# Quizbank/Sample PhysicsCalc2 exams

PhysicsCalc2152573593386

### PhysicsCalc2:T1:V0

PhysicsCalc2152573593386

1) Integrate the function, ${\displaystyle {\vec {F}}=r^{5}\theta ^{7}{\hat {r}}+r^{4}\theta ^{4}{\hat {\theta }}}$ , along the first quadrant of a circle of radius 9

a) 1.06E+05
b) 1.13E+05
c) 1.21E+05
d) 1.29E+05
e) 1.38E+05

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, 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

3) 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

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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {C}}=}$:

a) s−4
b) s−8
c) 4−s
d) 8−s
e) 4

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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {F}}=}$:

a) 3/2
b) 1/2
c) 2
d) 3
e) 2/3

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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {C}}=}$:

a) s − 9
b) 2 − s
c) s − 2
d) 9 − s
e) 2

7) The same parallel plate capacitor, with area 1.45 m2, plate separation 1.53mm, and an applied voltage of 2.55 kV. How much charge is stored?

a) 12.23 μC.
b) 14.07 μC.
c) 16.18 μC.
d) 18.61 μC.
e) 21.4 μC.

8) A parallel plate capacitor has both plates with an area of 1.15 m2. The separation between the plates is 0.63mm. Applied to the plates is a potential difference of 2.25 kV. What is the capacitance?

a) 16.16 nF.
b) 18.59 nF.
c) 21.37 nF.
d) 24.58 nF.
e) 28.27 nF.

9) How fast is a 2493 eV electron moving?

a) 1.3 x 107 m/s.
b) 2 x 107 m/s.
c) 3 x 107 m/s.
d) 4.4 x 107 m/s.
e) 6.7 x 107 m/s.

10) What voltage is required accelerate an electron at rest to a speed of 3 x 105 m/s?

a) 1.7 x 10-1 volts
b) 2.6 x 10-1 volts
c) 3.8 x 10-1 volts
d) 5.8 x 10-1 volts
e) 8.6 x 10-1 volts

11) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.17+1.5z)\rho ^{2}{\hat {\rho }}+8.75z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the entire surface of the cylinder.

a) 3.60E+02
b) 4.36E+02
c) 5.29E+02
d) 6.40E+02
e) 7.76E+02

12) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(1.93+2.31z)\rho ^{3}{\hat {\rho }}+7.21z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

a) 6.731E+02
b) 8.154E+02
c) 9.879E+02
d) 1.197E+03
e) 1.450E+03

### KEY:PhysicsCalc2:T1:V0

PhysicsCalc2152573593386

1) Integrate the function, ${\displaystyle {\vec {F}}=r^{5}\theta ^{7}{\hat {r}}+r^{4}\theta ^{4}{\hat {\theta }}}$ , along the first quadrant of a circle of radius 9

-a) 1.06E+05
+b) 1.13E+05
-c) 1.21E+05
-d) 1.29E+05
-e) 1.38E+05

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, 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

3) 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

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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {C}}=}$:

-a) s−4
-b) s−8
-c) 4−s
-d) 8−s
+e) 4

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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {F}}=}$:

+a) 3/2
-b) 1/2
-c) 2
-d) 3
-e) 2/3

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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {C}}=}$:

-a) s − 9
-b) 2 − s
-c) s − 2
+d) 9 − s
-e) 2

7) The same parallel plate capacitor, with area 1.45 m2, plate separation 1.53mm, and an applied voltage of 2.55 kV. How much charge is stored?

-a) 12.23 μC.
-b) 14.07 μC.
-c) 16.18 μC.
-d) 18.61 μC.
+e) 21.4 μC.

8) A parallel plate capacitor has both plates with an area of 1.15 m2. The separation between the plates is 0.63mm. Applied to the plates is a potential difference of 2.25 kV. What is the capacitance?

+a) 16.16 nF.
-b) 18.59 nF.
-c) 21.37 nF.
-d) 24.58 nF.
-e) 28.27 nF.

9) How fast is a 2493 eV electron moving?

-a) 1.3 x 107 m/s.
-b) 2 x 107 m/s.
+c) 3 x 107 m/s.
-d) 4.4 x 107 m/s.
-e) 6.7 x 107 m/s.

10) What voltage is required accelerate an electron at rest to a speed of 3 x 105 m/s?

-a) 1.7 x 10-1 volts
+b) 2.6 x 10-1 volts
-c) 3.8 x 10-1 volts
-d) 5.8 x 10-1 volts
-e) 8.6 x 10-1 volts

11) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.17+1.5z)\rho ^{2}{\hat {\rho }}+8.75z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the entire surface of the cylinder.

-a) 3.60E+02
+b) 4.36E+02
-c) 5.29E+02
-d) 6.40E+02
-e) 7.76E+02

12) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(1.93+2.31z)\rho ^{3}{\hat {\rho }}+7.21z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

-a) 6.731E+02
+b) 8.154E+02
-c) 9.879E+02
-d) 1.197E+03
-e) 1.450E+03

### PhysicsCalc2:T1:V1

PhysicsCalc2152573593386

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) =( 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

2) What voltage is required accelerate an electron at rest to a speed of 9.5 x 106 m/s?

a) 1.1 x 102 volts
b) 1.7 x 102 volts
c) 2.6 x 102 volts
d) 3.8 x 102 volts
e) 5.8 x 102 volts

3) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.12+1.85z)\rho ^{3}{\hat {\rho }}+8.88z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the entire surface of the cylinder.

a) 3.96E+02
b) 4.79E+02
c) 5.81E+02
d) 7.04E+02
e) 8.53E+02

4) The same parallel plate capacitor, with area 0.75 m2, plate separation 0.53mm, and an applied voltage of 3.55 kV. How much charge is stored?

a) 29.25 μC.
b) 33.63 μC.
c) 38.68 μC.
d) 44.48 μC.
e) 51.15 μC.

5) Integrate the function, ${\displaystyle {\vec {F}}=r^{6}\theta ^{5}{\hat {r}}+r^{9}\theta ^{7}{\hat {\theta }}}$ , along the first quadrant of a circle of radius 3

a) 2.09E+05
b) 2.23E+05
c) 2.39E+05
d) 2.56E+05
e) 2.74E+05

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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {C}}=}$:

a) s − 9
b) s − 2
c) 9 − s
d) 2
e) 2 − 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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {C}}=}$:

a) s−4
b) 4
c) 8−s
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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {F}}=}$:

a) 2/3
b) 2
c) 3
d) 3/2
e) 1/2

9) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.05+2.05z)\rho ^{2}{\hat {\rho }}+9.62z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

a) 4.489E+02
b) 5.438E+02
c) 6.589E+02
d) 7.983E+02
e) 9.671E+02

10) A parallel plate capacitor has both plates with an area of 1.15 m2. The separation between the plates is 0.63mm. Applied to the plates is a potential difference of 2.25 kV. What is the capacitance?

a) 16.16 nF.
b) 18.59 nF.
c) 21.37 nF.
d) 24.58 nF.
e) 28.27 nF.

11) How fast is a 2928 eV electron moving?

a) 6.3 x 106 m/s.
b) 9.5 x 106 m/s.
c) 1.4 x 107 m/s.
d) 2.1 x 107 m/s.
e) 3.2 x 107 m/s.

12) 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

### KEY:PhysicsCalc2:T1:V1

PhysicsCalc2152573593386

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) =( 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

2) What voltage is required accelerate an electron at rest to a speed of 9.5 x 106 m/s?

-a) 1.1 x 102 volts
-b) 1.7 x 102 volts
+c) 2.6 x 102 volts
-d) 3.8 x 102 volts
-e) 5.8 x 102 volts

3) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.12+1.85z)\rho ^{3}{\hat {\rho }}+8.88z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the entire surface of the cylinder.

-a) 3.96E+02
-b) 4.79E+02
-c) 5.81E+02
-d) 7.04E+02
+e) 8.53E+02

4) The same parallel plate capacitor, with area 0.75 m2, plate separation 0.53mm, and an applied voltage of 3.55 kV. How much charge is stored?

-a) 29.25 μC.
-b) 33.63 μC.
-c) 38.68 μC.
+d) 44.48 μC.
-e) 51.15 μC.

5) Integrate the function, ${\displaystyle {\vec {F}}=r^{6}\theta ^{5}{\hat {r}}+r^{9}\theta ^{7}{\hat {\theta }}}$ , along the first quadrant of a circle of radius 3

-a) 2.09E+05
-b) 2.23E+05
-c) 2.39E+05
-d) 2.56E+05
+e) 2.74E+05

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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {C}}=}$:

-a) s − 9
-b) s − 2
+c) 9 − s
-d) 2
-e) 2 − 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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {C}}=}$:

-a) s−4
+b) 4
-c) 8−s
-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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {F}}=}$:

-a) 2/3
-b) 2
-c) 3
+d) 3/2
-e) 1/2

9) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.05+2.05z)\rho ^{2}{\hat {\rho }}+9.62z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

-a) 4.489E+02
-b) 5.438E+02
-c) 6.589E+02
-d) 7.983E+02
+e) 9.671E+02

10) A parallel plate capacitor has both plates with an area of 1.15 m2. The separation between the plates is 0.63mm. Applied to the plates is a potential difference of 2.25 kV. What is the capacitance?

+a) 16.16 nF.
-b) 18.59 nF.
-c) 21.37 nF.
-d) 24.58 nF.
-e) 28.27 nF.

11) How fast is a 2928 eV electron moving?

-a) 6.3 x 106 m/s.
-b) 9.5 x 106 m/s.
-c) 1.4 x 107 m/s.
-d) 2.1 x 107 m/s.
+e) 3.2 x 107 m/s.

12) 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

### PhysicsCalc2:T1:V2

PhysicsCalc2152573593386

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) Integrate the function, ${\displaystyle {\vec {F}}=r^{8}\theta ^{5}{\hat {r}}+r^{4}\theta ^{6}{\hat {\theta }}}$ , along the first quadrant of a circle of radius 4

a) 2.63E+03
b) 2.82E+03
c) 3.01E+03
d) 3.23E+03
e) 3.45E+03

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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {C}}=}$:

a) 2 − s
b) s − 9
c) 2
d) s − 2
e) 9 − s

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, 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

5) What voltage is required accelerate an electron at rest to a speed of 1.7 x 105 m/s?

a) 1.6 x 10-2 volts
b) 2.4 x 10-2 volts
c) 3.7 x 10-2 volts
d) 5.5 x 10-2 volts
e) 8.2 x 10-2 volts

6) A parallel plate capacitor has both plates with an area of 1.35 m2. The separation between the plates is 1.23mm. Applied to the plates is a potential difference of 2.65 kV. What is the capacitance?

a) 7.35 nF.
b) 8.45 nF.
c) 9.72 nF.
d) 11.18 nF.
e) 12.85 nF.

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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {F}}=}$:

a) 2
b) 1/2
c) 2/3
d) 3
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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {C}}=}$:

a) s−4
b) 4−s
c) 8−s
d) 4
e) s−8

9) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(1.88+1.29z)\rho ^{2}{\hat {\rho }}+7.2z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

a) 1.248E+03
b) 1.512E+03
c) 1.832E+03
d) 2.220E+03
e) 2.689E+03

10) How fast is a 2648 eV electron moving?

a) 3.1 x 107 m/s.
b) 4.6 x 107 m/s.
c) 6.9 x 107 m/s.
d) 1 x 108 m/s.
e) 1.5 x 108 m/s.

11) The same parallel plate capacitor, with area 0.75 m2, plate separation 1.53mm, and an applied voltage of 5.05 kV. How much charge is stored?

a) 16.57 μC.
b) 19.06 μC.
c) 21.92 μC.
d) 25.21 μC.
e) 28.99 μC.

12) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.21+1.16z)\rho ^{2}{\hat {\rho }}+7.96z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the entire surface of the cylinder.

a) 6.69E+03
b) 8.10E+03
c) 9.81E+03
d) 1.19E+04
e) 1.44E+04

### KEY:PhysicsCalc2:T1:V2

PhysicsCalc2152573593386

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) Integrate the function, ${\displaystyle {\vec {F}}=r^{8}\theta ^{5}{\hat {r}}+r^{4}\theta ^{6}{\hat {\theta }}}$ , along the first quadrant of a circle of radius 4

-a) 2.63E+03
-b) 2.82E+03
-c) 3.01E+03
-d) 3.23E+03
+e) 3.45E+03

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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {C}}=}$:

-a) 2 − s
-b) s − 9
-c) 2
-d) s − 2
+e) 9 − s

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, 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

5) What voltage is required accelerate an electron at rest to a speed of 1.7 x 105 m/s?

