# User:Stambaugh tom/sandbox

PhysicsCalc2149994633029

### PhysicsCalc2:T1:V1

1) How fast is a 2952 eV electron moving?

a) 6.4 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.

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

a) 3.38 x 10-3 unit
b) 4.1 x 10-3 unit
c) 4.96 x 10-3 unit
d) 6.01 x 10-3 unit
e) 7.28 x 10-3 unit

3) Integrate the line integral of ${\displaystyle {\vec {F}}=3.7xy{\hat {x}}+8.4x{\hat {y}}}$ from the origin to the point at x = 2.6 and y = 3.4

a) 5.00E+01
b) 5.34E+01
c) 5.72E+01
d) 6.12E+01
e) 6.55E+01

4) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
${\displaystyle Answer}$ (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) 3−s
b) s−7
c) 7−s
d) 3
e) s−3

5) 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.

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

a) 5.28 x 10-1N/C
b) 6.1 x 10-1N/C
c) 7.04 x 10-1N/C
d) 8.13 x 10-1N/C
e) 9.39 x 10-1N/C

7) A 0.8 Farad capacitor is charged with 1.7 Coulombs. What is the value of the electric field if the plates are 0.5 mm apart?

a) 2.43 kV/m.
b) 2.79 kV/m.
c) 3.21 kV/m.
d) 3.7 kV/m.
e) 4.25 kV/m.

8) 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,
${\displaystyle {\vec {\mathfrak {F}}}=(2.24+1.11z)\rho ^{3}{\hat {\rho }}+8.16z^{3}{\hat {z}}}$
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) 2.769E+03
b) 3.354E+03
c) 4.064E+03
d) 4.923E+03
e) 5.965E+03

9) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
${\displaystyle Answer}$ (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) 3
d) 1/2

10) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
${\displaystyle Answer}$ (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 ${\displaystyle {\mathcal {D}}^{2}+{\mathcal {E}}^{2}=}$:

a) 22 + (9-s)2
b) 72 + (2-s)2
c) 92 + (7-s)2
d) 22 + (7-s)2
e) 92 + (2-s)2

11) What voltage is required accelerate an electron at rest to a speed of 2.8 x 103 m/s?

a) 4.4 x 10-6 volts
b) 6.6 x 10-6 volts
c) 9.9 x 10-6 volts
d) 1.5 x 10-5 volts
e) 2.2 x 10-5 volts

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,
${\displaystyle {\vec {\mathfrak {F}}}=(2.24+2.08z)\rho ^{2}{\hat {\rho }}+8.93z^{3}{\hat {z}}}$
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) 3.13E+03
b) 3.79E+03
c) 4.59E+03
d) 5.56E+03
e) 6.74E+03

### KEY:PhysicsCalc2:T1:V1

PhysicsCalc2149994633029

1) How fast is a 2952 eV electron moving?

-a) 6.4 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.

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

-a) 3.38 x 10-3 unit
-b) 4.1 x 10-3 unit
-c) 4.96 x 10-3 unit
-d) 6.01 x 10-3 unit
+e) 7.28 x 10-3 unit

3) Integrate the line integral of ${\displaystyle {\vec {F}}=3.7xy{\hat {x}}+8.4x{\hat {y}}}$ from the origin to the point at x = 2.6 and y = 3.4

-a) 5.00E+01
-b) 5.34E+01
-c) 5.72E+01
-d) 6.12E+01
+e) 6.55E+01

4) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
${\displaystyle Answer}$ (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) 3−s
-b) s−7
+c) 7−s
-d) 3
-e) s−3

5) 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.

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

-a) 5.28 x 10-1N/C
-b) 6.1 x 10-1N/C
-c) 7.04 x 10-1N/C
-d) 8.13 x 10-1N/C
+e) 9.39 x 10-1N/C

7) A 0.8 Farad capacitor is charged with 1.7 Coulombs. What is the value of the electric field if the plates are 0.5 mm apart?

-a) 2.43 kV/m.
-b) 2.79 kV/m.
-c) 3.21 kV/m.
-d) 3.7 kV/m.
+e) 4.25 kV/m.

8) 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,
${\displaystyle {\vec {\mathfrak {F}}}=(2.24+1.11z)\rho ^{3}{\hat {\rho }}+8.16z^{3}{\hat {z}}}$
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) 2.769E+03
-b) 3.354E+03
-c) 4.064E+03
-d) 4.923E+03
-e) 5.965E+03

9) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
${\displaystyle Answer}$ (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) 3
-d) 1/2

10) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
${\displaystyle Answer}$ (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 ${\displaystyle {\mathcal {D}}^{2}+{\mathcal {E}}^{2}=}$:

+a) 22 + (9-s)2
-b) 72 + (2-s)2
-c) 92 + (7-s)2
-d) 22 + (7-s)2
-e) 92 + (2-s)2

11) What voltage is required accelerate an electron at rest to a speed of 2.8 x 103 m/s?

-a) 4.4 x 10-6 volts
-b) 6.6 x 10-6 volts
-c) 9.9 x 10-6 volts
-d) 1.5 x 10-5 volts
+e) 2.2 x 10-5 volts

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,
${\displaystyle {\vec {\mathfrak {F}}}=(2.24+2.08z)\rho ^{2}{\hat {\rho }}+8.93z^{3}{\hat {z}}}$
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) 3.13E+03
-b) 3.79E+03
-c) 4.59E+03
-d) 5.56E+03
+e) 6.74E+03

### PhysicsCalc2:T1:V2

1) Integrate the line integral of ${\displaystyle {\vec {F}}=2xy{\hat {x}}+7.2x{\hat {y}}}$ from the origin to the point at x = 2.4 and y = 3.2

a) 3.05E+01
b) 3.26E+01
c) 3.49E+01
d) 3.73E+01
e) 3.99E+01

2) 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,
${\displaystyle {\vec {\mathfrak {F}}}=(1.96+2.52z)\rho ^{2}{\hat {\rho }}+7.11z^{2}{\hat {z}}}$
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) 4.522E+02
b) 5.478E+02
c) 6.637E+02
d) 8.041E+02
e) 9.742E+02

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

4) A 1.2 Farad capacitor charged with 1.6 Coulombs. What is the force between the plates if they are 0.4 mm apart?

a) 2319 N.
b) 2667 N.
c) 3067 N.
d) 3527 N.
e) 4056 N.

5) 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,
${\displaystyle {\vec {\mathfrak {F}}}=(2.07+2.87z)\rho ^{2}{\hat {\rho }}+9.56z^{3}{\hat {z}}}$
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) 1.59E+03
b) 1.93E+03
c) 2.34E+03
d) 2.83E+03
e) 3.43E+03

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

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
${\displaystyle Answer}$ (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) 7−s
b) 3−s
c) 3
d) s−7
e) s−3

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

a) 4.87 x 10-1N/C
b) 5.62 x 10-1N/C
c) 6.49 x 10-1N/C
d) 7.49 x 10-1N/C
e) 8.65 x 10-1N/C

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 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

11) A 0.8 Farad capacitor is charged with 1.7 Coulombs. What is the value of the electric field if the plates are 0.5 mm apart?

a) 2.43 kV/m.
b) 2.79 kV/m.
c) 3.21 kV/m.
d) 3.7 kV/m.
e) 4.25 kV/m.

12) 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 ${\displaystyle {\mathcal {D}}^{2}+{\mathcal {E}}^{2}=}$:

a) 22 + (7-s)2
b) 22 + (9-s)2
c) 72 + (2-s)2
d) 92 + (2-s)2
e) 92 + (7-s)2

### KEY:PhysicsCalc2:T1:V2

PhysicsCalc2149994633029

1) Integrate the line integral of ${\displaystyle {\vec {F}}=2xy{\hat {x}}+7.2x{\hat {y}}}$ from the origin to the point at x = 2.4 and y = 3.2

-a) 3.05E+01
-b) 3.26E+01
-c) 3.49E+01
-d) 3.73E+01
+e) 3.99E+01

2) 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,
${\displaystyle {\vec {\mathfrak {F}}}=(1.96+2.52z)\rho ^{2}{\hat {\rho }}+7.11z^{2}{\hat {z}}}$
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) 4.522E+02
-b) 5.478E+02
-c) 6.637E+02
+d) 8.041E+02
-e) 9.742E+02

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

4) A 1.2 Farad capacitor charged with 1.6 Coulombs. What is the force between the plates if they are 0.4 mm apart?

-a) 2319 N.
+b) 2667 N.
-c) 3067 N.
-d) 3527 N.
-e) 4056 N.

5) 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,
${\displaystyle {\vec {\mathfrak {F}}}=(2.07+2.87z)\rho ^{2}{\hat {\rho }}+9.56z^{3}{\hat {z}}}$
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) 1.59E+03
-b) 1.93E+03
+c) 2.34E+03
-d) 2.83E+03
-e) 3.43E+03

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

7) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
${\displaystyle Answer}$ (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) 7−s
-b) 3−s
-c) 3
-d) s−7
-e) s−3

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

-a) 4.87 x 10-1N/C
-b) 5.62 x 10-1N/C
+c) 6.49 x 10-1N/C
-d) 7.49 x 10-1N/C
-e) 8.65 x 10-1N/C

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 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

11) A 0.8 Farad capacitor is charged with 1.7 Coulombs. What is the value of the electric field if the plates are 0.5 mm apart?

-a) 2.43 kV/m.
-b) 2.79 kV/m.
-c) 3.21 kV/m.
-d) 3.7 kV/m.
+e) 4.25 kV/m.

