x 10^-1 unit

+c) 3.47 x 10^-1 unit

-d) 4.2 x 10^-1 unit

-e) 5.09 x 10^-1 unit

6) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−4

-b) 5−s

+c) 5

-d) s−1

-e) 1−s

7) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

-a) 1/2

-b) 8

+c) 4

-d) 2

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−8

-b) 8−s

+c) 4

-d) s−4

-e) 4−s

9) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s − 2

-b) 2

-c) s − 9

+d) 9 − s

-e) 2 − s

10) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

+a) 7−s

-b) 3−s

-c) s−7

-d) s−3

-e) 3

Key: X1

1) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

-a) 1/2

-b) 8

-c) 2

+d) 4

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=6e$?

-a) 2.544E-14 N

-b) 2.798E-14 N

-c) 3.078E-14 N

+d) 3.385E-14 N

-e) 3.724E-14 N

3) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

+a) 7−s

-b) 3−s

-c) s−7

-d) s−3

-e) 3

4) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 9 − s

-b) 2 − s

-c) s − 2

-d) 2

-e) s − 9

5)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.8{\text{ m}}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=1.1{\text{ m}}$.

-a) 7.517E+00 V/m²

-b) 8.269E+00 V/m²

-c) 9.096E+00 V/m²

-d) 1.001E+01 V/m²

+e) 1.101E+01 V/m²

6) What is the magnitude of the electric field at the origin if a 1.8 nC charge is placed at x = 5.2 m, and a 3.1 nC charge is placed at y = 7.6 m?

+a) 7.69 x 10^-1N/C

-b) 8.88 x 10^-1N/C

-c) 1.03 x 10⁰N/C

-d) 1.18 x 10⁰N/C

-e) 1.37 x 10⁰N/C

7)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=4e$?

-a) 5.377E+01 degrees

-b) 5.914E+01 degrees

-c) 6.506E+01 degrees

+d) 7.157E+01 degrees

-e) 7.872E+01 degrees

8) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−1

+b) 5

-c) 5−s

-d) 1−s

-e) s−4

9) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 4−s

+b) 4

-c) s−4

-d) 8−s

-e) s−8

10) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 1.95 x 10^-1 unit

-b) 2.36 x 10^-1 unit

-c) 2.86 x 10^-1 unit

+d) 3.47 x 10^-1 unit

-e) 4.2 x 10^-1 unit

Key: X2

1) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 1.61 x 10^-1 unit

-b) 1.95 x 10^-1 unit

-c) 2.36 x 10^-1 unit

-d) 2.86 x 10^-1 unit

+e) 3.47 x 10^-1 unit

2) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

+a) 7−s

-b) s−3

-c) 3−s

-d) 3

-e) s−7

3) What is the magnitude of the electric field at the origin if a 1.8 nC charge is placed at x = 9.6 m, and a 2 nC charge is placed at y = 8.7 m?

+a) 2.95 x 10^-1N/C

-b) 3.41 x 10^-1N/C

-c) 3.94 x 10^-1N/C

-d) 4.55 x 10^-1N/C

-e) 5.25 x 10^-1N/C

4) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 4

-b) s−8

-c) 4−s

-d) s−4

-e) 8−s

5)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.9{\text{ m}}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=4.3{\text{ m}}$.

-a) 8.924E-01 V/m²

-b) 9.816E-01 V/m²

+c) 1.080E+00 V/m²

-d) 1.188E+00 V/m²

-e) 1.307E+00 V/m²

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=1e$, $q_{2}=-7e$, and $q_{3}=4e$?

-a) 4.091E+01 degrees

+b) 4.500E+01 degrees

-c) 4.950E+01 degrees

-d) 5.445E+01 degrees

-e) 5.990E+01 degrees

7) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 2 − s

-b) 2

-c) s − 9

-d) s − 2

+e) 9 − s

8) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 1−s

-b) s−1

-c) 5−s

+d) 5

-e) s−4

9)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-7e$, and $q_{3}=6e$?