-a) 1.6 x 10-2 volts
-b) 2.4 x 10-2 volts
-c) 3.7 x 10-2 volts
-d) 5.5 x 10-2 volts
+e) 8.2 x 10-2 volts

6) A parallel plate capacitor has both plates with an area of 1.35 m2. The separation between the plates is 1.23mm. Applied to the plates is a potential difference of 2.65 kV. What is the capacitance?

-a) 7.35 nF.
-b) 8.45 nF.
+c) 9.72 nF.
-d) 11.18 nF.
-e) 12.85 nF.

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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {F}}=}$:

-a) 2
-b) 1/2
-c) 2/3
-d) 3
+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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {C}}=}$:

-a) s−4
-b) 4−s
-c) 8−s
+d) 4
-e) s−8

9) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(1.88+1.29z)\rho ^{2}{\hat {\rho }}+7.2z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

-a) 1.248E+03
-b) 1.512E+03
+c) 1.832E+03
-d) 2.220E+03
-e) 2.689E+03

10) How fast is a 2648 eV electron moving?

+a) 3.1 x 107 m/s.
-b) 4.6 x 107 m/s.
-c) 6.9 x 107 m/s.
-d) 1 x 108 m/s.
-e) 1.5 x 108 m/s.

11) The same parallel plate capacitor, with area 0.75 m2, plate separation 1.53mm, and an applied voltage of 5.05 kV. How much charge is stored?

-a) 16.57 μC.
-b) 19.06 μC.
+c) 21.92 μC.
-d) 25.21 μC.
-e) 28.99 μC.

12) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.21+1.16z)\rho ^{2}{\hat {\rho }}+7.96z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the entire surface of the cylinder.

-a) 6.69E+03
-b) 8.10E+03
-c) 9.81E+03
-d) 1.19E+04
+e) 1.44E+04

### PhysicsCalc2:T2:V0

PhysicsCalc2152573593386

1) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
b) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
c) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
d) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
e) none of these are correct

2) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) none of these are correct
b) ${\displaystyle \varepsilon _{0}E=H\rho }$
c) ${\displaystyle \varepsilon _{0}E=H\rho z}$
d) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
e) ${\displaystyle \varepsilon _{0}E=\rho z}$

3) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) none of these are correct
b) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
c) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
d) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
e) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

4) The diameter of a copper wire is 8.7 mm, and it carries a current of 22 amps. What is the drift velocity if copper has a density of 8.8E3 kg/m3 and an atomic mass of 63.54 g/mol? (1 mol = 6.02E23 atoms, and copper has one free electron per atom.)

a) 2.77 x 10-5m/s
b) 3.36 x 10-5m/s
c) 4.06 x 10-5m/s
d) 4.92 x 10-5m/s
e) 5.97 x 10-5m/s

5) A 5.8 volt battery moves 95 Coulombs of charge in 0.3 hours. What is the power?

a) 4.21 x 10-1 W
b) 5.1 x 10-1 W
c) 6.18 x 10-1 W
d) 7.49 x 10-1 W
e) 9.07 x 10-1 W
6) What is the current through R1, R2, R3, and R4 in the figure shown?
a) ${\displaystyle I_{1}=0.25A}$; ${\displaystyle I_{2}=0.33A}$; ${\displaystyle I_{3}=0.5A}$; ${\displaystyle I_{4}=0.1A}$.
b) ${\displaystyle I_{1}=10A}$; ${\displaystyle I_{2}=50A}$; ${\displaystyle I_{3}=33A}$; ${\displaystyle I_{4}=25A}$..
c) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=5A}$; ${\displaystyle I_{3}=3.3A}$; ${\displaystyle I_{4}=2.5A}$.
d) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=0.5A}$; ${\displaystyle I_{3}=0.33A}$; ${\displaystyle I_{4}=0.25A}$.

7) A 5 ohm and a 2 ohm resistor are connected in parallel. What is the total resistance?

a) ${\displaystyle {\frac {10}{6}}\Omega }$.
b) ${\displaystyle {\frac {7}{10}}\Omega }$.
c) ${\displaystyle {\frac {10}{7}}\Omega }$.
d) ${\displaystyle {\frac {6}{10}}\Omega }$.

8) A resistor has a voltage of 5 volts and a resistance of 15 ohms. What is the power consumed?

a) 11.67 Joules
b) 1.67 Watts
c) 2.5 Watts
d) None of these are ture.

9) If you plot voltage vs. current in a circuit, and you get a linear line, what is the significance of the slope?

a) Resistance.
b) Power.
c) None of these are true.
d) Discriminant.

10) A 1 ohm, 2 ohm, and 3 ohm resistor are connected in series. What is the total resistance?

a) ${\displaystyle R_{Total}=3\Omega }$.
b) None of these are true.
c) ${\displaystyle R_{Total}=0.5454\Omega }$.
d) ${\displaystyle R_{Total}=6\Omega }$.

11) Two 9.4 ohm resistors are connected in parallel. This combination is then connected in series to a 2.4 ohm resistor. What is the net resistance?

a) 5.4 ohms.
b) 6.2 ohms.
c) 7.1 ohms.
d) 8.2 ohms.
e) 9.4 ohms.

12) A 8.1 ohm resistor is connected in series to a pair of 5.2 ohm resistors that are in parallel. What is the net resistance?

a) 6.1 ohms.
b) 7 ohms.
c) 8.1 ohms.
d) 9.3 ohms.
e) 10.7 ohms.

### KEY:PhysicsCalc2:T2:V0

PhysicsCalc2152573593386

1) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius equal to R. What formula describes the electric field at a distance r < R?

+a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
-b) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
-c) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
-d) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
-e) none of these are correct

2) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) none of these are correct
-b) ${\displaystyle \varepsilon _{0}E=H\rho }$
-c) ${\displaystyle \varepsilon _{0}E=H\rho z}$
+d) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
-e) ${\displaystyle \varepsilon _{0}E=\rho z}$

3) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) none of these are correct
+b) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
-c) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
-d) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
-e) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

4) The diameter of a copper wire is 8.7 mm, and it carries a current of 22 amps. What is the drift velocity if copper has a density of 8.8E3 kg/m3 and an atomic mass of 63.54 g/mol? (1 mol = 6.02E23 atoms, and copper has one free electron per atom.)

+a) 2.77 x 10-5m/s
-b) 3.36 x 10-5m/s
-c) 4.06 x 10-5m/s
-d) 4.92 x 10-5m/s
-e) 5.97 x 10-5m/s

5) A 5.8 volt battery moves 95 Coulombs of charge in 0.3 hours. What is the power?

-a) 4.21 x 10-1 W
+b) 5.1 x 10-1 W
-c) 6.18 x 10-1 W
-d) 7.49 x 10-1 W
-e) 9.07 x 10-1 W
6) What is the current through R1, R2, R3, and R4 in the figure shown?
-a) ${\displaystyle I_{1}=0.25A}$; ${\displaystyle I_{2}=0.33A}$; ${\displaystyle I_{3}=0.5A}$; ${\displaystyle I_{4}=0.1A}$.
-b) ${\displaystyle I_{1}=10A}$; ${\displaystyle I_{2}=50A}$; ${\displaystyle I_{3}=33A}$; ${\displaystyle I_{4}=25A}$..
-c) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=5A}$; ${\displaystyle I_{3}=3.3A}$; ${\displaystyle I_{4}=2.5A}$.
+d) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=0.5A}$; ${\displaystyle I_{3}=0.33A}$; ${\displaystyle I_{4}=0.25A}$.

7) A 5 ohm and a 2 ohm resistor are connected in parallel. What is the total resistance?

-a) ${\displaystyle {\frac {10}{6}}\Omega }$.
-b) ${\displaystyle {\frac {7}{10}}\Omega }$.
+c) ${\displaystyle {\frac {10}{7}}\Omega }$.
-d) ${\displaystyle {\frac {6}{10}}\Omega }$.

8) A resistor has a voltage of 5 volts and a resistance of 15 ohms. What is the power consumed?

-a) 11.67 Joules
+b) 1.67 Watts
-c) 2.5 Watts
-d) None of these are ture.

9) If you plot voltage vs. current in a circuit, and you get a linear line, what is the significance of the slope?

+a) Resistance.
-b) Power.
-c) None of these are true.
-d) Discriminant.

10) A 1 ohm, 2 ohm, and 3 ohm resistor are connected in series. What is the total resistance?

-a) ${\displaystyle R_{Total}=3\Omega }$.
-b) None of these are true.
-c) ${\displaystyle R_{Total}=0.5454\Omega }$.
+d) ${\displaystyle R_{Total}=6\Omega }$.

11) Two 9.4 ohm resistors are connected in parallel. This combination is then connected in series to a 2.4 ohm resistor. What is the net resistance?

-a) 5.4 ohms.
-b) 6.2 ohms.
+c) 7.1 ohms.
-d) 8.2 ohms.
-e) 9.4 ohms.

12) A 8.1 ohm resistor is connected in series to a pair of 5.2 ohm resistors that are in parallel. What is the net resistance?

-a) 6.1 ohms.
-b) 7 ohms.
-c) 8.1 ohms.
-d) 9.3 ohms.
+e) 10.7 ohms.

### PhysicsCalc2:T2:V1

PhysicsCalc2152573593386

1) A 5 ohm and a 2 ohm resistor are connected in parallel. What is the total resistance?

a) ${\displaystyle {\frac {10}{7}}\Omega }$.
b) ${\displaystyle {\frac {7}{10}}\Omega }$.
c) ${\displaystyle {\frac {6}{10}}\Omega }$.
d) ${\displaystyle {\frac {10}{6}}\Omega }$.

2) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) none of these are correct
b) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
c) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
d) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
e) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
3) What is the current through R1, R2, R3, and R4 in the figure shown?
a) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=0.5A}$; ${\displaystyle I_{3}=0.33A}$; ${\displaystyle I_{4}=0.25A}$.
b) ${\displaystyle I_{1}=0.25A}$; ${\displaystyle I_{2}=0.33A}$; ${\displaystyle I_{3}=0.5A}$; ${\displaystyle I_{4}=0.1A}$.
c) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=5A}$; ${\displaystyle I_{3}=3.3A}$; ${\displaystyle I_{4}=2.5A}$.
d) ${\displaystyle I_{1}=10A}$; ${\displaystyle I_{2}=50A}$; ${\displaystyle I_{3}=33A}$; ${\displaystyle I_{4}=25A}$..

4) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
d) none of these are correct
e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$

5) A 8.1 ohm resistor is connected in series to a pair of 5.2 ohm resistors that are in parallel. What is the net resistance?

a) 6.1 ohms.
b) 7 ohms.
c) 8.1 ohms.
d) 9.3 ohms.
e) 10.7 ohms.

6) The diameter of a copper wire is 8.3 mm, and it carries a current of 87 amps. What is the drift velocity if copper has a density of 8.8E3 kg/m3 and an atomic mass of 63.54 g/mol? (1 mol = 6.02E23 atoms, and copper has one free electron per atom.)

a) 6.77 x 10-5m/s
b) 8.2 x 10-5m/s
c) 9.93 x 10-5m/s
d) 1.2 x 10-4m/s
e) 1.46 x 10-4m/s

7) A 1 ohm, 2 ohm, and 3 ohm resistor are connected in series. What is the total resistance?

a) ${\displaystyle R_{Total}=0.5454\Omega }$.
b) None of these are true.
c) ${\displaystyle R_{Total}=3\Omega }$.
d) ${\displaystyle R_{Total}=6\Omega }$.

8) A resistor has a voltage of 5 volts and a resistance of 15 ohms. What is the power consumed?

a) None of these are ture.
b) 1.67 Watts
c) 2.5 Watts
d) 11.67 Joules

9) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) ${\displaystyle \varepsilon _{0}E=\rho z}$
b) ${\displaystyle \varepsilon _{0}E=H\rho }$
c) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
d) none of these are correct
e) ${\displaystyle \varepsilon _{0}E=H\rho z}$

10) If you plot voltage vs. current in a circuit, and you get a linear line, what is the significance of the slope?

a) None of these are true.
b) Power.
c) Discriminant.
d) Resistance.

11) A 5.1 volt battery moves 43 Coulombs of charge in 1.5 hours. What is the power?

a) 4.06 x 10-2 W
b) 4.92 x 10-2 W
c) 5.96 x 10-2 W
d) 7.22 x 10-2 W
e) 8.75 x 10-2 W

12) Two 6.2 ohm resistors are connected in parallel. This combination is then connected in series to a 3.4 ohm resistor. What is the net resistance?

a) 6.5 ohms.
b) 7.5 ohms.
c) 8.6 ohms.
d) 9.9 ohms.
e) 11.4 ohms.

### KEY:PhysicsCalc2:T2:V1

PhysicsCalc2152573593386

1) A 5 ohm and a 2 ohm resistor are connected in parallel. What is the total resistance?