12) 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 ${\displaystyle {\mathcal {D}}^{2}+{\mathcal {E}}^{2}=}$:

-a) 22 + (7-s)2
+b) 22 + (9-s)2
-c) 72 + (2-s)2
-d) 92 + (2-s)2
-e) 92 + (7-s)2

### PhysicsCalc2:T1:V3

1) 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 ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

a) 5.043E+02
b) 6.109E+02
c) 7.402E+02
d) 8.967E+02
e) 1.086E+03

2) How fast is a 2758 eV electron moving?

a) 9.2 x 106 m/s.
b) 1.4 x 107 m/s.
c) 2.1 x 107 m/s.
d) 3.1 x 107 m/s.
e) 4.7 x 107 m/s.

3) What voltage is required accelerate an electron at rest to a speed of 5.6 x 104 m/s?

a) 5.9 x 10-3 volts
b) 8.9 x 10-3 volts
c) 1.3 x 10-2 volts
d) 2 x 10-2 volts
e) 3 x 10-2 volts

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

a) 4.87 x 10-1N/C
b) 5.62 x 10-1N/C
c) 6.49 x 10-1N/C
d) 7.49 x 10-1N/C
e) 8.65 x 10-1N/C

5) Integrate the line integral of ${\displaystyle {\vec {F}}=2.6xy{\hat {x}}+8.6x{\hat {y}}}$ from the origin to the point at x = 2.9 and y = 3.7

a) 7.31E+01
b) 7.82E+01
c) 8.37E+01
d) 8.96E+01
e) 9.58E+01

6) A 0.8 Farad capacitor is charged with 1.7 Coulombs. What is the value of the electric field if the plates are 0.5 mm apart?

a) 2.43 kV/m.
b) 2.79 kV/m.
c) 3.21 kV/m.
d) 3.7 kV/m.
e) 4.25 kV/m.

7) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
${\displaystyle Answer}$ (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 ${\displaystyle {\mathcal {D}}^{2}+{\mathcal {E}}^{2}=}$:

a) 72 + (2-s)2
b) 92 + (2-s)2
c) 22 + (7-s)2
d) 22 + (9-s)2
e) 92 + (7-s)2

8) A 1.4 Farad capacitor charged with 2.3 Coulombs. What is the force between the plates if they are 0.6 mm apart?

a) 2381 N.
b) 2738 N.
c) 3149 N.
d) 3621 N.
e) 4164 N.

9) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
${\displaystyle Answer}$ (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) 7−s
b) 3
c) s−7
d) 3−s
e) s−3

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) =( 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

11) 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) 3/2
b) 2
c) 3
d) 1/2

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,
${\displaystyle {\vec {\mathfrak {F}}}=(1.85+1.33z)\rho ^{3}{\hat {\rho }}+7.52z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the entire surface of the cylinder.

a) 3.18E+03
b) 3.85E+03
c) 4.66E+03
d) 5.65E+03
e) 6.84E+03

### KEY:PhysicsCalc2:T1:V3

PhysicsCalc2149994633029

1) 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 ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

-a) 5.043E+02
-b) 6.109E+02
-c) 7.402E+02
+d) 8.967E+02
-e) 1.086E+03

2) How fast is a 2758 eV electron moving?

-a) 9.2 x 106 m/s.
-b) 1.4 x 107 m/s.
-c) 2.1 x 107 m/s.
+d) 3.1 x 107 m/s.
-e) 4.7 x 107 m/s.

3) What voltage is required accelerate an electron at rest to a speed of 5.6 x 104 m/s?

-a) 5.9 x 10-3 volts
+b) 8.9 x 10-3 volts
-c) 1.3 x 10-2 volts
-d) 2 x 10-2 volts
-e) 3 x 10-2 volts

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

-a) 4.87 x 10-1N/C
-b) 5.62 x 10-1N/C
+c) 6.49 x 10-1N/C
-d) 7.49 x 10-1N/C
-e) 8.65 x 10-1N/C

5) Integrate the line integral of ${\displaystyle {\vec {F}}=2.6xy{\hat {x}}+8.6x{\hat {y}}}$ from the origin to the point at x = 2.9 and y = 3.7

+a) 7.31E+01
-b) 7.82E+01
-c) 8.37E+01
-d) 8.96E+01
-e) 9.58E+01

6) A 0.8 Farad capacitor is charged with 1.7 Coulombs. What is the value of the electric field if the plates are 0.5 mm apart?

-a) 2.43 kV/m.
-b) 2.79 kV/m.
-c) 3.21 kV/m.
-d) 3.7 kV/m.
+e) 4.25 kV/m.

7) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
${\displaystyle Answer}$ (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 ${\displaystyle {\mathcal {D}}^{2}+{\mathcal {E}}^{2}=}$:

-a) 72 + (2-s)2
-b) 92 + (2-s)2
-c) 22 + (7-s)2
+d) 22 + (9-s)2
-e) 92 + (7-s)2

8) A 1.4 Farad capacitor charged with 2.3 Coulombs. What is the force between the plates if they are 0.6 mm apart?

-a) 2381 N.
-b) 2738 N.
+c) 3149 N.
-d) 3621 N.
-e) 4164 N.

9) A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
${\displaystyle Answer}$ (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) 7−s
-b) 3
-c) s−7
-d) 3−s
-e) s−3

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) =( 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

11) 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) 3/2
-b) 2
-c) 3
-d) 1/2

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,
${\displaystyle {\vec {\mathfrak {F}}}=(1.85+1.33z)\rho ^{3}{\hat {\rho }}+7.52z^{2}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\oint {\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the entire surface of the cylinder.

-a) 3.18E+03
-b) 3.85E+03
-c) 4.66E+03
+d) 5.65E+03
-e) 6.84E+03

### PhysicsCalc2:T2:V1

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

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

3) An ideal 8.9 V voltage source is connected to two resistors in parallel. One is 2.1${\displaystyle k\Omega }$, and the other is 4.4 ${\displaystyle k\Omega }$. What is the current through the larger resistor?

a) 1.37 mA.
b) 1.57 mA.
c) 1.81 mA.
d) 2.08 mA.
e) 2.39 mA.

4) A battery has an emf of 5.5 volts, and an internal resistance of 296 ${\displaystyle k\Omega }$. It is connected to a 3.3 ${\displaystyle M\Omega }$ resistor. What power is developed in the 3.3 ${\displaystyle M\Omega }$ resistor?

a) 7.72 ${\displaystyle \mu }$W.
b) 8.88 ${\displaystyle \mu }$W.
c) 10.21 ${\displaystyle \mu }$W.
d) 11.74 ${\displaystyle \mu }$W.
e) 13.5 ${\displaystyle \mu }$W.

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

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

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

a) ${\displaystyle {\frac {6}{3}}\Omega }$.
b) ${\displaystyle {\frac {11}{6}}\Omega }$.
c) ${\displaystyle {\frac {6}{11}}\Omega }$.
d) ${\displaystyle {\frac {3}{6}}\Omega }$.

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

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

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

9) A power supply delivers 138 watts of power to a 206 ohm resistor. What was the applied voltage?

a) 1.39 x 102 volts
b) 1.69 x 102 volts
c) 2.04 x 102 volts
d) 2.47 x 102 volts
e) 3 x 102 volts

10) 3 amps flow through a 1 Ohm resistor. What is the voltage?

a) ${\displaystyle 1V}$
b) None these are correct.
c) ${\displaystyle 3V}$
d) ${\displaystyle {\frac {1}{3}}V}$

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 identical resistors are connected in series. The voltage across both of them is 250 volts. What is the voltage across each one?

a) None of these are true.
b) ${\displaystyle R_{1}=150V}$ and ${\displaystyle R_{2}=100V}$.
c) ${\displaystyle R_{1}=125V}$ and ${\displaystyle R_{2}=125V}$.
d) ${\displaystyle R_{1}=250V}$ and ${\displaystyle R_{2}=0V}$.

### KEY:PhysicsCalc2:T2:V1

PhysicsCalc2149994633029

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

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

3) An ideal 8.9 V voltage source is connected to two resistors in parallel. One is 2.1${\displaystyle k\Omega }$, and the other is 4.4 ${\displaystyle k\Omega }$. What is the current through the larger resistor?

+a) 1.37 mA.
-b) 1.57 mA.
-c) 1.81 mA.
-d) 2.08 mA.
-e) 2.39 mA.

4) A battery has an emf of 5.5 volts, and an internal resistance of 296 ${\displaystyle k\Omega }$. It is connected to a 3.3 ${\displaystyle M\Omega }$ resistor. What power is developed in the 3.3 ${\displaystyle M\Omega }$ resistor?

+a) 7.72 ${\displaystyle \mu }$W.
-b) 8.88 ${\displaystyle \mu }$W.
-c) 10.21 ${\displaystyle \mu }$W.
-d) 11.74 ${\displaystyle \mu }$W.
-e) 13.5 ${\displaystyle \mu }$W.

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

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

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

-a) ${\displaystyle {\frac {6}{3}}\Omega }$.
-b) ${\displaystyle {\frac {11}{6}}\Omega }$.
+c) ${\displaystyle {\frac {6}{11}}\Omega }$.
-d) ${\displaystyle {\frac {3}{6}}\Omega }$.

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

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

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

9) A power supply delivers 138 watts of power to a 206 ohm resistor. What was the applied voltage?