-a) 1.028E-14 N

-b) 1.130E-14 N

-c) 1.244E-14 N

-d) 1.368E-14 N

+e) 1.505E-14 N

10) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

-a) 2

-b) 8

+c) 4

-d) 1/2

Key: Y0

1)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.2{\text{ m}}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=3.6{\text{ m}}$.

+a) 1.606E+00 V/m²

-b) 1.767E+00 V/m²

-c) 1.943E+00 V/m²

-d) 2.138E+00 V/m²

-e) 2.351E+00 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-9e$, and $q_{3}=4e$?

-a) 5.014E-14 N

-b) 5.515E-14 N

-c) 6.067E-14 N

-d) 6.674E-14 N

+e) 7.341E-14 N

3)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.4 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.69 m, b=2.2 m. The total charge on the rod is 6 nC.

-a) 3.161E+00 V/m²

-b) 3.477E+00 V/m²

-c) 3.825E+00 V/m²

-d) 4.208E+00 V/m²

+e) 4.628E+00 V/m²

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

-a) 1.09 x 10^-3 unit

-b) 1.33 x 10^-3 unit

+c) 1.61 x 10^-3 unit

-d) 1.95 x 10^-3 unit

-e) 2.36 x 10^-3 unit

5) What is the magnitude of the electric field at the origin if a 3 nC charge is placed at x = 5.1 m, and a 2 nC charge is placed at y = 8.6 m?

-a) 7.99 x 10^-1N/C

-b) 9.22 x 10^-1N/C

+c) 1.07 x 10⁰N/C

-d) 1.23 x 10⁰N/C

-e) 1.42 x 10⁰N/C

6) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 8−s

-b) s−4

-c) 4−s

+d) 4

-e) s−8

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) −3

-b) −3

-c) 3

+d) 2

-e) −7

8) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−3

-b) s−7

-c) 3−s

-d) 8

+e) 7−s

9) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 9 − s

-b) 2

-c) s − 9

-d) 2 − s

-e) s − 2

10) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 9² + (2-s)²

-b) 9² + (7-s)²

-c) 7² + (2-s)²

+d) 2² + (9-s)²

-e) 2² + (7-s)²

Key: Y1

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=3e$, $q_{2}=-9e$, and $q_{3}=6e$?

-a) 1.308E-13 N

-b) 1.439E-13 N

-c) 1.583E-13 N

+d) 1.741E-13 N

-e) 1.915E-13 N

2)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.2 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.52 m, b=1.6 m. The total charge on the rod is 7 nC.

-a) 9.655E+00 V/m²

-b) 1.062E+01 V/m²

-c) 1.168E+01 V/m²

+d) 1.285E+01 V/m²

-e) 1.414E+01 V/m²

3) What is the magnitude of the electric field at the origin if a 1.4 nC charge is placed at x = 8.2 m, and a 2.3 nC charge is placed at y = 5.9 m?

-a) 5.39 x 10^-1N/C

+b) 6.23 x 10^-1N/C

-c) 7.19 x 10^-1N/C

-d) 8.31 x 10^-1N/C

-e) 9.59 x 10^-1N/C

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 4a) is βkQ/a², where β equals

-a) 1.33 x 10^-3 unit

-b) 1.61 x 10^-3 unit

-c) 1.95 x 10^-3 unit

-d) 2.37 x 10^-3 unit

+e) 2.87 x 10^-3 unit

5)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.9{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=5.1{\text{ m}}$.

-a) 8.253E-01 V/m²

-b) 9.079E-01 V/m²

+c) 9.987E-01 V/m²

-d) 1.099E+00 V/m²

-e) 1.208E+00 V/m²

6) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s − 2

+b) 9 − s

-c) 2

-d) 2 − s

-e) s − 9

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

+a) 2

-b) −7

-c) 3

-d) −3

-e) −3

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 8−s

+b) 4

-c) 4−s

-d) s−4

-e) s−8

9) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

-a) 9² + (2-s)²

+b) 2² + (9-s)²

-c) 7² + (2-s)²

-d) 2² + (7-s)²

-e) 9² + (7-s)²

10) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−3

-b) s−7

-c) 8

+d) 7−s

-e) 3−s

Key: Y2

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=5e$?