+a) ${\displaystyle {\frac {10}{7}}\Omega }$.
-b) ${\displaystyle {\frac {7}{10}}\Omega }$.
-c) ${\displaystyle {\frac {6}{10}}\Omega }$.
-d) ${\displaystyle {\frac {10}{6}}\Omega }$.

2) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) none of these are correct
+b) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
-c) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
-d) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
-e) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
3) What is the current through R1, R2, R3, and R4 in the figure shown?
+a) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=0.5A}$; ${\displaystyle I_{3}=0.33A}$; ${\displaystyle I_{4}=0.25A}$.
-b) ${\displaystyle I_{1}=0.25A}$; ${\displaystyle I_{2}=0.33A}$; ${\displaystyle I_{3}=0.5A}$; ${\displaystyle I_{4}=0.1A}$.
-c) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=5A}$; ${\displaystyle I_{3}=3.3A}$; ${\displaystyle I_{4}=2.5A}$.
-d) ${\displaystyle I_{1}=10A}$; ${\displaystyle I_{2}=50A}$; ${\displaystyle I_{3}=33A}$; ${\displaystyle I_{4}=25A}$..

4) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
-b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
+c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
-d) none of these are correct
-e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$

5) A 8.1 ohm resistor is connected in series to a pair of 5.2 ohm resistors that are in parallel. What is the net resistance?

-a) 6.1 ohms.
-b) 7 ohms.
-c) 8.1 ohms.
-d) 9.3 ohms.
+e) 10.7 ohms.

6) The diameter of a copper wire is 8.3 mm, and it carries a current of 87 amps. What is the drift velocity if copper has a density of 8.8E3 kg/m3 and an atomic mass of 63.54 g/mol? (1 mol = 6.02E23 atoms, and copper has one free electron per atom.)

-a) 6.77 x 10-5m/s
-b) 8.2 x 10-5m/s
-c) 9.93 x 10-5m/s
+d) 1.2 x 10-4m/s
-e) 1.46 x 10-4m/s

7) A 1 ohm, 2 ohm, and 3 ohm resistor are connected in series. What is the total resistance?

-a) ${\displaystyle R_{Total}=0.5454\Omega }$.
-b) None of these are true.
-c) ${\displaystyle R_{Total}=3\Omega }$.
+d) ${\displaystyle R_{Total}=6\Omega }$.

8) A resistor has a voltage of 5 volts and a resistance of 15 ohms. What is the power consumed?

-a) None of these are ture.
+b) 1.67 Watts
-c) 2.5 Watts
-d) 11.67 Joules

9) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) ${\displaystyle \varepsilon _{0}E=\rho z}$
-b) ${\displaystyle \varepsilon _{0}E=H\rho }$
+c) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
-d) none of these are correct
-e) ${\displaystyle \varepsilon _{0}E=H\rho z}$

10) If you plot voltage vs. current in a circuit, and you get a linear line, what is the significance of the slope?

-a) None of these are true.
-b) Power.
-c) Discriminant.
+d) Resistance.

11) A 5.1 volt battery moves 43 Coulombs of charge in 1.5 hours. What is the power?

+a) 4.06 x 10-2 W
-b) 4.92 x 10-2 W
-c) 5.96 x 10-2 W
-d) 7.22 x 10-2 W
-e) 8.75 x 10-2 W

12) Two 6.2 ohm resistors are connected in parallel. This combination is then connected in series to a 3.4 ohm resistor. What is the net resistance?

+a) 6.5 ohms.
-b) 7.5 ohms.
-c) 8.6 ohms.
-d) 9.9 ohms.
-e) 11.4 ohms.

### PhysicsCalc2:T2:V2

PhysicsCalc2152573593386

1) Two 6.2 ohm resistors are connected in parallel. This combination is then connected in series to a 3.4 ohm resistor. What is the net resistance?

a) 6.5 ohms.
b) 7.5 ohms.
c) 8.6 ohms.
d) 9.9 ohms.
e) 11.4 ohms.
2) What is the current through R1, R2, R3, and R4 in the figure shown?
a) ${\displaystyle I_{1}=0.25A}$; ${\displaystyle I_{2}=0.33A}$; ${\displaystyle I_{3}=0.5A}$; ${\displaystyle I_{4}=0.1A}$.
b) ${\displaystyle I_{1}=10A}$; ${\displaystyle I_{2}=50A}$; ${\displaystyle I_{3}=33A}$; ${\displaystyle I_{4}=25A}$..
c) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=0.5A}$; ${\displaystyle I_{3}=0.33A}$; ${\displaystyle I_{4}=0.25A}$.
d) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=5A}$; ${\displaystyle I_{3}=3.3A}$; ${\displaystyle I_{4}=2.5A}$.

3) A 1 ohm, 2 ohm, and 3 ohm resistor are connected in series. What is the total resistance?

a) None of these are true.
b) ${\displaystyle R_{Total}=3\Omega }$.
c) ${\displaystyle R_{Total}=6\Omega }$.
d) ${\displaystyle R_{Total}=0.5454\Omega }$.

4) A 1.4 volt battery moves 87 Coulombs of charge in 2 hours. What is the power?

a) 7.85 x 10-3 W
b) 9.51 x 10-3 W
c) 1.15 x 10-2 W
d) 1.4 x 10-2 W
e) 1.69 x 10-2 W

5) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

a) none of these are correct
b) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
c) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
d) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
e) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$

6) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

a) ${\displaystyle \varepsilon _{0}E=\rho z}$
b) ${\displaystyle \varepsilon _{0}E=H\rho }$
c) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
d) ${\displaystyle \varepsilon _{0}E=H\rho z}$
e) none of these are correct

7) A 5 ohm and a 2 ohm resistor are connected in parallel. What is the total resistance?

a) ${\displaystyle {\frac {7}{10}}\Omega }$.
b) ${\displaystyle {\frac {10}{6}}\Omega }$.
c) ${\displaystyle {\frac {6}{10}}\Omega }$.
d) ${\displaystyle {\frac {10}{7}}\Omega }$.

8) The diameter of a copper wire is 8.3 mm, and it carries a current of 87 amps. What is the drift velocity if copper has a density of 8.8E3 kg/m3 and an atomic mass of 63.54 g/mol? (1 mol = 6.02E23 atoms, and copper has one free electron per atom.)

a) 6.77 x 10-5m/s
b) 8.2 x 10-5m/s
c) 9.93 x 10-5m/s
d) 1.2 x 10-4m/s
e) 1.46 x 10-4m/s

9) A 6.4 ohm resistor is connected in series to a pair of 7.4 ohm resistors that are in parallel. What is the net resistance?

a) 10.1 ohms.
b) 11.6 ohms.
c) 13.4 ohms.
d) 15.4 ohms.
e) 17.7 ohms.

10) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
c) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
e) none of these are correct

11) If you plot voltage vs. current in a circuit, and you get a linear line, what is the significance of the slope?

a) Discriminant.
b) Power.
c) Resistance.
d) None of these are true.

12) A resistor has a voltage of 5 volts and a resistance of 15 ohms. What is the power consumed?

a) 11.67 Joules
b) 1.67 Watts
c) None of these are ture.
d) 2.5 Watts

### KEY:PhysicsCalc2:T2:V2

PhysicsCalc2152573593386

1) Two 6.2 ohm resistors are connected in parallel. This combination is then connected in series to a 3.4 ohm resistor. What is the net resistance?

+a) 6.5 ohms.
-b) 7.5 ohms.
-c) 8.6 ohms.
-d) 9.9 ohms.
-e) 11.4 ohms.
2) What is the current through R1, R2, R3, and R4 in the figure shown?
-a) ${\displaystyle I_{1}=0.25A}$; ${\displaystyle I_{2}=0.33A}$; ${\displaystyle I_{3}=0.5A}$; ${\displaystyle I_{4}=0.1A}$.
-b) ${\displaystyle I_{1}=10A}$; ${\displaystyle I_{2}=50A}$; ${\displaystyle I_{3}=33A}$; ${\displaystyle I_{4}=25A}$..
+c) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=0.5A}$; ${\displaystyle I_{3}=0.33A}$; ${\displaystyle I_{4}=0.25A}$.
-d) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=5A}$; ${\displaystyle I_{3}=3.3A}$; ${\displaystyle I_{4}=2.5A}$.

3) A 1 ohm, 2 ohm, and 3 ohm resistor are connected in series. What is the total resistance?

-a) None of these are true.
-b) ${\displaystyle R_{Total}=3\Omega }$.
+c) ${\displaystyle R_{Total}=6\Omega }$.
-d) ${\displaystyle R_{Total}=0.5454\Omega }$.

4) A 1.4 volt battery moves 87 Coulombs of charge in 2 hours. What is the power?

-a) 7.85 x 10-3 W
-b) 9.51 x 10-3 W
-c) 1.15 x 10-2 W
-d) 1.4 x 10-2 W
+e) 1.69 x 10-2 W

5) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

-a) none of these are correct
+b) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
-c) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
-d) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
-e) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$

6) A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

-a) ${\displaystyle \varepsilon _{0}E=\rho z}$
-b) ${\displaystyle \varepsilon _{0}E=H\rho }$
+c) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
-d) ${\displaystyle \varepsilon _{0}E=H\rho z}$
-e) none of these are correct

7) A 5 ohm and a 2 ohm resistor are connected in parallel. What is the total resistance?

-a) ${\displaystyle {\frac {7}{10}}\Omega }$.
-b) ${\displaystyle {\frac {10}{6}}\Omega }$.
-c) ${\displaystyle {\frac {6}{10}}\Omega }$.
+d) ${\displaystyle {\frac {10}{7}}\Omega }$.

8) The diameter of a copper wire is 8.3 mm, and it carries a current of 87 amps. What is the drift velocity if copper has a density of 8.8E3 kg/m3 and an atomic mass of 63.54 g/mol? (1 mol = 6.02E23 atoms, and copper has one free electron per atom.)

-a) 6.77 x 10-5m/s
-b) 8.2 x 10-5m/s
-c) 9.93 x 10-5m/s
+d) 1.2 x 10-4m/s
-e) 1.46 x 10-4m/s

9) A 6.4 ohm resistor is connected in series to a pair of 7.4 ohm resistors that are in parallel. What is the net resistance?

+a) 10.1 ohms.
-b) 11.6 ohms.
-c) 13.4 ohms.
-d) 15.4 ohms.
-e) 17.7 ohms.

10) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius equal to R. What formula describes the electric field at a distance r < R?

+a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
-b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
-c) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
-d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
-e) none of these are correct

11) If you plot voltage vs. current in a circuit, and you get a linear line, what is the significance of the slope?

-a) Discriminant.
-b) Power.
+c) Resistance.
-d) None of these are true.

12) A resistor has a voltage of 5 volts and a resistance of 15 ohms. What is the power consumed?

-a) 11.67 Joules
+b) 1.67 Watts
-c) None of these are ture.
-d) 2.5 Watts

### PhysicsCalc2:T3:V0

PhysicsCalc2152573593386

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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {F}}=}$:

a) 1/2
b) 3/2
c) 2
d) 2/3
e) 3

2) A 1 ohm resistor has 5 volts DC across its terminals. What is the current (I) and the power consumed?

a) I = 5A & P = 5W.
b) I = 5A & P = 9W
c) I = 5A & P = 3W.
d) I = 5A & P = 25W.

3) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

4) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm. What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?

a) 5.14 x 10-5 Volts
b) 1.62 x 10-4 Volts
c) 5.14 x 10-4 Volts
d) 1.62 x 10-3 Volts
e) 5.14 x 10-3 Volts

5) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?

a) 2.36 x 10-3 newtons
b) 7.47 x 10-3 newtons
c) 2.36 x 10-2 newtons
d) 7.47 x 10-2 newtons
e) 2.36 x 10-1 newtons

6) An loop of wire with 43 turns has a radius of 0.27 meters, and is oriented with its axis parallel to a magetic field of 0.68 Tesla. What is the induced voltage if this field is reduced to 36% of its original value in 3.8 seconds?

a) 6.34 x 10-1 volts
b) 7.68 x 10-1 volts
c) 9.31 x 10-1 volts
d) 1.13 x 100 volts
e) 1.37 x 100 volts

7) When light passes from air to glass

a) it does not bend
b) it bends towards the normal
c) the frequency increases
d) the frequency decreases
e) it bends away from the normal

8) The focal point is where

a) rays meet whenever they pass through a lens
b) rays meet whenever they are forming an image
c) the center of the lens
d) rays meet if they were parallel to the optical axis before striking a lens
e) rays meet if they are parallel to each other

9) When light passes from glass to air

a) it bends towards the normal
b) it bends away from the normal
c) the frequency decreases
d) it does not bend
e) the frequency increases
10)
Shown is a corrective lens by a person who needs glasses. This ray diagram illustrates
a) how a farsighted person might see a distant object
b) how a farsighted person might see an object that is too close for comfort
c) how a nearsighted person might see a distant object
d) how a nearsighted person might see an object that is too close for comfort

11) An object is placed 10.8 cm to the left of a diverging lens with a focal length of 15.6 cm. On the side, at a distance of 5.7 cm from the diverging lens is a converging lens with focal length equal to 4 cm. How far is the final image from the converging lens?

a) 5.98 x 10-1 cm
b) 1.89 x 100 cm
c) 5.98 x 100 cm
d) 1.89 x 101 cm
e) 5.98 x 101 cm

12) An object is placed 4.85 cm to the left of a converging lens with a focal length of 4 cm. How far is the image from the lens?

a) 4.06 x 100 cm
b) 7.22 x 100 cm
c) 1.28 x 101 cm
d) 2.28 x 101 cm
e) 4.06 x 101 cm

### KEY:PhysicsCalc2:T3:V0

PhysicsCalc2152573593386

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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {F}}=}$:

-a) 1/2
+b) 3/2
-c) 2
-d) 2/3
-e) 3

2) A 1 ohm resistor has 5 volts DC across its terminals. What is the current (I) and the power consumed?