-a) 1.39 x 102 volts
+b) 1.69 x 102 volts
-c) 2.04 x 102 volts
-d) 2.47 x 102 volts
-e) 3 x 102 volts

10) 3 amps flow through a 1 Ohm resistor. What is the voltage?

-a) ${\displaystyle 1V}$
-b) None these are correct.
+c) ${\displaystyle 3V}$
-d) ${\displaystyle {\frac {1}{3}}V}$

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 identical resistors are connected in series. The voltage across both of them is 250 volts. What is the voltage across each one?

-a) None of these are true.
-b) ${\displaystyle R_{1}=150V}$ and ${\displaystyle R_{2}=100V}$.
+c) ${\displaystyle R_{1}=125V}$ and ${\displaystyle R_{2}=125V}$.
-d) ${\displaystyle R_{1}=250V}$ and ${\displaystyle R_{2}=0V}$.

### PhysicsCalc2:T2:V2

1) 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) Discriminant.
c) None of these are true.
d) Power.

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

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

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

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

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

6) A battery has an emf of 7.1 volts, and an internal resistance of 246 ${\displaystyle k\Omega }$. It is connected to a 3.3 ${\displaystyle M\Omega }$ resistor. What power is developed in the 3.3 ${\displaystyle M\Omega }$ resistor?

a) 10 ${\displaystyle \mu }$W.
b) 11.5 ${\displaystyle \mu }$W.
c) 13.23 ${\displaystyle \mu }$W.
d) 15.21 ${\displaystyle \mu }$W.
e) 17.5 ${\displaystyle \mu }$W.

7) An ideal 8.8 V voltage source is connected to two resistors in parallel. One is 0.8${\displaystyle k\Omega }$, and the other is 2.9 ${\displaystyle k\Omega }$. What is the current through the larger resistor?

a) 1.56 mA.
b) 1.8 mA.
c) 2.07 mA.
d) 2.38 mA.
e) 2.74 mA.

8) Two identical resistors are connected in series. The voltage across both of them is 250 volts. What is the voltage across each one?

a) ${\displaystyle R_{1}=125V}$ and ${\displaystyle R_{2}=125V}$.
b) ${\displaystyle R_{1}=150V}$ and ${\displaystyle R_{2}=100V}$.
c) ${\displaystyle R_{1}=250V}$ and ${\displaystyle R_{2}=0V}$.
d) None of these are true.

9) 3 amps flow through a 1 Ohm resistor. What is the voltage?

a) ${\displaystyle 1V}$
b) ${\displaystyle 3V}$
c) ${\displaystyle {\frac {1}{3}}V}$
d) None these are correct.

10) A power supply delivers 138 watts of power to a 206 ohm resistor. What was the applied voltage?

a) 1.39 x 102 volts
b) 1.69 x 102 volts
c) 2.04 x 102 volts
d) 2.47 x 102 volts
e) 3 x 102 volts

11) A 3.1 volt battery moves 40 Coulombs of charge in 0.9 hours. What is the power?

a) 2.61 x 10-2 W
b) 3.16 x 10-2 W
c) 3.83 x 10-2 W
d) 4.64 x 10-2 W
e) 5.62 x 10-2 W

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

a) ${\displaystyle {\frac {11}{6}}\Omega }$.
b) ${\displaystyle {\frac {6}{11}}\Omega }$.
c) ${\displaystyle {\frac {6}{3}}\Omega }$.
d) ${\displaystyle {\frac {3}{6}}\Omega }$.

### KEY:PhysicsCalc2:T2:V2

PhysicsCalc2149994633029

1) 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) Discriminant.
-c) None of these are true.
-d) Power.

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

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

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

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

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

6) A battery has an emf of 7.1 volts, and an internal resistance of 246 ${\displaystyle k\Omega }$. It is connected to a 3.3 ${\displaystyle M\Omega }$ resistor. What power is developed in the 3.3 ${\displaystyle M\Omega }$ resistor?

-a) 10 ${\displaystyle \mu }$W.
-b) 11.5 ${\displaystyle \mu }$W.
+c) 13.23 ${\displaystyle \mu }$W.
-d) 15.21 ${\displaystyle \mu }$W.
-e) 17.5 ${\displaystyle \mu }$W.

7) An ideal 8.8 V voltage source is connected to two resistors in parallel. One is 0.8${\displaystyle k\Omega }$, and the other is 2.9 ${\displaystyle k\Omega }$. What is the current through the larger resistor?

-a) 1.56 mA.
-b) 1.8 mA.
-c) 2.07 mA.
+d) 2.38 mA.
-e) 2.74 mA.

8) Two identical resistors are connected in series. The voltage across both of them is 250 volts. What is the voltage across each one?

+a) ${\displaystyle R_{1}=125V}$ and ${\displaystyle R_{2}=125V}$.
-b) ${\displaystyle R_{1}=150V}$ and ${\displaystyle R_{2}=100V}$.
-c) ${\displaystyle R_{1}=250V}$ and ${\displaystyle R_{2}=0V}$.
-d) None of these are true.

9) 3 amps flow through a 1 Ohm resistor. What is the voltage?

-a) ${\displaystyle 1V}$
+b) ${\displaystyle 3V}$
-c) ${\displaystyle {\frac {1}{3}}V}$
-d) None these are correct.

10) A power supply delivers 138 watts of power to a 206 ohm resistor. What was the applied voltage?

-a) 1.39 x 102 volts
+b) 1.69 x 102 volts
-c) 2.04 x 102 volts
-d) 2.47 x 102 volts
-e) 3 x 102 volts

11) A 3.1 volt battery moves 40 Coulombs of charge in 0.9 hours. What is the power?

-a) 2.61 x 10-2 W
-b) 3.16 x 10-2 W
+c) 3.83 x 10-2 W
-d) 4.64 x 10-2 W
-e) 5.62 x 10-2 W

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

-a) ${\displaystyle {\frac {11}{6}}\Omega }$.
+b) ${\displaystyle {\frac {6}{11}}\Omega }$.
-c) ${\displaystyle {\frac {6}{3}}\Omega }$.
-d) ${\displaystyle {\frac {3}{6}}\Omega }$.

### PhysicsCalc2:T2:V3

1) 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) None of these are true.
c) Resistance.
d) Power.

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

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

4) 3 amps flow through a 1 Ohm resistor. What is the voltage?

a) ${\displaystyle {\frac {1}{3}}V}$
b) None these are correct.
c) ${\displaystyle 3V}$
d) ${\displaystyle 1V}$

5) A 3.1 volt battery moves 40 Coulombs of charge in 0.9 hours. What is the power?

a) 2.61 x 10-2 W
b) 3.16 x 10-2 W
c) 3.83 x 10-2 W
d) 4.64 x 10-2 W
e) 5.62 x 10-2 W

6) 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) ${\displaystyle {\frac {10}{6}}\Omega }$.
d) ${\displaystyle {\frac {6}{10}}\Omega }$.

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

a) ${\displaystyle {\frac {3}{6}}\Omega }$.
b) ${\displaystyle {\frac {11}{6}}\Omega }$.
c) ${\displaystyle {\frac {6}{3}}\Omega }$.
d) ${\displaystyle {\frac {6}{11}}\Omega }$.

8) A battery has an emf of 6.5 volts, and an internal resistance of 446 ${\displaystyle k\Omega }$. It is connected to a 3.5 ${\displaystyle M\Omega }$ resistor. What power is developed in the 3.5 ${\displaystyle M\Omega }$ resistor?

a) 8.26 ${\displaystyle \mu }$W.
b) 9.5 ${\displaystyle \mu }$W.
c) 10.92 ${\displaystyle \mu }$W.
d) 12.56 ${\displaystyle \mu }$W.
e) 14.44 ${\displaystyle \mu }$W.

9) Two identical resistors are connected in series. The voltage across both of them is 250 volts. What is the voltage across each one?

a) ${\displaystyle R_{1}=250V}$ and ${\displaystyle R_{2}=0V}$.
b) None of these are true.
c) ${\displaystyle R_{1}=150V}$ and ${\displaystyle R_{2}=100V}$.
d) ${\displaystyle R_{1}=125V}$ and ${\displaystyle R_{2}=125V}$.

10) An ideal 3.6 V voltage source is connected to two resistors in parallel. One is 2.2${\displaystyle k\Omega }$, and the other is 4.2 ${\displaystyle k\Omega }$. What is the current through the larger resistor?

a) 0.43 mA.
b) 0.49 mA.
c) 0.56 mA.
d) 0.65 mA.
e) 0.74 mA.

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

12) A power supply delivers 145 watts of power to a 244 ohm resistor. What was the applied voltage?

a) 1.88 x 102 volts
b) 2.28 x 102 volts
c) 2.76 x 102 volts
d) 3.34 x 102 volts
e) 4.05 x 102 volts

### KEY:PhysicsCalc2:T2:V3

PhysicsCalc2149994633029

1) 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) None of these are true.
+c) Resistance.
-d) Power.

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

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

4) 3 amps flow through a 1 Ohm resistor. What is the voltage?

-a) ${\displaystyle {\frac {1}{3}}V}$
-b) None these are correct.
+c) ${\displaystyle 3V}$
-d) ${\displaystyle 1V}$

5) A 3.1 volt battery moves 40 Coulombs of charge in 0.9 hours. What is the power?

-a) 2.61 x 10-2 W
-b) 3.16 x 10-2 W
+c) 3.83 x 10-2 W
-d) 4.64 x 10-2 W
-e) 5.62 x 10-2 W

6) 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) ${\displaystyle {\frac {10}{6}}\Omega }$.
-d) ${\displaystyle {\frac {6}{10}}\Omega }$.