-a) 2.248E-14 N

-b) 2.473E-14 N

+c) 2.721E-14 N

-d) 2.993E-14 N

-e) 3.292E-14 N

2) What is the magnitude of the electric field at the origin if a 2.7 nC charge is placed at x = 9.1 m, and a 2.5 nC charge is placed at y = 5.9 m?

-a) 3.99 x 10^-1N/C

-b) 4.6 x 10^-1N/C

-c) 5.32 x 10^-1N/C

-d) 6.14 x 10^-1N/C

+e) 7.09 x 10^-1N/C

3) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 3−s

+b) 7−s

-c) 8

-d) s−7

-e) s−3

4) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

+a) 2² + (9-s)²

-b) 9² + (2-s)²

-c) 7² + (2-s)²

-d) 9² + (7-s)²

-e) 2² + (7-s)²

5)

 $E_{z}(x=0,z)=\int _{-a}^{b}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m. Evaluate $f(x,y)$ at x=0.83 m if a=0.82 m, b=1.3 m. The total charge on the rod is 7 nC.

-a) 8.690E+00 V/m²

-b) 9.559E+00 V/m²

+c) 1.051E+01 V/m²

-d) 1.157E+01 V/m²

-e) 1.272E+01 V/m²

6) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

-a) 3

-b) −3

+c) 2

-d) −3

-e) −7

7) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−4

-b) 4−s

+c) 4

-d) 8−s

-e) s−8

8) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 2

-b) s − 9

-c) s − 2

+d) 9 − s

-e) 2 − s

9)  $E(z)=\int _{0}^{R}f(r',z)dr'$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.9{\text{ m}}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^{3}$. Evaluate $f(r',z)$ at $r'=5.1{\text{ m}}$.

-a) 8.253E-01 V/m²

-b) 9.079E-01 V/m²

+c) 9.987E-01 V/m²

-d) 1.099E+00 V/m²

-e) 1.208E+00 V/m²

10) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 6a, 5a) is βkQ/a², where β equals

+a) 1.61 x 10^-3 unit

-b) 1.95 x 10^-3 unit

-c) 2.36 x 10^-3 unit

-d) 2.86 x 10^-3 unit

-e) 3.46 x 10^-3 unit

Key: Z0

1)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

-a) 2.013E+09 N/C²

-b) 2.214E+09 N/C²

-c) 2.435E+09 N/C²

-d) 2.679E+09 N/C²

+e) 2.947E+09 N/C²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=1e$, $q_{2}=-9e$, and $q_{3}=4e$?

-a) 5.014E-14 N

-b) 5.515E-14 N

-c) 6.067E-14 N

-d) 6.674E-14 N

+e) 7.341E-14 N

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-9e$, and $q_{3}=4e$?

-a) 4.766E+01 degrees

-b) 5.243E+01 degrees

-c) 5.767E+01 degrees

+d) 6.343E+01 degrees

-e) 6.978E+01 degrees

4) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 2.36 x 10^-1 unit

-b) 2.86 x 10^-1 unit

+c) 3.47 x 10^-1 unit

-d) 4.2 x 10^-1 unit

-e) 5.09 x 10^-1 unit

5) What is the magnitude of the electric field at the origin if a 2.7 nC charge is placed at x = 9.1 m, and a 2.5 nC charge is placed at y = 5.9 m?

-a) 3.99 x 10^-1N/C

-b) 4.6 x 10^-1N/C

-c) 5.32 x 10^-1N/C

-d) 6.14 x 10^-1N/C

+e) 7.09 x 10^-1N/C

6) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−4

+b) 1−s

-c) s−1

-d) 5−s

-e) 5

7) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 4

+b) 8−s

-c) s−4

-d) 4−s

-e) s−8

8) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

+a) 3/2

-b) 2

-c) 1/2

-d) 2/3

-e) 3

9) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 4

-b) s−4

-c) 4−s

-d) s−8

-e) 8−s

10) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 3−s

+b) 7−s

-c) s−3

-d) 8

-e) s−7

Key: Z1

1) What is the magnitude of the electric field at the origin if a 3 nC charge is placed at x = 5.1 m, and a 2 nC charge is placed at y = 8.6 m?