-a) I = 5A & P = 5W.
-b) I = 5A & P = 9W
-c) I = 5A & P = 3W.
+d) I = 5A & P = 25W.

3) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

+a) 1.88 x 109 s.
-b) 5.93 x 109 s.
-c) 1.88 x 1010 s.
-d) 5.93 x 1010 s.
-e) 1.88 x 1011 s.

4) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm. What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?

-a) 5.14 x 10-5 Volts
+b) 1.62 x 10-4 Volts
-c) 5.14 x 10-4 Volts
-d) 1.62 x 10-3 Volts
-e) 5.14 x 10-3 Volts

5) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?

-a) 2.36 x 10-3 newtons
-b) 7.47 x 10-3 newtons
-c) 2.36 x 10-2 newtons
+d) 7.47 x 10-2 newtons
-e) 2.36 x 10-1 newtons

6) An loop of wire with 43 turns has a radius of 0.27 meters, and is oriented with its axis parallel to a magetic field of 0.68 Tesla. What is the induced voltage if this field is reduced to 36% of its original value in 3.8 seconds?

-a) 6.34 x 10-1 volts
-b) 7.68 x 10-1 volts
-c) 9.31 x 10-1 volts
+d) 1.13 x 100 volts
-e) 1.37 x 100 volts

7) When light passes from air to glass

-a) it does not bend
+b) it bends towards the normal
-c) the frequency increases
-d) the frequency decreases
-e) it bends away from the normal

8) The focal point is where

-a) rays meet whenever they pass through a lens
-b) rays meet whenever they are forming an image
-c) the center of the lens
+d) rays meet if they were parallel to the optical axis before striking a lens
-e) rays meet if they are parallel to each other

9) When light passes from glass to air

-a) it bends towards the normal
+b) it bends away from the normal
-c) the frequency decreases
-d) it does not bend
-e) the frequency increases
10)
Shown is a corrective lens by a person who needs glasses. This ray diagram illustrates
-a) how a farsighted person might see a distant object
-b) how a farsighted person might see an object that is too close for comfort
+c) how a nearsighted person might see a distant object
-d) how a nearsighted person might see an object that is too close for comfort

11) An object is placed 10.8 cm to the left of a diverging lens with a focal length of 15.6 cm. On the side, at a distance of 5.7 cm from the diverging lens is a converging lens with focal length equal to 4 cm. How far is the final image from the converging lens?

-a) 5.98 x 10-1 cm
-b) 1.89 x 100 cm
+c) 5.98 x 100 cm
-d) 1.89 x 101 cm
-e) 5.98 x 101 cm

12) An object is placed 4.85 cm to the left of a converging lens with a focal length of 4 cm. How far is the image from the lens?

-a) 4.06 x 100 cm
-b) 7.22 x 100 cm
-c) 1.28 x 101 cm
+d) 2.28 x 101 cm
-e) 4.06 x 101 cm

### PhysicsCalc2:T3:V1

PhysicsCalc2152573593386

1) A 1 ohm resistor has 5 volts DC across its terminals. What is the current (I) and the power consumed?

a) I = 5A & P = 9W
b) I = 5A & P = 25W.
c) I = 5A & P = 5W.
d) I = 5A & P = 3W.
2)
Shown is a corrective lens by a person who needs glasses. This ray diagram illustrates
a) how a farsighted person might see a distant object
b) how a farsighted person might see an object that is too close for comfort
c) how a nearsighted person might see an object that is too close for comfort
d) how a nearsighted person might see a distant object

3) An object is placed 4.35 cm to the left of a converging lens with a focal length of 5.7 cm. How far is the image from the lens?

a) 1.03 x 101 cm
b) 1.84 x 101 cm
c) 3.27 x 101 cm
d) 5.81 x 101 cm
e) 1.03 x 102 cm

4) The focal point is where

a) rays meet whenever they are forming an image
b) the center of the lens
c) rays meet if they were parallel to the optical axis before striking a lens
d) rays meet if they are parallel to each other
e) rays meet whenever they pass through a lens

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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {F}}=}$:

a) 3/2
b) 2
c) 2/3
d) 1/2
e) 3

6) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?

a) 2.36 x 10-3 newtons
b) 7.47 x 10-3 newtons
c) 2.36 x 10-2 newtons
d) 7.47 x 10-2 newtons
e) 2.36 x 10-1 newtons

7) When light passes from glass to air

a) it does not bend
b) it bends away from the normal
c) the frequency increases
d) the frequency decreases
e) it bends towards the normal

8) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm. What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?

a) 5.14 x 10-5 Volts
b) 1.62 x 10-4 Volts
c) 5.14 x 10-4 Volts
d) 1.62 x 10-3 Volts
e) 5.14 x 10-3 Volts

9) An object is placed 10.8 cm to the left of a diverging lens with a focal length of 15.6 cm. On the side, at a distance of 5.7 cm from the diverging lens is a converging lens with focal length equal to 4 cm. How far is the final image from the converging lens?

a) 5.98 x 10-1 cm
b) 1.89 x 100 cm
c) 5.98 x 100 cm
d) 1.89 x 101 cm
e) 5.98 x 101 cm

10) An loop of wire with 33 turns has a radius of 0.55 meters, and is oriented with its axis parallel to a magetic field of 0.74 Tesla. What is the induced voltage if this field is reduced to 32% of its original value in 2.4 seconds?

a) 5.43 x 100 volts
b) 6.58 x 100 volts
c) 7.97 x 100 volts
d) 9.65 x 100 volts
e) 1.17 x 101 volts

11) When light passes from air to glass

a) the frequency decreases
b) it does not bend
c) the frequency increases
d) it bends towards the normal
e) it bends away from the normal

12) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

### KEY:PhysicsCalc2:T3:V1

PhysicsCalc2152573593386

1) A 1 ohm resistor has 5 volts DC across its terminals. What is the current (I) and the power consumed?

-a) I = 5A & P = 9W
+b) I = 5A & P = 25W.
-c) I = 5A & P = 5W.
-d) I = 5A & P = 3W.
2)
Shown is a corrective lens by a person who needs glasses. This ray diagram illustrates
-a) how a farsighted person might see a distant object
-b) how a farsighted person might see an object that is too close for comfort
-c) how a nearsighted person might see an object that is too close for comfort
+d) how a nearsighted person might see a distant object

3) An object is placed 4.35 cm to the left of a converging lens with a focal length of 5.7 cm. How far is the image from the lens?

-a) 1.03 x 101 cm
+b) 1.84 x 101 cm
-c) 3.27 x 101 cm
-d) 5.81 x 101 cm
-e) 1.03 x 102 cm

4) The focal point is where

-a) rays meet whenever they are forming an image
-b) the center of the lens
+c) rays meet if they were parallel to the optical axis before striking a lens
-d) rays meet if they are parallel to each other
-e) rays meet whenever they pass through a lens

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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {F}}=}$:

+a) 3/2
-b) 2
-c) 2/3
-d) 1/2
-e) 3

6) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?

-a) 2.36 x 10-3 newtons
-b) 7.47 x 10-3 newtons
-c) 2.36 x 10-2 newtons
+d) 7.47 x 10-2 newtons
-e) 2.36 x 10-1 newtons

7) When light passes from glass to air

-a) it does not bend
+b) it bends away from the normal
-c) the frequency increases
-d) the frequency decreases
-e) it bends towards the normal

8) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm. What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?

-a) 5.14 x 10-5 Volts
+b) 1.62 x 10-4 Volts
-c) 5.14 x 10-4 Volts
-d) 1.62 x 10-3 Volts
-e) 5.14 x 10-3 Volts

9) An object is placed 10.8 cm to the left of a diverging lens with a focal length of 15.6 cm. On the side, at a distance of 5.7 cm from the diverging lens is a converging lens with focal length equal to 4 cm. How far is the final image from the converging lens?

-a) 5.98 x 10-1 cm
-b) 1.89 x 100 cm
+c) 5.98 x 100 cm
-d) 1.89 x 101 cm
-e) 5.98 x 101 cm

10) An loop of wire with 33 turns has a radius of 0.55 meters, and is oriented with its axis parallel to a magetic field of 0.74 Tesla. What is the induced voltage if this field is reduced to 32% of its original value in 2.4 seconds?

-a) 5.43 x 100 volts
+b) 6.58 x 100 volts
-c) 7.97 x 100 volts
-d) 9.65 x 100 volts
-e) 1.17 x 101 volts

11) When light passes from air to glass

-a) the frequency decreases
-b) it does not bend
-c) the frequency increases
+d) it bends towards the normal
-e) it bends away from the normal

12) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

+a) 1.88 x 109 s.
-b) 5.93 x 109 s.
-c) 1.88 x 1010 s.
-d) 5.93 x 1010 s.
-e) 1.88 x 1011 s.

### PhysicsCalc2:T3:V2

PhysicsCalc2152573593386

1) An loop of wire with 33 turns has a radius of 0.55 meters, and is oriented with its axis parallel to a magetic field of 0.74 Tesla. What is the induced voltage if this field is reduced to 32% of its original value in 2.4 seconds?

a) 5.43 x 100 volts
b) 6.58 x 100 volts
c) 7.97 x 100 volts
d) 9.65 x 100 volts
e) 1.17 x 101 volts

2) A 1 ohm resistor has 5 volts DC across its terminals. What is the current (I) and the power consumed?

a) I = 5A & P = 9W
b) I = 5A & P = 5W.
c) I = 5A & P = 3W.
d) I = 5A & P = 25W.

3) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

a) 1.88 x 109 s.
b) 5.93 x 109 s.
c) 1.88 x 1010 s.
d) 5.93 x 1010 s.
e) 1.88 x 1011 s.

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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {F}}=}$:

a) 3/2
b) 2
c) 2/3
d) 1/2
e) 3

5) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm. What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?

a) 5.14 x 10-5 Volts
b) 1.62 x 10-4 Volts
c) 5.14 x 10-4 Volts
d) 1.62 x 10-3 Volts
e) 5.14 x 10-3 Volts

6) When light passes from air to glass

a) it bends towards the normal
b) it does not bend
c) the frequency increases
d) the frequency decreases
e) it bends away from the normal

7) An object is placed 10.8 cm to the left of a diverging lens with a focal length of 15.6 cm. On the side, at a distance of 5.7 cm from the diverging lens is a converging lens with focal length equal to 4 cm. How far is the final image from the converging lens?

a) 5.98 x 10-1 cm
b) 1.89 x 100 cm
c) 5.98 x 100 cm
d) 1.89 x 101 cm
e) 5.98 x 101 cm

8) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?

a) 2.36 x 10-3 newtons
b) 7.47 x 10-3 newtons
c) 2.36 x 10-2 newtons
d) 7.47 x 10-2 newtons
e) 2.36 x 10-1 newtons
9)
Shown is a corrective lens by a person who needs glasses. This ray diagram illustrates
a) how a farsighted person might see an object that is too close for comfort
b) how a nearsighted person might see a distant object
c) how a nearsighted person might see an object that is too close for comfort
d) how a farsighted person might see a distant object

10) When light passes from glass to air

a) it bends towards the normal
b) it bends away from the normal
c) the frequency increases
d) the frequency decreases
e) it does not bend

11) An object is placed 4.65 cm to the left of a converging lens with a focal length of 6.2 cm. How far is the image from the lens?

a) 1.86 x 100 cm
b) 3.31 x 100 cm
c) 5.88 x 100 cm
d) 1.05 x 101 cm
e) 1.86 x 101 cm

12) The focal point is where

a) rays meet if they were parallel to the optical axis before striking a lens
b) the center of the lens
c) rays meet if they are parallel to each other
d) rays meet whenever they are forming an image
e) rays meet whenever they pass through a lens

### KEY:PhysicsCalc2:T3:V2

PhysicsCalc2152573593386

1) An loop of wire with 33 turns has a radius of 0.55 meters, and is oriented with its axis parallel to a magetic field of 0.74 Tesla. What is the induced voltage if this field is reduced to 32% of its original value in 2.4 seconds?