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

-a) ${\displaystyle {\frac {3}{6}}\Omega }$.
-b) ${\displaystyle {\frac {11}{6}}\Omega }$.
-c) ${\displaystyle {\frac {6}{3}}\Omega }$.
+d) ${\displaystyle {\frac {6}{11}}\Omega }$.

8) A battery has an emf of 6.5 volts, and an internal resistance of 446 ${\displaystyle k\Omega }$. It is connected to a 3.5 ${\displaystyle M\Omega }$ resistor. What power is developed in the 3.5 ${\displaystyle M\Omega }$ resistor?

-a) 8.26 ${\displaystyle \mu }$W.
+b) 9.5 ${\displaystyle \mu }$W.
-c) 10.92 ${\displaystyle \mu }$W.
-d) 12.56 ${\displaystyle \mu }$W.
-e) 14.44 ${\displaystyle \mu }$W.

9) Two identical resistors are connected in series. The voltage across both of them is 250 volts. What is the voltage across each one?

-a) ${\displaystyle R_{1}=250V}$ and ${\displaystyle R_{2}=0V}$.
-b) None of these are true.
-c) ${\displaystyle R_{1}=150V}$ and ${\displaystyle R_{2}=100V}$.
+d) ${\displaystyle R_{1}=125V}$ and ${\displaystyle R_{2}=125V}$.

10) An ideal 3.6 V voltage source is connected to two resistors in parallel. One is 2.2${\displaystyle k\Omega }$, and the other is 4.2 ${\displaystyle k\Omega }$. What is the current through the larger resistor?

-a) 0.43 mA.
-b) 0.49 mA.
+c) 0.56 mA.
-d) 0.65 mA.
-e) 0.74 mA.

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

12) A power supply delivers 145 watts of power to a 244 ohm resistor. What was the applied voltage?

+a) 1.88 x 102 volts
-b) 2.28 x 102 volts
-c) 2.76 x 102 volts
-d) 3.34 x 102 volts
-e) 4.05 x 102 volts

### PhysicsCalc2:T3:V1

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) An object is placed 3.5 cm to the left of a diverging lens with a focal length of 5.6 cm. How far is the image from the lens?

a) 2.15 x 10-1 cm
b) 3.83 x 10-1 cm
c) 6.81 x 10-1 cm
d) 1.21 x 100 cm
e) 2.15 x 100 cm

3) A resistor has 8 volts across it and 3 Amps going through it. What is the power consumed?

a) 8W
b) 24W
c) 2.2W
d) 3W
4)
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 an object that is too close for comfort
c) how a nearsighted person might see a distant object
d) how a farsighted person might see a distant object

5) An object of height 0.64 cm is placed 112 cm behind a diverging lens with a focal length of 65 cm. What is the height of the image?

a) 1.36 x 10-1 cm
b) 1.63 x 10-1 cm
c) 1.96 x 10-1 cm
d) 2.35 x 10-1 cm
e) 2.82 x 10-1 cm

6) When light passes from glass to air

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

7) When light passes from air to glass

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

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) 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 ${\displaystyle {\mathcal {A}}=}$:

a) 8
b) 2
c) 1/2
d) 4

10) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 μT. The kinetic energy is 437 keV. What is the radius of particle's orbit?

a) 1.3 x 102 m.
b) 4.1 x 102 m.
c) 1.3 x 103 m.
d) 4.1 x 103 m.
e) 1.3 x 104 m.

11) An loop of wire with 80 turns has a radius of 0.52 meters, and is oriented with its axis parallel to a magetic field of 0.15 Tesla. What is the induced voltage if this field is reduced to 19% of its original value in 3.6 seconds?

a) 1.06 x 100 volts
b) 1.29 x 100 volts
c) 1.56 x 100 volts
d) 1.89 x 100 volts
e) 2.29 x 100 volts

12) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 1.08 x 101 s.
b) 3.4 x 101 s.
c) 1.08 x 102 s.
d) 3.4 x 102 s.
e) 1.08 x 103 s.

### KEY:PhysicsCalc2:T3:V1

PhysicsCalc2149994633029

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) An object is placed 3.5 cm to the left of a diverging lens with a focal length of 5.6 cm. How far is the image from the lens?

-a) 2.15 x 10-1 cm
-b) 3.83 x 10-1 cm
-c) 6.81 x 10-1 cm
-d) 1.21 x 100 cm
+e) 2.15 x 100 cm

3) A resistor has 8 volts across it and 3 Amps going through it. What is the power consumed?

-a) 8W
+b) 24W
-c) 2.2W
-d) 3W
4)
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 an object that is too close for comfort
-c) how a nearsighted person might see a distant object
-d) how a farsighted person might see a distant object

5) An object of height 0.64 cm is placed 112 cm behind a diverging lens with a focal length of 65 cm. What is the height of the image?

-a) 1.36 x 10-1 cm
-b) 1.63 x 10-1 cm
-c) 1.96 x 10-1 cm
+d) 2.35 x 10-1 cm
-e) 2.82 x 10-1 cm

6) When light passes from glass to air

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

7) When light passes from air to glass

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

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) 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 ${\displaystyle {\mathcal {A}}=}$:

-a) 8
-b) 2
-c) 1/2
+d) 4

10) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 μT. The kinetic energy is 437 keV. What is the radius of particle's orbit?

-a) 1.3 x 102 m.
-b) 4.1 x 102 m.
-c) 1.3 x 103 m.
-d) 4.1 x 103 m.
+e) 1.3 x 104 m.

11) An loop of wire with 80 turns has a radius of 0.52 meters, and is oriented with its axis parallel to a magetic field of 0.15 Tesla. What is the induced voltage if this field is reduced to 19% of its original value in 3.6 seconds?

-a) 1.06 x 100 volts
-b) 1.29 x 100 volts
-c) 1.56 x 100 volts
-d) 1.89 x 100 volts
+e) 2.29 x 100 volts

12) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

-a) 1.08 x 101 s.
-b) 3.4 x 101 s.
+c) 1.08 x 102 s.
-d) 3.4 x 102 s.
-e) 1.08 x 103 s.

### PhysicsCalc2:T3:V2

1) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
${\displaystyle Answer}$ (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 ${\displaystyle {\mathcal {A}}=}$:

a) 4
b) 2
c) 8
d) 1/2

2) An object of height 0.64 cm is placed 112 cm behind a diverging lens with a focal length of 65 cm. What is the height of the image?

a) 1.36 x 10-1 cm
b) 1.63 x 10-1 cm
c) 1.96 x 10-1 cm
d) 2.35 x 10-1 cm
e) 2.82 x 10-1 cm

3) When light passes from glass to air

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

4) The focal point is where

a) rays meet whenever they pass through a lens
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 are forming an image

5) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 1.08 x 101 s.
b) 3.4 x 101 s.
c) 1.08 x 102 s.
d) 3.4 x 102 s.
e) 1.08 x 103 s.
6)
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 nearsighted person might see a distant object
c) how a farsighted person might see an object that is too close for comfort
d) how a nearsighted person might see an object that is too close for comfort

7) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 μT. The kinetic energy is 437 keV. What is the radius of particle's orbit?

a) 1.3 x 102 m.
b) 4.1 x 102 m.
c) 1.3 x 103 m.
d) 4.1 x 103 m.
e) 1.3 x 104 m.

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) A resistor has 8 volts across it and 3 Amps going through it. What is the power consumed?

a) 24W
b) 2.2W
c) 3W
d) 8W

10) When light passes from air to glass

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

11) An loop of wire with 80 turns has a radius of 0.52 meters, and is oriented with its axis parallel to a magetic field of 0.15 Tesla. What is the induced voltage if this field is reduced to 19% of its original value in 3.6 seconds?

a) 1.06 x 100 volts
b) 1.29 x 100 volts
c) 1.56 x 100 volts
d) 1.89 x 100 volts
e) 2.29 x 100 volts

12) An object is placed 8.4 cm to the left of a diverging lens with a focal length of 6.2 cm. How far is the image from the lens?

a) 2.01 x 100 cm
b) 3.57 x 100 cm
c) 6.34 x 100 cm
d) 1.13 x 101 cm
e) 2.01 x 101 cm

### KEY:PhysicsCalc2:T3:V2

PhysicsCalc2149994633029

1) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
${\displaystyle Answer}$ (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 ${\displaystyle {\mathcal {A}}=}$:

+a) 4
-b) 2
-c) 8
-d) 1/2

2) An object of height 0.64 cm is placed 112 cm behind a diverging lens with a focal length of 65 cm. What is the height of the image?

-a) 1.36 x 10-1 cm
-b) 1.63 x 10-1 cm
-c) 1.96 x 10-1 cm
+d) 2.35 x 10-1 cm
-e) 2.82 x 10-1 cm

3) When light passes from glass to air

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

4) The focal point is where

-a) rays meet whenever they pass through a lens
-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 are forming an image

5) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

-a) 1.08 x 101 s.
-b) 3.4 x 101 s.
+c) 1.08 x 102 s.
-d) 3.4 x 102 s.
-e) 1.08 x 103 s.
6)
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 nearsighted person might see a distant object
+c) how a farsighted person might see an object that is too close for comfort
-d) how a nearsighted person might see an object that is too close for comfort

7) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 μT. The kinetic energy is 437 keV. What is the radius of particle's orbit?