-a) 7.99 x 10^-1N/C

-b) 9.22 x 10^-1N/C

+c) 1.07 x 10⁰N/C

-d) 1.23 x 10⁰N/C

-e) 1.42 x 10⁰N/C

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=4e$?

-a) 8.613E-15 N

-b) 9.474E-15 N

-c) 1.042E-14 N

+d) 1.146E-14 N

-e) 1.261E-14 N

3) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 2.36 x 10^-1 unit

-b) 2.86 x 10^-1 unit

+c) 3.47 x 10^-1 unit

-d) 4.2 x 10^-1 unit

-e) 5.09 x 10^-1 unit

4) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 5

-b) s−4

+c) 1−s

-d) 5−s

-e) s−1

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-7e$, and $q_{3}=3e$?

-a) 4.743E+01 degrees

-b) 5.217E+01 degrees

-c) 5.739E+01 degrees

-d) 6.313E+01 degrees

+e) 6.944E+01 degrees

6) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−8

-b) 4−s

-c) 4

+d) 8−s

-e) s−4

7)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

-a) 2.013E+09 N/C²

-b) 2.214E+09 N/C²

-c) 2.435E+09 N/C²

-d) 2.679E+09 N/C²

+e) 2.947E+09 N/C²

8) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 3−s

-b) s−3

-c) s−7

-d) 8

+e) 7−s

9) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) s−4

-b) 8−s

+c) 4

-d) s−8

-e) 4−s

10) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 1/2

-b) 3

+c) 3/2

-d) 2

-e) 2/3

Key: Z2

1) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

-a) 2.86 x 10^-1 unit

+b) 3.47 x 10^-1 unit

-c) 4.2 x 10^-1 unit

-d) 5.09 x 10^-1 unit

-e) 6.17 x 10^-1 unit

2) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

-a) 1/2

-b) 2/3

-c) 2

+d) 3/2

-e) 3

3) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 4−s

+b) 8−s

-c) s−4

-d) 4

-e) s−8

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}{\text{m}}$.what angle does the force on $q_{2}$ make above the $-x$ axis if $q_{1}=2e$, $q_{2}=-9e$, and $q_{3}=4e$?

-a) 5.243E+01 degrees

-b) 5.767E+01 degrees

+c) 6.343E+01 degrees

-d) 6.978E+01 degrees

-e) 7.676E+01 degrees

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}{\text{m}}$. What is the magnitude of the net force on $q_{2}$ if $q_{1}=2e$, $q_{2}=-8e$, and $q_{3}=3e$?

-a) 2.036E-14 N

-b) 2.240E-14 N

+c) 2.464E-14 N

-d) 2.710E-14 N

-e) 2.981E-14 N

6) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 5

-b) s−1

-c) s−4

+d) 1−s

-e) 5−s

7)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.5 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.33 m (on axis) away from the loop's center?

-a) 1.353E+09 N/C²

-b) 1.488E+09 N/C²

+c) 1.637E+09 N/C²

-d) 1.801E+09 N/C²

-e) 1.981E+09 N/C²

8) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

+a) 4

-b) 8−s

-c) s−4

-d) s−8

-e) 4−s

9) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

-a) 3−s

+b) 7−s

-c) s−3

-d) s−7

-e) 8

10) What is the magnitude of the electric field at the origin if a 2.1 nC charge is placed at x = 7 m, and a 2.1 nC charge is placed at y = 8.6 m?

-a) 3 x 10^-1N/C

-b) 3.47 x 10^-1N/C

-c) 4 x 10^-1N/C

+d) 4.62 x 10^-1N/C

-e) 5.34 x 10^-1N/C