-a) 5.43 x 100 volts
+b) 6.58 x 100 volts
-c) 7.97 x 100 volts
-d) 9.65 x 100 volts
-e) 1.17 x 101 volts

2) A 1 ohm resistor has 5 volts DC across its terminals. What is the current (I) and the power consumed?

-a) I = 5A & P = 9W
-b) I = 5A & P = 5W.
-c) I = 5A & P = 3W.
+d) I = 5A & P = 25W.

3) A 727 mF capacitor is connected in series to a 860 MΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)

+a) 1.88 x 109 s.
-b) 5.93 x 109 s.
-c) 1.88 x 1010 s.
-d) 5.93 x 1010 s.
-e) 1.88 x 1011 s.

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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {F}}=}$:

+a) 3/2
-b) 2
-c) 2/3
-d) 1/2
-e) 3

5) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm. What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?

-a) 5.14 x 10-5 Volts
+b) 1.62 x 10-4 Volts
-c) 5.14 x 10-4 Volts
-d) 1.62 x 10-3 Volts
-e) 5.14 x 10-3 Volts

6) When light passes from air to glass

+a) it bends towards the normal
-b) it does not bend
-c) the frequency increases
-d) the frequency decreases
-e) it bends away from the normal

7) An object is placed 10.8 cm to the left of a diverging lens with a focal length of 15.6 cm. On the side, at a distance of 5.7 cm from the diverging lens is a converging lens with focal length equal to 4 cm. How far is the final image from the converging lens?

-a) 5.98 x 10-1 cm
-b) 1.89 x 100 cm
+c) 5.98 x 100 cm
-d) 1.89 x 101 cm
-e) 5.98 x 101 cm

8) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?

-a) 2.36 x 10-3 newtons
-b) 7.47 x 10-3 newtons
-c) 2.36 x 10-2 newtons
+d) 7.47 x 10-2 newtons
-e) 2.36 x 10-1 newtons
9)
Shown is a corrective lens by a person who needs glasses. This ray diagram illustrates
-a) how a farsighted person might see an object that is too close for comfort
+b) how a nearsighted person might see a distant object
-c) how a nearsighted person might see an object that is too close for comfort
-d) how a farsighted person might see a distant object

10) When light passes from glass to air

-a) it bends towards the normal
+b) it bends away from the normal
-c) the frequency increases
-d) the frequency decreases
-e) it does not bend

11) An object is placed 4.65 cm to the left of a converging lens with a focal length of 6.2 cm. How far is the image from the lens?

-a) 1.86 x 100 cm
-b) 3.31 x 100 cm
-c) 5.88 x 100 cm
-d) 1.05 x 101 cm
+e) 1.86 x 101 cm

12) The focal point is where

+a) rays meet if they were parallel to the optical axis before striking a lens
-b) the center of the lens
-c) rays meet if they are parallel to each other
-d) rays meet whenever they are forming an image
-e) rays meet whenever they pass through a lens

### PhysicsCalc2:T4:V0

PhysicsCalc2152573593386

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, 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

2) An object of height 0.7 cm is placed 117 cm behind a diverging lens with a focal length of 70 cm. What is the height of the image?

a) 2.62 x 10-1 cm
b) 3.14 x 10-1 cm
c) 3.77 x 10-1 cm
d) 4.53 x 10-1 cm
e) 5.43 x 10-1 cm

3) If this represents the eye looking at an object, where is this object?

a) directly in front of the eye (almost touching)
b) very far away
c) Two (of the other answers) are true
d) One focal length in front of the eye
e) at infinity

4) Mr. Smith is gazing at something as shown in the figure to the left. Suppose he does not refocus, but attempts to stare at the star shown in the figures below. Which diagram depicts how the rays from the star would travel if he does not refocus?

a)
b)
c)

5) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H_{y}}$ at the point (3.2194,2.9992) if a current of 5.8A flows through a wire that runs along the z axis?

a) 1.06E-01 A/m
b) 1.16E-01 A/m
c) 1.28E-01 A/m
d) 1.40E-01 A/m
e) 1.54E-01 A/m

6) A very long and thin solenoid has 2175 turns and is 134 meters long. The wire carrys a current of 7.6A. What is the magnetic field in the center?

a) 1.29E-04 Tesla
b) 1.41E-04 Tesla
c) 1.55E-04 Tesla
d) 1.70E-04 Tesla
e) 1.86E-04 Tesla

7) A very long and thin solenoid has 1847 turns and is 162 meters long. The wire carrys a current of 8.7A. If this solenoid is sufficiently thin, what is the line integral of${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$ along an on-axis path that starts 42 meters from the center and stops 103 meters from the center?

a) 2.68E+03 A
b) 2.93E+03 A
c) 3.22E+03 A
d) 3.53E+03 A
e) 3.87E+03 A

8) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H}$ at a distance of 6.3m from a wire carrying a current of 7.4A?

a) 1.87E-01 A/m
b) 2.05E-01 A/m
c) 2.25E-01 A/m
d) 2.46E-01 A/m
e) 2.70E-01 A/m

9) H is defined by, B=μ0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (0,4.1) to the point (4.1,0).

a) 1.28E+01 amps
b) 1.40E+01 amps
c) 1.54E+01 amps
d) 1.69E+01 amps
e) 1.85E+01 amps

10) H is defined by, B=μ0H, where B is magnetic field. A current of 87A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (-6.1, 6.1) to the point (6.1, 6.1).

a) 1.50E+01 amps
b) 1.65E+01 amps
c) 1.81E+01 amps
d) 1.98E+01 amps
e) 2.18E+01 amps

11) A circlular capactitor of radius 3.1 m has a gap of 9 mm, and a charge of 85 μC. The capacitor is discharged through a 5 kΩ resistor. What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)

a) 2.33E-08 Tesla
b) 2.93E-08 Tesla
c) 3.69E-08 Tesla
d) 4.65E-08 Tesla
e) 5.85E-08 Tesla

12) A circlular capactitor of radius 4.8 m has a gap of 12 mm, and a charge of 29 μC. Compute the surface integral ${\displaystyle c^{-2}\oint {\vec {E}}\cdot d{\vec {A}}}$ over an inner face of the capacitor.

a) 2.05E-11 Vs2m-1
b) 2.48E-11 Vs2m-1
c) 3.01E-11 Vs2m-1
d) 3.64E-11 Vs2m-1
e) 4.42E-11 Vs2m-1

### KEY:PhysicsCalc2:T4:V0

PhysicsCalc2152573593386

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, 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

2) An object of height 0.7 cm is placed 117 cm behind a diverging lens with a focal length of 70 cm. What is the height of the image?

+a) 2.62 x 10-1 cm
-b) 3.14 x 10-1 cm
-c) 3.77 x 10-1 cm
-d) 4.53 x 10-1 cm
-e) 5.43 x 10-1 cm

3) If this represents the eye looking at an object, where is this object?

-a) directly in front of the eye (almost touching)
-b) very far away
+c) Two (of the other answers) are true
-d) One focal length in front of the eye
-e) at infinity

4) Mr. Smith is gazing at something as shown in the figure to the left. Suppose he does not refocus, but attempts to stare at the star shown in the figures below. Which diagram depicts how the rays from the star would travel if he does not refocus?

-a)
+b)
-c)

5) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H_{y}}$ at the point (3.2194,2.9992) if a current of 5.8A flows through a wire that runs along the z axis?

-a) 1.06E-01 A/m
-b) 1.16E-01 A/m
-c) 1.28E-01 A/m
-d) 1.40E-01 A/m
+e) 1.54E-01 A/m

6) A very long and thin solenoid has 2175 turns and is 134 meters long. The wire carrys a current of 7.6A. What is the magnetic field in the center?

-a) 1.29E-04 Tesla
-b) 1.41E-04 Tesla
+c) 1.55E-04 Tesla
-d) 1.70E-04 Tesla
-e) 1.86E-04 Tesla

7) A very long and thin solenoid has 1847 turns and is 162 meters long. The wire carrys a current of 8.7A. If this solenoid is sufficiently thin, what is the line integral of${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$ along an on-axis path that starts 42 meters from the center and stops 103 meters from the center?

-a) 2.68E+03 A
-b) 2.93E+03 A
-c) 3.22E+03 A
-d) 3.53E+03 A
+e) 3.87E+03 A

8) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H}$ at a distance of 6.3m from a wire carrying a current of 7.4A?

+a) 1.87E-01 A/m
-b) 2.05E-01 A/m
-c) 2.25E-01 A/m
-d) 2.46E-01 A/m
-e) 2.70E-01 A/m

9) H is defined by, B=μ0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (0,4.1) to the point (4.1,0).

-a) 1.28E+01 amps
-b) 1.40E+01 amps
-c) 1.54E+01 amps
-d) 1.69E+01 amps
+e) 1.85E+01 amps

10) H is defined by, B=μ0H, where B is magnetic field. A current of 87A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (-6.1, 6.1) to the point (6.1, 6.1).

-a) 1.50E+01 amps
-b) 1.65E+01 amps
-c) 1.81E+01 amps
-d) 1.98E+01 amps
+e) 2.18E+01 amps

11) A circlular capactitor of radius 3.1 m has a gap of 9 mm, and a charge of 85 μC. The capacitor is discharged through a 5 kΩ resistor. What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)

-a) 2.33E-08 Tesla
-b) 2.93E-08 Tesla
+c) 3.69E-08 Tesla
-d) 4.65E-08 Tesla
-e) 5.85E-08 Tesla

12) A circlular capactitor of radius 4.8 m has a gap of 12 mm, and a charge of 29 μC. Compute the surface integral ${\displaystyle c^{-2}\oint {\vec {E}}\cdot d{\vec {A}}}$ over an inner face of the capacitor.

-a) 2.05E-11 Vs2m-1
-b) 2.48E-11 Vs2m-1
-c) 3.01E-11 Vs2m-1
+d) 3.64E-11 Vs2m-1
-e) 4.42E-11 Vs2m-1

### PhysicsCalc2:T4:V1

PhysicsCalc2152573593386

1) A circlular capactitor of radius 3.4 m has a gap of 8 mm, and a charge of 34 μC. Compute the surface integral ${\displaystyle c^{-2}\oint {\vec {E}}\cdot d{\vec {A}}}$ over an inner face of the capacitor.

a) 3.53E-11 Vs2m-1
b) 4.27E-11 Vs2m-1
c) 5.18E-11 Vs2m-1
d) 6.27E-11 Vs2m-1
e) 7.60E-11 Vs2m-1

2) A very long and thin solenoid has 2918 turns and is 144 meters long. The wire carrys a current of 9A. If this solenoid is sufficiently thin, what is the line integral of${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$ along an on-axis path that starts 38 meters from the center and stops 89 meters from the center?

a) 6.20E+03 A
b) 6.80E+03 A
c) 7.45E+03 A
d) 8.17E+03 A
e) 8.96E+03 A

3) A circlular capactitor of radius 4.7 m has a gap of 16 mm, and a charge of 12 μC. The capacitor is discharged through a 8 kΩ resistor. What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)

a) 6.62E-10 Tesla
b) 8.33E-10 Tesla
c) 1.05E-09 Tesla
d) 1.32E-09 Tesla
e) 1.66E-09 Tesla

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) Mr. Smith is gazing at something as shown in the figure to the left. Suppose he does not refocus, but attempts to stare at the star shown in the figures below. Which diagram depicts how the rays from the star would travel if he does not refocus?

a)
b)
c)

6) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H_{y}}$ at the point (6.1539,7.7549) if a current of 6.9A flows through a wire that runs along the z axis?

a) 5.23E-02 A/m
b) 5.74E-02 A/m
c) 6.29E-02 A/m
d) 6.90E-02 A/m
e) 7.56E-02 A/m

7) An object of height 0.75 cm is placed 147 cm behind a diverging lens with a focal length of 86 cm. What is the height of the image?

a) 2.77 x 10-1 cm
b) 3.32 x 10-1 cm
c) 3.99 x 10-1 cm
d) 4.78 x 10-1 cm
e) 5.74 x 10-1 cm

8) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H}$ at a distance of 8.3m from a wire carrying a current of 7.3A?

a) 1.40E-01 A/m
b) 1.53E-01 A/m
c) 1.68E-01 A/m
d) 1.85E-01 A/m
e) 2.02E-01 A/m

9) H is defined by, B=μ0H, where B is magnetic field. A current of 96A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (-6.4, 6.4) to the point (6.4, 6.4).

a) 2.00E+01 amps
b) 2.19E+01 amps
c) 2.40E+01 amps
d) 2.63E+01 amps
e) 2.89E+01 amps

10) A very long and thin solenoid has 1634 turns and is 122 meters long. The wire carrys a current of 9.5A. What is the magnetic field in the center?

a) 1.60E-04 Tesla
b) 1.75E-04 Tesla
c) 1.92E-04 Tesla
d) 2.11E-04 Tesla
e) 2.31E-04 Tesla

11) If this represents the eye looking at an object, where is this object?

a) very far away
b) at infinity
c) directly in front of the eye (almost touching)
d) Two (of the other answers) are true
e) One focal length in front of the eye

12) H is defined by, B=μ0H, where B is magnetic field. A current of 92A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (0,6.4) to the point (6.4,0).

a) 2.10E+01 amps
b) 2.30E+01 amps
c) 2.52E+01 amps
d) 2.77E+01 amps
e) 3.03E+01 amps

### KEY:PhysicsCalc2:T4:V1

PhysicsCalc2152573593386

1) A circlular capactitor of radius 3.4 m has a gap of 8 mm, and a charge of 34 μC. Compute the surface integral ${\displaystyle c^{-2}\oint {\vec {E}}\cdot d{\vec {A}}}$ over an inner face of the capacitor.