-a) 1.3 x 102 m.
-b) 4.1 x 102 m.
-c) 1.3 x 103 m.
-d) 4.1 x 103 m.
+e) 1.3 x 104 m.

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) A resistor has 8 volts across it and 3 Amps going through it. What is the power consumed?

+a) 24W
-b) 2.2W
-c) 3W
-d) 8W

10) When light passes from air to glass

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

11) An loop of wire with 80 turns has a radius of 0.52 meters, and is oriented with its axis parallel to a magetic field of 0.15 Tesla. What is the induced voltage if this field is reduced to 19% of its original value in 3.6 seconds?

-a) 1.06 x 100 volts
-b) 1.29 x 100 volts
-c) 1.56 x 100 volts
-d) 1.89 x 100 volts
+e) 2.29 x 100 volts

12) An object is placed 8.4 cm to the left of a diverging lens with a focal length of 6.2 cm. How far is the image from the lens?

-a) 2.01 x 100 cm
+b) 3.57 x 100 cm
-c) 6.34 x 100 cm
-d) 1.13 x 101 cm
-e) 2.01 x 101 cm

### PhysicsCalc2:T3:V3

1) A resistor has 8 volts across it and 3 Amps going through it. What is the power consumed?

a) 8W
b) 2.2W
c) 3W
d) 24W
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 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 an object that is too close for comfort

3) 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

4) 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

5) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 μT. The kinetic energy is 437 keV. What is the radius of particle's orbit?

a) 1.3 x 102 m.
b) 4.1 x 102 m.
c) 1.3 x 103 m.
d) 4.1 x 103 m.
e) 1.3 x 104 m.

6) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 1.08 x 101 s.
b) 3.4 x 101 s.
c) 1.08 x 102 s.
d) 3.4 x 102 s.
e) 1.08 x 103 s.

7) 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 whenever they pass through a lens
d) rays meet whenever they are forming an image
e) rays meet if they are parallel to each other

8) An object is placed 6.3 cm to the left of a diverging lens with a focal length of 8.9 cm. How far is the image from the lens?

a) 1.17 x 100 cm
b) 2.07 x 100 cm
c) 3.69 x 100 cm
d) 6.56 x 100 cm
e) 1.17 x 101 cm

9) When light passes from glass to air

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

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) 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 ${\displaystyle {\mathcal {A}}=}$:

a) 4
b) 1/2
c) 2
d) 8

12) When light passes from air to glass

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

### KEY:PhysicsCalc2:T3:V3

PhysicsCalc2149994633029

1) A resistor has 8 volts across it and 3 Amps going through it. What is the power consumed?

-a) 8W
-b) 2.2W
-c) 3W
+d) 24W
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 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 an object that is too close for comfort

3) 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

4) 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

5) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 μT. The kinetic energy is 437 keV. What is the radius of particle's orbit?

-a) 1.3 x 102 m.
-b) 4.1 x 102 m.
-c) 1.3 x 103 m.
-d) 4.1 x 103 m.
+e) 1.3 x 104 m.

6) A 65 μF capacitor is connected in series to a 414 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

-a) 1.08 x 101 s.
-b) 3.4 x 101 s.
+c) 1.08 x 102 s.
-d) 3.4 x 102 s.
-e) 1.08 x 103 s.

7) 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 whenever they pass through a lens
-d) rays meet whenever they are forming an image
-e) rays meet if they are parallel to each other

8) An object is placed 6.3 cm to the left of a diverging lens with a focal length of 8.9 cm. How far is the image from the lens?

-a) 1.17 x 100 cm
-b) 2.07 x 100 cm
+c) 3.69 x 100 cm
-d) 6.56 x 100 cm
-e) 1.17 x 101 cm

9) When light passes from glass to air

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

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) 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 ${\displaystyle {\mathcal {A}}=}$:

+a) 4
-b) 1/2
-c) 2
-d) 8

12) When light passes from air to glass

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

### PhysicsCalc2:T4:V1

1) An object is placed 10.2 cm to the left of a diverging lens with a focal length of 16.6 cm. On the side, at a distance of 5.6 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) 6.02 x 10-1 cm
b) 1.9 x 100 cm
c) 6.02 x 100 cm
d) 1.9 x 101 cm
e) 6.02 x 101 cm

2) Which lens has the shorter focal length?

a)
b) They have the same focal lengh.
c)

3) A circlular capactitor of radius 4.2 m has a gap of 12 mm, and a charge of 94 μC. What is the electric field between the plates?

a) 1.92E+05 N/C (or V/m)
b) 2.32E+05 N/C (or V/m)
c) 2.81E+05 N/C (or V/m)
d) 3.41E+05 N/C (or V/m)
e) 4.13E+05 N/C (or V/m)

4) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H_{y}}$ at the point (8.0883,5.5335) if a current of 9.6A flows through a wire that runs along the z axis?

a) 8.90E-02 A/m
b) 9.76E-02 A/m
c) 1.07E-01 A/m
d) 1.17E-01 A/m
e) 1.29E-01 A/m

5) What is the sum of 3.4 apples plus 62 apples?

a) 4.96E+01 apples
b) 5.44E+01 apples
c) 5.96E+01 apples
d) 6.54E+01 apples
e) 7.17E+01 apples

6) A circlular capactitor of radius 3.8 m has a gap of 14 mm, and a charge of 83 μC. Compute the surface integral ${\displaystyle c^{-2}\oint {\vec {E}}\cdot d{\vec {A}}}$ over an inner face of the capacitor.

a) 7.11E-11 Vs2m-1
b) 8.61E-11 Vs2m-1
c) 1.04E-10 Vs2m-1
d) 1.26E-10 Vs2m-1
e) 1.53E-10 Vs2m-1

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

a) 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

8) Amphere's law for magnetostatic currents is that ${\displaystyle \oint {\vec {H}}\cdot {\vec {d\ell }}=\int {\vec {J}}\cdot {\vec {dA}}}$ equals the current enclosed by the closed loop, and ${\displaystyle B=\mu _{0}H}$ is the magnetic field. A current of 6.7A flows upward along the z axis. Noting that for this geometry, ${\displaystyle \oint {\vec {B}}\cdot {\vec {d\ell }}=B\oint d\ell }$, calculate the line integral ${\displaystyle \oint d\ell }$ for a circle of radius 4.1m.

a) 2.58E+01 m
b) 2.82E+01 m
c) 3.10E+01 m
d) 3.40E+01 m
e) 3.72E+01 m

9) H is defined by, B=μ0H, where B is magnetic field. A current of 89A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (0,4.8) to the point (4.8,4.8).

a) 9.25E+00 amps
b) 1.01E+01 amps
c) 1.11E+01 amps
d) 1.22E+01 amps
e) 1.34E+01 amps

10) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H}$ at a distance of 9.8m from a wire carrying a current of 6.9A?

a) 1.02E-01 A/m
b) 1.12E-01 A/m
c) 1.23E-01 A/m
d) 1.35E-01 A/m
e) 1.48E-01 A/m

11) After passing through a the lens of a camera or the eye, the focal point is defined as where the rays meet.

a) true
b) false

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

PhysicsCalc2149994633029

1) An object is placed 10.2 cm to the left of a diverging lens with a focal length of 16.6 cm. On the side, at a distance of 5.6 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) 6.02 x 10-1 cm
-b) 1.9 x 100 cm
+c) 6.02 x 100 cm
-d) 1.9 x 101 cm
-e) 6.02 x 101 cm

2) Which lens has the shorter focal length?

-a)
-b) They have the same focal lengh.
+c)

3) A circlular capactitor of radius 4.2 m has a gap of 12 mm, and a charge of 94 μC. What is the electric field between the plates?

+a) 1.92E+05 N/C (or V/m)
-b) 2.32E+05 N/C (or V/m)
-c) 2.81E+05 N/C (or V/m)
-d) 3.41E+05 N/C (or V/m)
-e) 4.13E+05 N/C (or V/m)

4) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H_{y}}$ at the point (8.0883,5.5335) if a current of 9.6A flows through a wire that runs along the z axis?

-a) 8.90E-02 A/m
-b) 9.76E-02 A/m
-c) 1.07E-01 A/m
-d) 1.17E-01 A/m
+e) 1.29E-01 A/m

5) What is the sum of 3.4 apples plus 62 apples?

-a) 4.96E+01 apples
-b) 5.44E+01 apples
-c) 5.96E+01 apples
+d) 6.54E+01 apples
-e) 7.17E+01 apples

6) A circlular capactitor of radius 3.8 m has a gap of 14 mm, and a charge of 83 μC. Compute the surface integral ${\displaystyle c^{-2}\oint {\vec {E}}\cdot d{\vec {A}}}$ over an inner face of the capacitor.

-a) 7.11E-11 Vs2m-1
-b) 8.61E-11 Vs2m-1
+c) 1.04E-10 Vs2m-1
-d) 1.26E-10 Vs2m-1
-e) 1.53E-10 Vs2m-1

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

-a) 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

8) Amphere's law for magnetostatic currents is that ${\displaystyle \oint {\vec {H}}\cdot {\vec {d\ell }}=\int {\vec {J}}\cdot {\vec {dA}}}$ equals the current enclosed by the closed loop, and ${\displaystyle B=\mu _{0}H}$ is the magnetic field. A current of 6.7A flows upward along the z axis. Noting that for this geometry, ${\displaystyle \oint {\vec {B}}\cdot {\vec {d\ell }}=B\oint d\ell }$, calculate the line integral ${\displaystyle \oint d\ell }$ for a circle of radius 4.1m.