-a) 3.53E-11 Vs2m-1
+b) 4.27E-11 Vs2m-1
-c) 5.18E-11 Vs2m-1
-d) 6.27E-11 Vs2m-1
-e) 7.60E-11 Vs2m-1

2) A very long and thin solenoid has 2918 turns and is 144 meters long. The wire carrys a current of 9A. If this solenoid is sufficiently thin, what is the line integral of${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$ along an on-axis path that starts 38 meters from the center and stops 89 meters from the center?

+a) 6.20E+03 A
-b) 6.80E+03 A
-c) 7.45E+03 A
-d) 8.17E+03 A
-e) 8.96E+03 A

3) A circlular capactitor of radius 4.7 m has a gap of 16 mm, and a charge of 12 μC. The capacitor is discharged through a 8 kΩ resistor. What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)

-a) 6.62E-10 Tesla
-b) 8.33E-10 Tesla
-c) 1.05E-09 Tesla
-d) 1.32E-09 Tesla
+e) 1.66E-09 Tesla

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) Mr. Smith is gazing at something as shown in the figure to the left. Suppose he does not refocus, but attempts to stare at the star shown in the figures below. Which diagram depicts how the rays from the star would travel if he does not refocus?

-a)
+b)
-c)

6) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H_{y}}$ at the point (6.1539,7.7549) if a current of 6.9A flows through a wire that runs along the z axis?

-a) 5.23E-02 A/m
-b) 5.74E-02 A/m
-c) 6.29E-02 A/m
+d) 6.90E-02 A/m
-e) 7.56E-02 A/m

7) An object of height 0.75 cm is placed 147 cm behind a diverging lens with a focal length of 86 cm. What is the height of the image?

+a) 2.77 x 10-1 cm
-b) 3.32 x 10-1 cm
-c) 3.99 x 10-1 cm
-d) 4.78 x 10-1 cm
-e) 5.74 x 10-1 cm

8) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H}$ at a distance of 8.3m from a wire carrying a current of 7.3A?

+a) 1.40E-01 A/m
-b) 1.53E-01 A/m
-c) 1.68E-01 A/m
-d) 1.85E-01 A/m
-e) 2.02E-01 A/m

9) H is defined by, B=μ0H, where B is magnetic field. A current of 96A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (-6.4, 6.4) to the point (6.4, 6.4).

-a) 2.00E+01 amps
-b) 2.19E+01 amps
+c) 2.40E+01 amps
-d) 2.63E+01 amps
-e) 2.89E+01 amps

10) A very long and thin solenoid has 1634 turns and is 122 meters long. The wire carrys a current of 9.5A. What is the magnetic field in the center?

+a) 1.60E-04 Tesla
-b) 1.75E-04 Tesla
-c) 1.92E-04 Tesla
-d) 2.11E-04 Tesla
-e) 2.31E-04 Tesla

11) If this represents the eye looking at an object, where is this object?

-a) very far away
-b) at infinity
-c) directly in front of the eye (almost touching)
+d) Two (of the other answers) are true
-e) One focal length in front of the eye

12) H is defined by, B=μ0H, where B is magnetic field. A current of 92A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (0,6.4) to the point (6.4,0).

-a) 2.10E+01 amps
+b) 2.30E+01 amps
-c) 2.52E+01 amps
-d) 2.77E+01 amps
-e) 3.03E+01 amps

### PhysicsCalc2:T4:V2

PhysicsCalc2152573593386

1) H is defined by, B=μ0H, where B is magnetic field. A current of 47A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (0,9) to the point (9,0).

a) 8.91E+00 amps
b) 9.77E+00 amps
c) 1.07E+01 amps
d) 1.18E+01 amps
e) 1.29E+01 amps

2) A very long and thin solenoid has 1847 turns and is 162 meters long. The wire carrys a current of 8.7A. If this solenoid is sufficiently thin, what is the line integral of${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$ along an on-axis path that starts 42 meters from the center and stops 103 meters from the center?

a) 2.68E+03 A
b) 2.93E+03 A
c) 3.22E+03 A
d) 3.53E+03 A
e) 3.87E+03 A

3) If this represents the eye looking at an object, where is this object?

a) Two (of the other answers) are true
b) One focal length in front of the eye
c) at infinity
d) directly in front of the eye (almost touching)
e) very far away

4) A circlular capactitor of radius 3.2 m has a gap of 19 mm, and a charge of 46 μC. Compute the surface integral ${\displaystyle c^{-2}\oint {\vec {E}}\cdot d{\vec {A}}}$ over an inner face of the capacitor.

a) 5.78E-11 Vs2m-1
b) 7.00E-11 Vs2m-1
c) 8.48E-11 Vs2m-1
d) 1.03E-10 Vs2m-1
e) 1.25E-10 Vs2m-1

5) A circlular capactitor of radius 4.1 m has a gap of 9 mm, and a charge of 79 μC. The capacitor is discharged through a 6 kΩ resistor. What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)

a) 7.80E-09 Tesla
b) 9.82E-09 Tesla
c) 1.24E-08 Tesla
d) 1.56E-08 Tesla
e) 1.96E-08 Tesla

6) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H_{y}}$ at the point (3.854,4.8566) if a current of 4.8A flows through a wire that runs along the z axis?

a) 6.37E-02 A/m
b) 6.99E-02 A/m
c) 7.66E-02 A/m
d) 8.40E-02 A/m
e) 9.21E-02 A/m

7) An object of height 0.67 cm is placed 107 cm behind a diverging lens with a focal length of 70 cm. What is the height of the image?

a) 2.65 x 10-1 cm
b) 3.18 x 10-1 cm
c) 3.82 x 10-1 cm
d) 4.58 x 10-1 cm
e) 5.49 x 10-1 cm

8) Mr. Smith is gazing at something as shown in the figure to the left. Suppose he does not refocus, but attempts to stare at the star shown in the figures below. Which diagram depicts how the rays from the star would travel if he does not refocus?

a)
b)
c)

9) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H}$ at a distance of 9.9m from a wire carrying a current of 6.9A?

a) 1.11E-01 A/m
b) 1.22E-01 A/m
c) 1.33E-01 A/m
d) 1.46E-01 A/m
e) 1.60E-01 A/m

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) =( 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

11) A very long and thin solenoid has 1518 turns and is 156 meters long. The wire carrys a current of 8.9A. What is the magnetic field in the center?

a) 8.26E-05 Tesla
b) 9.05E-05 Tesla
c) 9.93E-05 Tesla
d) 1.09E-04 Tesla
e) 1.19E-04 Tesla

12) H is defined by, B=μ0H, where B is magnetic field. A current of 94A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (-5.8, 5.8) to the point (5.8, 5.8).

a) 1.78E+01 amps
b) 1.95E+01 amps
c) 2.14E+01 amps
d) 2.35E+01 amps
e) 2.58E+01 amps

### KEY:PhysicsCalc2:T4:V2

PhysicsCalc2152573593386

1) H is defined by, B=μ0H, where B is magnetic field. A current of 47A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (0,9) to the point (9,0).

-a) 8.91E+00 amps
-b) 9.77E+00 amps
-c) 1.07E+01 amps
+d) 1.18E+01 amps
-e) 1.29E+01 amps

2) A very long and thin solenoid has 1847 turns and is 162 meters long. The wire carrys a current of 8.7A. If this solenoid is sufficiently thin, what is the line integral of${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$ along an on-axis path that starts 42 meters from the center and stops 103 meters from the center?

-a) 2.68E+03 A
-b) 2.93E+03 A
-c) 3.22E+03 A
-d) 3.53E+03 A
+e) 3.87E+03 A

3) If this represents the eye looking at an object, where is this object?

+a) Two (of the other answers) are true
-b) One focal length in front of the eye
-c) at infinity
-d) directly in front of the eye (almost touching)
-e) very far away

4) A circlular capactitor of radius 3.2 m has a gap of 19 mm, and a charge of 46 μC. Compute the surface integral ${\displaystyle c^{-2}\oint {\vec {E}}\cdot d{\vec {A}}}$ over an inner face of the capacitor.

+a) 5.78E-11 Vs2m-1
-b) 7.00E-11 Vs2m-1
-c) 8.48E-11 Vs2m-1
-d) 1.03E-10 Vs2m-1
-e) 1.25E-10 Vs2m-1

5) A circlular capactitor of radius 4.1 m has a gap of 9 mm, and a charge of 79 μC. The capacitor is discharged through a 6 kΩ resistor. What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)

-a) 7.80E-09 Tesla
-b) 9.82E-09 Tesla
+c) 1.24E-08 Tesla
-d) 1.56E-08 Tesla
-e) 1.96E-08 Tesla

6) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H_{y}}$ at the point (3.854,4.8566) if a current of 4.8A flows through a wire that runs along the z axis?

-a) 6.37E-02 A/m
-b) 6.99E-02 A/m
+c) 7.66E-02 A/m
-d) 8.40E-02 A/m
-e) 9.21E-02 A/m

7) An object of height 0.67 cm is placed 107 cm behind a diverging lens with a focal length of 70 cm. What is the height of the image?

+a) 2.65 x 10-1 cm
-b) 3.18 x 10-1 cm
-c) 3.82 x 10-1 cm
-d) 4.58 x 10-1 cm
-e) 5.49 x 10-1 cm

8) Mr. Smith is gazing at something as shown in the figure to the left. Suppose he does not refocus, but attempts to stare at the star shown in the figures below. Which diagram depicts how the rays from the star would travel if he does not refocus?

-a)
+b)
-c)

9) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H}$ at a distance of 9.9m from a wire carrying a current of 6.9A?

+a) 1.11E-01 A/m
-b) 1.22E-01 A/m
-c) 1.33E-01 A/m
-d) 1.46E-01 A/m
-e) 1.60E-01 A/m

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) =( 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

11) A very long and thin solenoid has 1518 turns and is 156 meters long. The wire carrys a current of 8.9A. What is the magnetic field in the center?

-a) 8.26E-05 Tesla
-b) 9.05E-05 Tesla
-c) 9.93E-05 Tesla
+d) 1.09E-04 Tesla
-e) 1.19E-04 Tesla

12) H is defined by, B=μ0H, where B is magnetic field. A current of 94A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (-5.8, 5.8) to the point (5.8, 5.8).

-a) 1.78E+01 amps
-b) 1.95E+01 amps
-c) 2.14E+01 amps
+d) 2.35E+01 amps
-e) 2.58E+01 amps

### PhysicsCalc2:FE:V0

PhysicsCalc2152573593386

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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where${\displaystyle {\mathcal {F}}=}$

a) 1/2
b) 2
c) 3/2
d) 3

3) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
b) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
c) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
d) none of these are correct
e) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$

4) A 1.3 Farad capacitor charged with 1.9 Coulombs. What is the force between the plates if they are 0.3 mm apart?

a) 4025 N.
b) 4628 N.
c) 5322 N.
d) 6121 N.
e) 7039 N.