+a) 2.58E+01 m
-b) 2.82E+01 m
-c) 3.10E+01 m
-d) 3.40E+01 m
-e) 3.72E+01 m

9) H is defined by, B=μ0H, where B is magnetic field. A current of 89A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (0,4.8) to the point (4.8,4.8).

-a) 9.25E+00 amps
-b) 1.01E+01 amps
+c) 1.11E+01 amps
-d) 1.22E+01 amps
-e) 1.34E+01 amps

10) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H}$ at a distance of 9.8m from a wire carrying a current of 6.9A?

-a) 1.02E-01 A/m
+b) 1.12E-01 A/m
-c) 1.23E-01 A/m
-d) 1.35E-01 A/m
-e) 1.48E-01 A/m

11) After passing through a the lens of a camera or the eye, the focal point is defined as where the rays meet.

-a) true
+b) false

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

1) 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

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

a) 3.47 x 10-1 unit
b) 4.2 x 10-1 unit
c) 5.09 x 10-1 unit
d) 6.17 x 10-1 unit
e) 7.47 x 10-1 unit

3) Amphere's law for magnetostatic currents is that ${\displaystyle \oint {\vec {H}}\cdot {\vec {d\ell }}=\int {\vec {J}}\cdot {\vec {dA}}}$ equals the current enclosed by the closed loop, and ${\displaystyle B=\mu _{0}H}$ is the magnetic field. A current of 5.7A flows upward along the z axis. Noting that for this geometry, ${\displaystyle \oint {\vec {B}}\cdot {\vec {d\ell }}=B\oint d\ell }$, calculate the line integral ${\displaystyle \oint d\ell }$ for a circle of radius 9.2m.

a) 4.38E+01 m
b) 4.81E+01 m
c) 5.27E+01 m
d) 5.78E+01 m
e) 6.34E+01 m

4) What is the sum of 7.2 apples plus 9 apples?

a) 1.62E+01 apples
b) 1.78E+01 apples
c) 1.95E+01 apples
d) 2.14E+01 apples
e) 2.34E+01 apples

5) An object is placed 13.7 cm to the left of a diverging lens with a focal length of 17.7 cm. On the side, at a distance of 5.5 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) 5.73 x 10-2 cm
b) 1.81 x 10-1 cm
c) 5.73 x 10-1 cm
d) 1.81 x 100 cm
e) 5.73 x 100 cm

6) After passing through a the lens of a camera or the eye, the focal point is defined as where the rays meet.

a) true
b) false

7) A circlular capactitor of radius 4.2 m has a gap of 12 mm, and a charge of 94 μC. What is the electric field between the plates?

a) 1.92E+05 N/C (or V/m)
b) 2.32E+05 N/C (or V/m)
c) 2.81E+05 N/C (or V/m)
d) 3.41E+05 N/C (or V/m)
e) 4.13E+05 N/C (or V/m)

8) Which lens has the shorter focal length?

a) They have the same focal lengh.
b)
c)

9) H is defined by, B=μ0H, where B is magnetic field. A current of 37A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (0,8.4) to the point (8.4,0).

a) 8.44E+00 amps
b) 9.25E+00 amps
c) 1.01E+01 amps
d) 1.11E+01 amps
e) 1.22E+01 amps

10) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H_{y}}$ at the point (2.8594,3.6033) if a current of 9.8A flows through a wire that runs along the z axis?

a) 1.75E-01 A/m
b) 1.92E-01 A/m
c) 2.11E-01 A/m
d) 2.31E-01 A/m
e) 2.53E-01 A/m

11) 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

12) H is defined by, B=μ0H, where B is magnetic field. A current of 36A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (0,8.6) to the point (8.6,8.6).

a) 4.50E+00 amps
b) 4.93E+00 amps
c) 5.41E+00 amps
d) 5.93E+00 amps
e) 6.50E+00 amps

### KEY:PhysicsCalc2:T4:V2

PhysicsCalc2149994633029

1) 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

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

+a) 3.47 x 10-1 unit
-b) 4.2 x 10-1 unit
-c) 5.09 x 10-1 unit
-d) 6.17 x 10-1 unit
-e) 7.47 x 10-1 unit

3) Amphere's law for magnetostatic currents is that ${\displaystyle \oint {\vec {H}}\cdot {\vec {d\ell }}=\int {\vec {J}}\cdot {\vec {dA}}}$ equals the current enclosed by the closed loop, and ${\displaystyle B=\mu _{0}H}$ is the magnetic field. A current of 5.7A flows upward along the z axis. Noting that for this geometry, ${\displaystyle \oint {\vec {B}}\cdot {\vec {d\ell }}=B\oint d\ell }$, calculate the line integral ${\displaystyle \oint d\ell }$ for a circle of radius 9.2m.

-a) 4.38E+01 m
-b) 4.81E+01 m
-c) 5.27E+01 m
+d) 5.78E+01 m
-e) 6.34E+01 m

4) What is the sum of 7.2 apples plus 9 apples?

+a) 1.62E+01 apples
-b) 1.78E+01 apples
-c) 1.95E+01 apples
-d) 2.14E+01 apples
-e) 2.34E+01 apples

5) An object is placed 13.7 cm to the left of a diverging lens with a focal length of 17.7 cm. On the side, at a distance of 5.5 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) 5.73 x 10-2 cm
-b) 1.81 x 10-1 cm
-c) 5.73 x 10-1 cm
-d) 1.81 x 100 cm
+e) 5.73 x 100 cm

6) After passing through a the lens of a camera or the eye, the focal point is defined as where the rays meet.

-a) true
+b) false

7) A circlular capactitor of radius 4.2 m has a gap of 12 mm, and a charge of 94 μC. What is the electric field between the plates?

+a) 1.92E+05 N/C (or V/m)
-b) 2.32E+05 N/C (or V/m)
-c) 2.81E+05 N/C (or V/m)
-d) 3.41E+05 N/C (or V/m)
-e) 4.13E+05 N/C (or V/m)

8) Which lens has the shorter focal length?

-a) They have the same focal lengh.
-b)
+c)

9) H is defined by, B=μ0H, where B is magnetic field. A current of 37A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (0,8.4) to the point (8.4,0).

-a) 8.44E+00 amps
+b) 9.25E+00 amps
-c) 1.01E+01 amps
-d) 1.11E+01 amps
-e) 1.22E+01 amps

10) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H_{y}}$ at the point (2.8594,3.6033) if a current of 9.8A flows through a wire that runs along the z axis?

-a) 1.75E-01 A/m
-b) 1.92E-01 A/m
+c) 2.11E-01 A/m
-d) 2.31E-01 A/m
-e) 2.53E-01 A/m

11) 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

12) H is defined by, B=μ0H, where B is magnetic field. A current of 36A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (0,8.6) to the point (8.6,8.6).

+a) 4.50E+00 amps
-b) 4.93E+00 amps
-c) 5.41E+00 amps
-d) 5.93E+00 amps
-e) 6.50E+00 amps

### PhysicsCalc2:T4:V3

1) A circlular capactitor of radius 3.9 m has a gap of 19 mm, and a charge of 66 μC. What is the electric field between the plates?

a) 1.29E+05 N/C (or V/m)
b) 1.56E+05 N/C (or V/m)
c) 1.89E+05 N/C (or V/m)
d) 2.29E+05 N/C (or V/m)
e) 2.77E+05 N/C (or V/m)

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

a) 2.36 x 10-1 unit
b) 2.86 x 10-1 unit
c) 3.47 x 10-1 unit
d) 4.2 x 10-1 unit
e) 5.09 x 10-1 unit

3) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H}$ at a distance of 8.2m from a wire carrying a current of 7.2A?

a) 9.67E-02 A/m
b) 1.06E-01 A/m
c) 1.16E-01 A/m
d) 1.27E-01 A/m
e) 1.40E-01 A/m

4) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H_{y}}$ at the point (2.8594,3.6033) if a current of 9.8A flows through a wire that runs along the z axis?

a) 1.75E-01 A/m
b) 1.92E-01 A/m
c) 2.11E-01 A/m
d) 2.31E-01 A/m
e) 2.53E-01 A/m

5) Which lens has the shorter focal length?

a)
b) They have the same focal lengh.
c)

6) What is the sum of 0.2 apples plus 57 apples?

a) 5.72E+01 apples
b) 6.27E+01 apples
c) 6.88E+01 apples
d) 7.54E+01 apples
e) 8.27E+01 apples

7) H is defined by, B=μ0H, where B is magnetic field. A current of 88A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (0,6.6) to the point (6.6,6.6).

a) 9.15E+00 amps
b) 1.00E+01 amps
c) 1.10E+01 amps
d) 1.21E+01 amps
e) 1.32E+01 amps

8) 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

9) Amphere's law for magnetostatic currents is that ${\displaystyle \oint {\vec {H}}\cdot {\vec {d\ell }}=\int {\vec {J}}\cdot {\vec {dA}}}$ equals the current enclosed by the closed loop, and ${\displaystyle B=\mu _{0}H}$ is the magnetic field. A current of 8.6A flows upward along the z axis. Noting that for this geometry, ${\displaystyle \oint {\vec {B}}\cdot {\vec {d\ell }}=B\oint d\ell }$, calculate the line integral ${\displaystyle \oint d\ell }$ for a circle of radius 8.8m.

a) 3.83E+01 m
b) 4.19E+01 m
c) 4.60E+01 m
d) 5.04E+01 m
e) 5.53E+01 m

10) After passing through a the lens of a camera or the eye, the focal point is defined as where the rays meet.

a) true
b) false

11) 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

12) A circlular capactitor of radius 4.1 m has a gap of 8 mm, and a charge of 24 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) 2.49E-11 Vs2m-1
c) 3.02E-11 Vs2m-1
d) 3.65E-11 Vs2m-1
e) 4.43E-11 Vs2m-1

### KEY:PhysicsCalc2:T4:V3

PhysicsCalc2149994633029

1) A circlular capactitor of radius 3.9 m has a gap of 19 mm, and a charge of 66 μC. What is the electric field between the plates?

-a) 1.29E+05 N/C (or V/m)
+b) 1.56E+05 N/C (or V/m)
-c) 1.89E+05 N/C (or V/m)
-d) 2.29E+05 N/C (or V/m)
-e) 2.77E+05 N/C (or V/m)

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

-a) 2.36 x 10-1 unit
-b) 2.86 x 10-1 unit
+c) 3.47 x 10-1 unit
-d) 4.2 x 10-1 unit
-e) 5.09 x 10-1 unit

3) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H}$ at a distance of 8.2m from a wire carrying a current of 7.2A?

-a) 9.67E-02 A/m
-b) 1.06E-01 A/m
-c) 1.16E-01 A/m
-d) 1.27E-01 A/m
+e) 1.40E-01 A/m

4) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H_{y}}$ at the point (2.8594,3.6033) if a current of 9.8A flows through a wire that runs along the z axis?

-a) 1.75E-01 A/m
-b) 1.92E-01 A/m
+c) 2.11E-01 A/m
-d) 2.31E-01 A/m
-e) 2.53E-01 A/m

5) Which lens has the shorter focal length?

-a)
-b) They have the same focal lengh.
+c)

6) What is the sum of 0.2 apples plus 57 apples?

+a) 5.72E+01 apples
-b) 6.27E+01 apples
-c) 6.88E+01 apples
-d) 7.54E+01 apples
-e) 8.27E+01 apples

7) H is defined by, B=μ0H, where B is magnetic field. A current of 88A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (0,6.6) to the point (6.6,6.6).

-a) 9.15E+00 amps
-b) 1.00E+01 amps
+c) 1.10E+01 amps
-d) 1.21E+01 amps
-e) 1.32E+01 amps

8) 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

9) Amphere's law for magnetostatic currents is that ${\displaystyle \oint {\vec {H}}\cdot {\vec {d\ell }}=\int {\vec {J}}\cdot {\vec {dA}}}$ equals the current enclosed by the closed loop, and ${\displaystyle B=\mu _{0}H}$ is the magnetic field. A current of 8.6A flows upward along the z axis. Noting that for this geometry, ${\displaystyle \oint {\vec {B}}\cdot {\vec {d\ell }}=B\oint d\ell }$, calculate the line integral ${\displaystyle \oint d\ell }$ for a circle of radius 8.8m.

-a) 3.83E+01 m
-b) 4.19E+01 m
-c) 4.60E+01 m
-d) 5.04E+01 m
+e) 5.53E+01 m

10) After passing through a the lens of a camera or the eye, the focal point is defined as where the rays meet.

-a) true
+b) false

11) 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

12) A circlular capactitor of radius 4.1 m has a gap of 8 mm, and a charge of 24 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) 2.49E-11 Vs2m-1
+c) 3.02E-11 Vs2m-1
-d) 3.65E-11 Vs2m-1
-e) 4.43E-11 Vs2m-1

### PhysicsCalc2:FE:V1

1) 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

2) What voltage is required accelerate an electron at rest to a speed of 1.5 x 103 m/s?

a) 1.9 x 10-6 volts
b) 2.8 x 10-6 volts
c) 4.3 x 10-6 volts
d) 6.4 x 10-6 volts
e) 9.6 x 10-6 volts

3) 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.

4) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal. To counter the magnetic force, a voltage is applied between two large parallel plates that are 59 mm apart. What must be the applied voltage if the magnetic field is 45μT?

a) 1.1 x 100 volts
b) 3.6 x 100 volts
c) 1.1 x 101 volts
d) 3.6 x 101 volts
e) 1.1 x 102 volts

5) H is defined by, B=μ0H, where B is magnetic field. A current of 91A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (-9.6, 9.6) to the point (9.6, 9.6).

a) 1.73E+01 amps
b) 1.89E+01 amps
c) 2.07E+01 amps
d) 2.28E+01 amps
e) 2.49E+01 amps

6) 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

7) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
${\displaystyle Answer}$ (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) 8
b) 3−s
c) s−7
d) 7−s
e) s−3

8) 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,
${\displaystyle {\vec {\mathfrak {F}}}=(1.86+2.43z)\rho ^{2}{\hat {\rho }}+9.75z^{2}{\hat {z}}}$
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) 4.63E+02
b) 5.61E+02
c) 6.80E+02
d) 8.23E+02
e) 9.98E+02

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

a) 2.37 x 101degrees
b) 2.74 x 101degrees
c) 3.16 x 101degrees
d) 3.65 x 101degrees
e) 4.22 x 101degrees

10) A circlular capactitor of radius 4.6 m has a gap of 7 mm, and a charge of 18 μC. The capacitor is discharged through a 9 kΩ resistor. What is the decay time?

a) 6.25E-04 s
b) 7.57E-04 s
c) 9.17E-04 s
d) 1.11E-03 s
e) 1.35E-03 s

11) 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.

12) The same parallel plate capacitor, with area 1.05 m2, plate separation 0.63mm, and an applied voltage of 4.35 kV. How much charge is stored?

a) 42.21 μC.
b) 48.54 μC.
c) 55.82 μC.
d) 64.19 μC.
e) 73.82 μC.

13) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H_{y}}$ at the point (5.1588,1.5958) if a current of 5A flows through a wire that runs along the z axis?

a) 1.41E-01 A/m
b) 1.54E-01 A/m
c) 1.69E-01 A/m
d) 1.86E-01 A/m
e) 2.03E-01 A/m
14) 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) ${\displaystyle I_{1}=10A}$; ${\displaystyle I_{2}=50A}$; ${\displaystyle I_{3}=33A}$; ${\displaystyle I_{4}=25A}$..
c) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=5A}$; ${\displaystyle I_{3}=3.3A}$; ${\displaystyle I_{4}=2.5A}$.
d) ${\displaystyle I_{1}=0.25A}$; ${\displaystyle I_{2}=0.33A}$; ${\displaystyle I_{3}=0.5A}$; ${\displaystyle I_{4}=0.1A}$.

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

### KEY:PhysicsCalc2:FE:V1

PhysicsCalc2149994633029

1) 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

2) What voltage is required accelerate an electron at rest to a speed of 1.5 x 103 m/s?

-a) 1.9 x 10-6 volts
-b) 2.8 x 10-6 volts
-c) 4.3 x 10-6 volts
+d) 6.4 x 10-6 volts
-e) 9.6 x 10-6 volts

3) 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.

4) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal. To counter the magnetic force, a voltage is applied between two large parallel plates that are 59 mm apart. What must be the applied voltage if the magnetic field is 45μT?

-a) 1.1 x 100 volts
-b) 3.6 x 100 volts
-c) 1.1 x 101 volts
+d) 3.6 x 101 volts
-e) 1.1 x 102 volts

5) H is defined by, B=μ0H, where B is magnetic field. A current of 91A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (-9.6, 9.6) to the point (9.6, 9.6).

-a) 1.73E+01 amps
-b) 1.89E+01 amps
-c) 2.07E+01 amps
+d) 2.28E+01 amps
-e) 2.49E+01 amps

6) 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

7) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
${\displaystyle Answer}$ (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) 8
-b) 3−s
-c) s−7
+d) 7−s
-e) s−3

8) 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,
${\displaystyle {\vec {\mathfrak {F}}}=(1.86+2.43z)\rho ^{2}{\hat {\rho }}+9.75z^{2}{\hat {z}}}$
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) 4.63E+02
+b) 5.61E+02
-c) 6.80E+02
-d) 8.23E+02
-e) 9.98E+02

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

-a) 2.37 x 101degrees
+b) 2.74 x 101degrees
-c) 3.16 x 101degrees
-d) 3.65 x 101degrees
-e) 4.22 x 101degrees

10) A circlular capactitor of radius 4.6 m has a gap of 7 mm, and a charge of 18 μC. The capacitor is discharged through a 9 kΩ resistor. What is the decay time?

-a) 6.25E-04 s
+b) 7.57E-04 s
-c) 9.17E-04 s
-d) 1.11E-03 s
-e) 1.35E-03 s

11) 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.

12) The same parallel plate capacitor, with area 1.05 m2, plate separation 0.63mm, and an applied voltage of 4.35 kV. How much charge is stored?

-a) 42.21 μC.
-b) 48.54 μC.
-c) 55.82 μC.
+d) 64.19 μC.
-e) 73.82 μC.

13) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H_{y}}$ at the point (5.1588,1.5958) if a current of 5A flows through a wire that runs along the z axis?

+a) 1.41E-01 A/m
-b) 1.54E-01 A/m
-c) 1.69E-01 A/m
-d) 1.86E-01 A/m
-e) 2.03E-01 A/m
14) 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) ${\displaystyle I_{1}=10A}$; ${\displaystyle I_{2}=50A}$; ${\displaystyle I_{3}=33A}$; ${\displaystyle I_{4}=25A}$..
-c) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=5A}$; ${\displaystyle I_{3}=3.3A}$; ${\displaystyle I_{4}=2.5A}$.
-d) ${\displaystyle I_{1}=0.25A}$; ${\displaystyle I_{2}=0.33A}$; ${\displaystyle I_{3}=0.5A}$; ${\displaystyle I_{4}=0.1A}$.