5) What voltage is required to stop a proton moving at a speed of 5.2 x 107 m/s?

a) 9.4 x 106 volts
b) 1.4 x 107 volts
c) 2.1 x 107 volts
d) 3.2 x 107 volts
e) 4.8 x 107 volts

6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.45+2.26z)\rho ^{2}{\hat {\rho }}+8.92z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the curved side surface of the cylinder.

a) 3.356E+02
b) 4.066E+02
c) 4.926E+02
d) 5.968E+02
e) 7.230E+02

7) A 1.4 volt battery moves 87 Coulombs of charge in 2 hours. What is the power?

a) 7.85 x 10-3 W
b) 9.51 x 10-3 W
c) 1.15 x 10-2 W
d) 1.4 x 10-2 W
e) 1.69 x 10-2 W

8) If you put an infinite number of resistors in parallel, what would the total resistance be?

a) None of these are true.
b) ${\displaystyle R_{total}}$ would approach Zero as The No. of Resistors In parallel Approaches Infinity.
c) It is not possible to connect that Number of Resistors in parallel.
d) ${\displaystyle R_{total}}$ would approach 1 as The No. of Resistors In parallel Approaches Infinity

9) A battery has an emf of 5.3 volts, and an internal resistance of 428 ${\displaystyle k\Omega }$. It is connected to a 2.3 ${\displaystyle M\Omega }$ resistor. What power is developed in the 2.3 ${\displaystyle M\Omega }$ resistor?

a) 4.96 ${\displaystyle \mu }$W.
b) 5.71 ${\displaystyle \mu }$W.
c) 6.56 ${\displaystyle \mu }$W.
d) 7.55 ${\displaystyle \mu }$W.
e) 8.68 ${\displaystyle \mu }$W.

10) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?

a) 2.36 x 10-3 newtons
b) 7.47 x 10-3 newtons
c) 2.36 x 10-2 newtons
d) 7.47 x 10-2 newtons
e) 2.36 x 10-1 newtons

11) Two orbiting satellites are orbiting at a speed of 53 km/s perpendicular to a magnetic field of 58 μT. They are connected by a cable that is 29 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 7.36 x 104 volts.
b) 8.91 x 104 volts.
c) 1.08 x 105 volts.
d) 1.31 x 105 volts.
e) 1.59 x 105 volts.

12) An object is placed 10.8 cm to the left of a diverging lens with a focal length of 15.6 cm. On the side, at a distance of 5.7 cm from the diverging lens is a converging lens with focal length equal to 4 cm. How far is the final image from the converging lens?

a) 5.98 x 10-1 cm
b) 1.89 x 100 cm
c) 5.98 x 100 cm
d) 1.89 x 101 cm
e) 5.98 x 101 cm

13) A very long and thin solenoid has 1634 turns and is 122 meters long. The wire carrys a current of 9.5A. What is the magnetic field in the center?

a) 1.60E-04 Tesla
b) 1.75E-04 Tesla
c) 1.92E-04 Tesla
d) 2.11E-04 Tesla
e) 2.31E-04 Tesla

14) H is defined by, B=μ0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from (-∞,8.2) to (+,8.2).

a) 3.37E+01 amps
b) 3.70E+01 amps
c) 4.06E+01 amps
d) 4.45E+01 amps
e) 4.88E+01 amps

15) A circlular capactitor of radius 3.4 m has a gap of 8 mm, and a charge of 34 μC. Compute the surface integral ${\displaystyle c^{-2}\oint {\vec {E}}\cdot d{\vec {A}}}$ over an inner face of the capacitor.

a) 3.53E-11 Vs2m-1
b) 4.27E-11 Vs2m-1
c) 5.18E-11 Vs2m-1
d) 6.27E-11 Vs2m-1
e) 7.60E-11 Vs2m-1

### KEY:PhysicsCalc2:FE:V0

PhysicsCalc2152573593386

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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where${\displaystyle {\mathcal {F}}=}$

-a) 1/2
-b) 2
+c) 3/2
-d) 3

3) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
+b) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
-c) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
-d) none of these are correct
-e) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$

4) A 1.3 Farad capacitor charged with 1.9 Coulombs. What is the force between the plates if they are 0.3 mm apart?

-a) 4025 N.
+b) 4628 N.
-c) 5322 N.
-d) 6121 N.
-e) 7039 N.

5) What voltage is required to stop a proton moving at a speed of 5.2 x 107 m/s?

-a) 9.4 x 106 volts
+b) 1.4 x 107 volts
-c) 2.1 x 107 volts
-d) 3.2 x 107 volts
-e) 4.8 x 107 volts

6) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.45+2.26z)\rho ^{2}{\hat {\rho }}+8.92z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the curved side surface of the cylinder.

-a) 3.356E+02
-b) 4.066E+02
+c) 4.926E+02
-d) 5.968E+02
-e) 7.230E+02

7) A 1.4 volt battery moves 87 Coulombs of charge in 2 hours. What is the power?

-a) 7.85 x 10-3 W
-b) 9.51 x 10-3 W
-c) 1.15 x 10-2 W
-d) 1.4 x 10-2 W
+e) 1.69 x 10-2 W

8) If you put an infinite number of resistors in parallel, what would the total resistance be?

-a) None of these are true.
+b) ${\displaystyle R_{total}}$ would approach Zero as The No. of Resistors In parallel Approaches Infinity.
-c) It is not possible to connect that Number of Resistors in parallel.
-d) ${\displaystyle R_{total}}$ would approach 1 as The No. of Resistors In parallel Approaches Infinity

9) A battery has an emf of 5.3 volts, and an internal resistance of 428 ${\displaystyle k\Omega }$. It is connected to a 2.3 ${\displaystyle M\Omega }$ resistor. What power is developed in the 2.3 ${\displaystyle M\Omega }$ resistor?

-a) 4.96 ${\displaystyle \mu }$W.
-b) 5.71 ${\displaystyle \mu }$W.
-c) 6.56 ${\displaystyle \mu }$W.
-d) 7.55 ${\displaystyle \mu }$W.
+e) 8.68 ${\displaystyle \mu }$W.

10) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?

-a) 2.36 x 10-3 newtons
-b) 7.47 x 10-3 newtons
-c) 2.36 x 10-2 newtons
+d) 7.47 x 10-2 newtons
-e) 2.36 x 10-1 newtons

11) Two orbiting satellites are orbiting at a speed of 53 km/s perpendicular to a magnetic field of 58 μT. They are connected by a cable that is 29 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

-a) 7.36 x 104 volts.
+b) 8.91 x 104 volts.
-c) 1.08 x 105 volts.
-d) 1.31 x 105 volts.
-e) 1.59 x 105 volts.

12) An object is placed 10.8 cm to the left of a diverging lens with a focal length of 15.6 cm. On the side, at a distance of 5.7 cm from the diverging lens is a converging lens with focal length equal to 4 cm. How far is the final image from the converging lens?

-a) 5.98 x 10-1 cm
-b) 1.89 x 100 cm
+c) 5.98 x 100 cm
-d) 1.89 x 101 cm
-e) 5.98 x 101 cm

13) A very long and thin solenoid has 1634 turns and is 122 meters long. The wire carrys a current of 9.5A. What is the magnetic field in the center?

+a) 1.60E-04 Tesla
-b) 1.75E-04 Tesla
-c) 1.92E-04 Tesla
-d) 2.11E-04 Tesla
-e) 2.31E-04 Tesla

14) H is defined by, B=μ0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from (-∞,8.2) to (+,8.2).

-a) 3.37E+01 amps
+b) 3.70E+01 amps
-c) 4.06E+01 amps
-d) 4.45E+01 amps
-e) 4.88E+01 amps

15) A circlular capactitor of radius 3.4 m has a gap of 8 mm, and a charge of 34 μC. Compute the surface integral ${\displaystyle c^{-2}\oint {\vec {E}}\cdot d{\vec {A}}}$ over an inner face of the capacitor.

-a) 3.53E-11 Vs2m-1
+b) 4.27E-11 Vs2m-1
-c) 5.18E-11 Vs2m-1
-d) 6.27E-11 Vs2m-1
-e) 7.60E-11 Vs2m-1

### PhysicsCalc2:FE:V1

PhysicsCalc2152573593386

1) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?

a) 2.36 x 10-3 newtons
b) 7.47 x 10-3 newtons
c) 2.36 x 10-2 newtons
d) 7.47 x 10-2 newtons
e) 2.36 x 10-1 newtons

2) A 1.3 Farad capacitor charged with 1.9 Coulombs. What is the force between the plates if they are 0.3 mm apart?

a) 4025 N.
b) 4628 N.
c) 5322 N.
d) 6121 N.
e) 7039 N.

3) H is defined by, B=μ0H, where B is magnetic field. A current of 76A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from (-∞,9.6) to (+,9.6).

a) 3.16E+01 amps
b) 3.47E+01 amps
c) 3.80E+01 amps
d) 4.17E+01 amps
e) 4.57E+01 amps

4) A battery has an emf of 6.7 volts, and an internal resistance of 348 ${\displaystyle k\Omega }$. It is connected to a 3.8 ${\displaystyle M\Omega }$ resistor. What power is developed in the 3.8 ${\displaystyle M\Omega }$ resistor?

a) 9.91 ${\displaystyle \mu }$W.
b) 11.4 ${\displaystyle \mu }$W.
c) 13.11 ${\displaystyle \mu }$W.
d) 15.08 ${\displaystyle \mu }$W.
e) 17.34 ${\displaystyle \mu }$W.

5) Two orbiting satellites are orbiting at a speed of 83 km/s perpendicular to a magnetic field of 57 μT. They are connected by a cable that is 23 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 8.98 x 104 volts.
b) 1.09 x 105 volts.
c) 1.32 x 105 volts.
d) 1.6 x 105 volts.
e) 1.93 x 105 volts.

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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where${\displaystyle {\mathcal {F}}=}$

a) 2
b) 3
c) 3/2
d) 1/2

7) If you put an infinite number of resistors in parallel, what would the total resistance be?

a) ${\displaystyle R_{total}}$ would approach 1 as The No. of Resistors In parallel Approaches Infinity
b) None of these are true.
c) It is not possible to connect that Number of Resistors in parallel.
d) ${\displaystyle R_{total}}$ would approach Zero as The No. of Resistors In parallel Approaches Infinity.

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) What voltage is required to stop a proton moving at a speed of 8 x 107 m/s?

a) 3.3 x 107 volts
b) 5 x 107 volts
c) 7.5 x 107 volts
d) 1.1 x 108 volts
e) 1.7 x 108 volts

10) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
b) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
d) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
e) none of these are correct

11) An object is placed 10.9 cm to the left of a diverging lens with a focal length of 16.3 cm. On the side, at a distance of 5.7 cm from the diverging lens is a converging lens with focal length equal to 4 cm. How far is the final image from the converging lens?

a) 1.88 x 100 cm
b) 5.94 x 100 cm
c) 1.88 x 101 cm
d) 5.94 x 101 cm
e) 1.88 x 102 cm

12) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.05+2.05z)\rho ^{2}{\hat {\rho }}+9.62z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the curved side surface of the cylinder.

a) 2.318E+02
b) 2.808E+02
c) 3.402E+02
d) 4.122E+02
e) 4.994E+02

13) A 5.1 volt battery moves 43 Coulombs of charge in 1.5 hours. What is the power?

a) 4.06 x 10-2 W
b) 4.92 x 10-2 W
c) 5.96 x 10-2 W
d) 7.22 x 10-2 W
e) 8.75 x 10-2 W

14) A circlular capactitor of radius 3.9 m has a gap of 19 mm, and a charge of 78 μC. Compute the surface integral ${\displaystyle c^{-2}\oint {\vec {E}}\cdot d{\vec {A}}}$ over an inner face of the capacitor.

a) 4.55E-11 Vs2m-1
b) 5.51E-11 Vs2m-1
c) 6.68E-11 Vs2m-1
d) 8.09E-11 Vs2m-1
e) 9.80E-11 Vs2m-1

15) A very long and thin solenoid has 2890 turns and is 134 meters long. The wire carrys a current of 7.7A. What is the magnetic field in the center?

a) 1.90E-04 Tesla
b) 2.09E-04 Tesla
c) 2.29E-04 Tesla
d) 2.51E-04 Tesla
e) 2.75E-04 Tesla

### KEY:PhysicsCalc2:FE:V1

PhysicsCalc2152573593386

1) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?

-a) 2.36 x 10-3 newtons
-b) 7.47 x 10-3 newtons
-c) 2.36 x 10-2 newtons
+d) 7.47 x 10-2 newtons
-e) 2.36 x 10-1 newtons

2) A 1.3 Farad capacitor charged with 1.9 Coulombs. What is the force between the plates if they are 0.3 mm apart?

-a) 4025 N.
+b) 4628 N.
-c) 5322 N.
-d) 6121 N.
-e) 7039 N.

3) H is defined by, B=μ0H, where B is magnetic field. A current of 76A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from (-∞,9.6) to (+,9.6).

-a) 3.16E+01 amps
-b) 3.47E+01 amps
+c) 3.80E+01 amps
-d) 4.17E+01 amps
-e) 4.57E+01 amps

4) A battery has an emf of 6.7 volts, and an internal resistance of 348 ${\displaystyle k\Omega }$. It is connected to a 3.8 ${\displaystyle M\Omega }$ resistor. What power is developed in the 3.8 ${\displaystyle M\Omega }$ resistor?

+a) 9.91 ${\displaystyle \mu }$W.
-b) 11.4 ${\displaystyle \mu }$W.
-c) 13.11 ${\displaystyle \mu }$W.
-d) 15.08 ${\displaystyle \mu }$W.
-e) 17.34 ${\displaystyle \mu }$W.

5) Two orbiting satellites are orbiting at a speed of 83 km/s perpendicular to a magnetic field of 57 μT. They are connected by a cable that is 23 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

-a) 8.98 x 104 volts.
+b) 1.09 x 105 volts.
-c) 1.32 x 105 volts.
-d) 1.6 x 105 volts.
-e) 1.93 x 105 volts.

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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where${\displaystyle {\mathcal {F}}=}$

-a) 2
-b) 3
+c) 3/2
-d) 1/2

7) If you put an infinite number of resistors in parallel, what would the total resistance be?

-a) ${\displaystyle R_{total}}$ would approach 1 as The No. of Resistors In parallel Approaches Infinity
-b) None of these are true.
-c) It is not possible to connect that Number of Resistors in parallel.
+d) ${\displaystyle R_{total}}$ would approach Zero as The No. of Resistors In parallel Approaches Infinity.

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) What voltage is required to stop a proton moving at a speed of 8 x 107 m/s?

+a) 3.3 x 107 volts
-b) 5 x 107 volts
-c) 7.5 x 107 volts
-d) 1.1 x 108 volts
-e) 1.7 x 108 volts

10) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
+b) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
-c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
-d) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
-e) none of these are correct

11) An object is placed 10.9 cm to the left of a diverging lens with a focal length of 16.3 cm. On the side, at a distance of 5.7 cm from the diverging lens is a converging lens with focal length equal to 4 cm. How far is the final image from the converging lens?

-a) 1.88 x 100 cm
+b) 5.94 x 100 cm
-c) 1.88 x 101 cm
-d) 5.94 x 101 cm
-e) 1.88 x 102 cm

12) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(2.05+2.05z)\rho ^{2}{\hat {\rho }}+9.62z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the curved side surface of the cylinder.

-a) 2.318E+02
-b) 2.808E+02
-c) 3.402E+02
+d) 4.122E+02
-e) 4.994E+02

13) A 5.1 volt battery moves 43 Coulombs of charge in 1.5 hours. What is the power?

+a) 4.06 x 10-2 W
-b) 4.92 x 10-2 W
-c) 5.96 x 10-2 W
-d) 7.22 x 10-2 W
-e) 8.75 x 10-2 W

14) A circlular capactitor of radius 3.9 m has a gap of 19 mm, and a charge of 78 μC. Compute the surface integral ${\displaystyle c^{-2}\oint {\vec {E}}\cdot d{\vec {A}}}$ over an inner face of the capacitor.

-a) 4.55E-11 Vs2m-1
-b) 5.51E-11 Vs2m-1
-c) 6.68E-11 Vs2m-1
-d) 8.09E-11 Vs2m-1
+e) 9.80E-11 Vs2m-1

15) A very long and thin solenoid has 2890 turns and is 134 meters long. The wire carrys a current of 7.7A. What is the magnetic field in the center?

-a) 1.90E-04 Tesla
+b) 2.09E-04 Tesla
-c) 2.29E-04 Tesla
-d) 2.51E-04 Tesla
-e) 2.75E-04 Tesla

### PhysicsCalc2:FE:V2

PhysicsCalc2152573593386

1) A 0.8 Farad capacitor charged with 1.7 Coulombs. What is the force between the plates if they are 0.5 mm apart?

a) 2065 N.
b) 2375 N.
c) 2732 N.
d) 3141 N.
e) 3613 N.

2) An object is placed 10.8 cm to the left of a diverging lens with a focal length of 15.6 cm. On the side, at a distance of 5.7 cm from the diverging lens is a converging lens with focal length equal to 4 cm. How far is the final image from the converging lens?

a) 5.98 x 10-1 cm
b) 1.89 x 100 cm
c) 5.98 x 100 cm
d) 1.89 x 101 cm
e) 5.98 x 101 cm

3) Two orbiting satellites are orbiting at a speed of 53 km/s perpendicular to a magnetic field of 58 μT. They are connected by a cable that is 29 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

a) 7.36 x 104 volts.
b) 8.91 x 104 volts.
c) 1.08 x 105 volts.
d) 1.31 x 105 volts.
e) 1.59 x 105 volts.

4) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius equal to R. What formula describes the electric field at a distance r < R?

a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
b) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
c) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
d) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
e) none of these are correct

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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where${\displaystyle {\mathcal {F}}=}$

a) 2
b) 1/2
c) 3/2
d) 3

6) A very long and thin solenoid has 1946 turns and is 144 meters long. The wire carrys a current of 9A. What is the magnetic field in the center?

a) 1.06E-04 Tesla
b) 1.16E-04 Tesla
c) 1.27E-04 Tesla
d) 1.39E-04 Tesla
e) 1.53E-04 Tesla

7) H is defined by, B=μ0H, where B is magnetic field. A current of 31A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from (-∞,9.2) to (+,9.2).

a) 1.41E+01 amps
b) 1.55E+01 amps
c) 1.70E+01 amps
d) 1.86E+01 amps
e) 2.04E+01 amps

8) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(1.85+1.33z)\rho ^{3}{\hat {\rho }}+7.52z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the curved side surface of the cylinder.

a) 2.622E+03
b) 3.177E+03
c) 3.849E+03
d) 4.663E+03
e) 5.649E+03

9) A circlular capactitor of radius 4.1 m has a gap of 7 mm, and a charge of 50 μC. Compute the surface integral ${\displaystyle c^{-2}\oint {\vec {E}}\cdot d{\vec {A}}}$ over an inner face of the capacitor.

a) 2.92E-11 Vs2m-1
b) 3.53E-11 Vs2m-1
c) 4.28E-11 Vs2m-1
d) 5.19E-11 Vs2m-1
e) 6.28E-11 Vs2m-1

10) A 1.4 volt battery moves 87 Coulombs of charge in 2 hours. What is the power?

a) 7.85 x 10-3 W
b) 9.51 x 10-3 W
c) 1.15 x 10-2 W
d) 1.4 x 10-2 W
e) 1.69 x 10-2 W

11) 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

12) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?

a) 2.36 x 10-3 newtons
b) 7.47 x 10-3 newtons
c) 2.36 x 10-2 newtons
d) 7.47 x 10-2 newtons
e) 2.36 x 10-1 newtons

13) What voltage is required to stop a proton moving at a speed of 8.1 x 106 m/s?

a) 2.3 x 105 volts
b) 3.4 x 105 volts
c) 5.1 x 105 volts
d) 7.7 x 105 volts
e) 1.2 x 106 volts

14) If you put an infinite number of resistors in parallel, what would the total resistance be?

a) None of these are true.
b) ${\displaystyle R_{total}}$ would approach Zero as The No. of Resistors In parallel Approaches Infinity.
c) ${\displaystyle R_{total}}$ would approach 1 as The No. of Resistors In parallel Approaches Infinity
d) It is not possible to connect that Number of Resistors in parallel.

15) A battery has an emf of 5.6 volts, and an internal resistance of 460 ${\displaystyle k\Omega }$. It is connected to a 2.4 ${\displaystyle M\Omega }$ resistor. What power is developed in the 2.4 ${\displaystyle M\Omega }$ resistor?

a) 6.05 ${\displaystyle \mu }$W.
b) 6.96 ${\displaystyle \mu }$W.
c) 8 ${\displaystyle \mu }$W.
d) 9.2 ${\displaystyle \mu }$W.
e) 10.58 ${\displaystyle \mu }$W.

### KEY:PhysicsCalc2:FE:V2

PhysicsCalc2152573593386

1) A 0.8 Farad capacitor charged with 1.7 Coulombs. What is the force between the plates if they are 0.5 mm apart?

-a) 2065 N.
-b) 2375 N.
-c) 2732 N.
-d) 3141 N.
+e) 3613 N.

2) An object is placed 10.8 cm to the left of a diverging lens with a focal length of 15.6 cm. On the side, at a distance of 5.7 cm from the diverging lens is a converging lens with focal length equal to 4 cm. How far is the final image from the converging lens?

-a) 5.98 x 10-1 cm
-b) 1.89 x 100 cm
+c) 5.98 x 100 cm
-d) 1.89 x 101 cm
-e) 5.98 x 101 cm

3) Two orbiting satellites are orbiting at a speed of 53 km/s perpendicular to a magnetic field of 58 μT. They are connected by a cable that is 29 km long. A voltmeter is attached between a satellite and one end of the cable. The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit. What is the measured voltage?

-a) 7.36 x 104 volts.
+b) 8.91 x 104 volts.
-c) 1.08 x 105 volts.
-d) 1.31 x 105 volts.
-e) 1.59 x 105 volts.

4) A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius equal to R. What formula describes the electric field at a distance r < R?

-a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
+b) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
-c) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
-d) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$
-e) none of these are correct

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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where${\displaystyle {\mathcal {F}}=}$

-a) 2
-b) 1/2
+c) 3/2
-d) 3

6) A very long and thin solenoid has 1946 turns and is 144 meters long. The wire carrys a current of 9A. What is the magnetic field in the center?

-a) 1.06E-04 Tesla
-b) 1.16E-04 Tesla
-c) 1.27E-04 Tesla
-d) 1.39E-04 Tesla
+e) 1.53E-04 Tesla

7) H is defined by, B=μ0H, where B is magnetic field. A current of 31A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from (-∞,9.2) to (+,9.2).

-a) 1.41E+01 amps
+b) 1.55E+01 amps
-c) 1.70E+01 amps
-d) 1.86E+01 amps
-e) 2.04E+01 amps

8) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
${\displaystyle {\vec {\mathfrak {F}}}=(1.85+1.33z)\rho ^{3}{\hat {\rho }}+7.52z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the curved side surface of the cylinder.

-a) 2.622E+03
-b) 3.177E+03
-c) 3.849E+03
-d) 4.663E+03
+e) 5.649E+03

9) A circlular capactitor of radius 4.1 m has a gap of 7 mm, and a charge of 50 μC. Compute the surface integral ${\displaystyle c^{-2}\oint {\vec {E}}\cdot d{\vec {A}}}$ over an inner face of the capacitor.

-a) 2.92E-11 Vs2m-1
-b) 3.53E-11 Vs2m-1
-c) 4.28E-11 Vs2m-1
-d) 5.19E-11 Vs2m-1
+e) 6.28E-11 Vs2m-1

10) A 1.4 volt battery moves 87 Coulombs of charge in 2 hours. What is the power?

-a) 7.85 x 10-3 W
-b) 9.51 x 10-3 W
-c) 1.15 x 10-2 W
-d) 1.4 x 10-2 W
+e) 1.69 x 10-2 W

11) 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

12) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?

-a) 2.36 x 10-3 newtons
-b) 7.47 x 10-3 newtons
-c) 2.36 x 10-2 newtons
+d) 7.47 x 10-2 newtons
-e) 2.36 x 10-1 newtons

13) What voltage is required to stop a proton moving at a speed of 8.1 x 106 m/s?

-a) 2.3 x 105 volts
+b) 3.4 x 105 volts
-c) 5.1 x 105 volts
-d) 7.7 x 105 volts
-e) 1.2 x 106 volts

14) If you put an infinite number of resistors in parallel, what would the total resistance be?

-a) None of these are true.
+b) ${\displaystyle R_{total}}$ would approach Zero as The No. of Resistors In parallel Approaches Infinity.
-c) ${\displaystyle R_{total}}$ would approach 1 as The No. of Resistors In parallel Approaches Infinity
-d) It is not possible to connect that Number of Resistors in parallel.

15) A battery has an emf of 5.6 volts, and an internal resistance of 460 ${\displaystyle k\Omega }$. It is connected to a 2.4 ${\displaystyle M\Omega }$ resistor. What power is developed in the 2.4 ${\displaystyle M\Omega }$ resistor?

-a) 6.05 ${\displaystyle \mu }$W.
-b) 6.96 ${\displaystyle \mu }$W.
-c) 8 ${\displaystyle \mu }$W.
+d) 9.2 ${\displaystyle \mu }$W.
-e) 10.58 ${\displaystyle \mu }$W.