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

### PhysicsCalc2:FE:V2

1) Two orbiting satellites are orbiting at a speed of 58 km/s perpendicular to a magnetic field of 46 μT. They are connected by a cable that is 22 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) 2.72 x 104 volts.
b) 3.3 x 104 volts.
c) 4 x 104 volts.
d) 4.84 x 104 volts.
e) 5.87 x 104 volts.

2) A battery has an emf of 5.6 volts, and an internal resistance of 450 ${\displaystyle k\Omega }$. It is connected to a 2.7 ${\displaystyle M\Omega }$ resistor. What power is developed in the 2.7 ${\displaystyle M\Omega }$ resistor?

a) 4.88 ${\displaystyle \mu }$W.
b) 5.61 ${\displaystyle \mu }$W.
c) 6.45 ${\displaystyle \mu }$W.
d) 7.42 ${\displaystyle \mu }$W.
e) 8.53 ${\displaystyle \mu }$W.

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

4) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
${\displaystyle Answer}$ (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−3
b) 3−s
c) s−7
d) 8
e) 7−s

5) H is defined by, B=μ0H, where B is magnetic field. A current of 51A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (-6.8, 6.8) to the point (6.8, 6.8).

a) 1.06E+01 amps
b) 1.16E+01 amps
c) 1.28E+01 amps
d) 1.40E+01 amps
e) 1.53E+01 amps

6) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H_{y}}$ at the point (5.6728,2.7403) if a current of 7.4A flows through a wire that runs along the z axis?

a) 1.28E-01 A/m
b) 1.40E-01 A/m
c) 1.54E-01 A/m
d) 1.68E-01 A/m
e) 1.85E-01 A/m

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

a) 4.47 x 101degrees
b) 5.17 x 101degrees
c) 5.97 x 101degrees
d) 6.89 x 101degrees
e) 7.96 x 101degrees

8) A 4.7 volt battery moves 50 Coulombs of charge in 1.3 hours. What is the power?

a) 4.14 x 10-2 W
b) 5.02 x 10-2 W
c) 6.08 x 10-2 W
d) 7.37 x 10-2 W
e) 8.93 x 10-2 W

9) A circlular capactitor of radius 3.2 m has a gap of 8 mm, and a charge of 12 μC. The capacitor is discharged through a 7 kΩ resistor. What is the decay time?

a) 2.49E-04 s
b) 3.02E-04 s
c) 3.66E-04 s
d) 4.43E-04 s
e) 5.37E-04 s

10) 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

11) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal. To counter the magnetic force, a voltage is applied between two large parallel plates that are 59 mm apart. What must be the applied voltage if the magnetic field is 45μT?

a) 1.1 x 100 volts
b) 3.6 x 100 volts
c) 1.1 x 101 volts
d) 3.6 x 101 volts
e) 1.1 x 102 volts

12) 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

13) The same parallel plate capacitor, with area 1.15 m2, plate separation 0.63mm, and an applied voltage of 2.25 kV. How much charge is stored?

a) 23.91 μC.
b) 27.5 μC.
c) 31.62 μC.
d) 36.37 μC.
e) 41.82 μC.

14) An object is placed 10.9 cm to the left of a diverging lens with a focal length of 16.4 cm. On the side, at a distance of 6.8 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) 1.81 x 10-1 cm
b) 5.71 x 10-1 cm
c) 1.81 x 100 cm
d) 5.71 x 100 cm
e) 1.81 x 101 cm
15) What is the current through R1, R2, R3, and R4 in the figure shown?
a) ${\displaystyle I_{1}=10A}$; ${\displaystyle I_{2}=50A}$; ${\displaystyle I_{3}=33A}$; ${\displaystyle I_{4}=25A}$..
b) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=0.5A}$; ${\displaystyle I_{3}=0.33A}$; ${\displaystyle I_{4}=0.25A}$.
c) ${\displaystyle I_{1}=0.25A}$; ${\displaystyle I_{2}=0.33A}$; ${\displaystyle I_{3}=0.5A}$; ${\displaystyle I_{4}=0.1A}$.
d) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=5A}$; ${\displaystyle I_{3}=3.3A}$; ${\displaystyle I_{4}=2.5A}$.

### KEY:PhysicsCalc2:FE:V2

PhysicsCalc2149994633029

1) Two orbiting satellites are orbiting at a speed of 58 km/s perpendicular to a magnetic field of 46 μT. They are connected by a cable that is 22 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) 2.72 x 104 volts.
-b) 3.3 x 104 volts.
-c) 4 x 104 volts.
-d) 4.84 x 104 volts.
+e) 5.87 x 104 volts.

2) A battery has an emf of 5.6 volts, and an internal resistance of 450 ${\displaystyle k\Omega }$. It is connected to a 2.7 ${\displaystyle M\Omega }$ resistor. What power is developed in the 2.7 ${\displaystyle M\Omega }$ resistor?

-a) 4.88 ${\displaystyle \mu }$W.
-b) 5.61 ${\displaystyle \mu }$W.
-c) 6.45 ${\displaystyle \mu }$W.
-d) 7.42 ${\displaystyle \mu }$W.
+e) 8.53 ${\displaystyle \mu }$W.

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

4) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
${\displaystyle Answer}$ (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−3
-b) 3−s
-c) s−7
-d) 8
+e) 7−s

5) H is defined by, B=μ0H, where B is magnetic field. A current of 51A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (-6.8, 6.8) to the point (6.8, 6.8).

-a) 1.06E+01 amps
-b) 1.16E+01 amps
+c) 1.28E+01 amps
-d) 1.40E+01 amps
-e) 1.53E+01 amps

6) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H_{y}}$ at the point (5.6728,2.7403) if a current of 7.4A flows through a wire that runs along the z axis?

-a) 1.28E-01 A/m
-b) 1.40E-01 A/m
-c) 1.54E-01 A/m
+d) 1.68E-01 A/m
-e) 1.85E-01 A/m

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

-a) 4.47 x 101degrees
-b) 5.17 x 101degrees
+c) 5.97 x 101degrees
-d) 6.89 x 101degrees
-e) 7.96 x 101degrees

8) A 4.7 volt battery moves 50 Coulombs of charge in 1.3 hours. What is the power?

-a) 4.14 x 10-2 W
+b) 5.02 x 10-2 W
-c) 6.08 x 10-2 W
-d) 7.37 x 10-2 W
-e) 8.93 x 10-2 W

9) A circlular capactitor of radius 3.2 m has a gap of 8 mm, and a charge of 12 μC. The capacitor is discharged through a 7 kΩ resistor. What is the decay time?

+a) 2.49E-04 s
-b) 3.02E-04 s
-c) 3.66E-04 s
-d) 4.43E-04 s
-e) 5.37E-04 s

10) 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

11) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal. To counter the magnetic force, a voltage is applied between two large parallel plates that are 59 mm apart. What must be the applied voltage if the magnetic field is 45μT?

-a) 1.1 x 100 volts
-b) 3.6 x 100 volts
-c) 1.1 x 101 volts
+d) 3.6 x 101 volts
-e) 1.1 x 102 volts

12) 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

13) The same parallel plate capacitor, with area 1.15 m2, plate separation 0.63mm, and an applied voltage of 2.25 kV. How much charge is stored?

-a) 23.91 μC.
-b) 27.5 μC.
-c) 31.62 μC.
+d) 36.37 μC.
-e) 41.82 μC.

14) An object is placed 10.9 cm to the left of a diverging lens with a focal length of 16.4 cm. On the side, at a distance of 6.8 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) 1.81 x 10-1 cm
-b) 5.71 x 10-1 cm
-c) 1.81 x 100 cm
+d) 5.71 x 100 cm
-e) 1.81 x 101 cm
15) What is the current through R1, R2, R3, and R4 in the figure shown?
-a) ${\displaystyle I_{1}=10A}$; ${\displaystyle I_{2}=50A}$; ${\displaystyle I_{3}=33A}$; ${\displaystyle I_{4}=25A}$..
+b) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=0.5A}$; ${\displaystyle I_{3}=0.33A}$; ${\displaystyle I_{4}=0.25A}$.
-c) ${\displaystyle I_{1}=0.25A}$; ${\displaystyle I_{2}=0.33A}$; ${\displaystyle I_{3}=0.5A}$; ${\displaystyle I_{4}=0.1A}$.
-d) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=5A}$; ${\displaystyle I_{3}=3.3A}$; ${\displaystyle I_{4}=2.5A}$.

### PhysicsCalc2:FE:V3

1) 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 (-6.4, 6.4) to the point (6.4, 6.4).

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

2) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H_{y}}$ at the point (5.7188,7.2066) if a current of 5.7A flows through a wire that runs along the z axis?

a) 6.13E-02 A/m
b) 6.72E-02 A/m
c) 7.37E-02 A/m
d) 8.08E-02 A/m
e) 8.86E-02 A/m

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

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

a) 4.23 x 101degrees
b) 4.88 x 101degrees
c) 5.64 x 101degrees
d) 6.51 x 101degrees
e) 7.52 x 101degrees

5) Two orbiting satellites are orbiting at a speed of 70 km/s perpendicular to a magnetic field of 46 μT. They are connected by a cable that is 30 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) 4.48 x 104 volts.
b) 5.43 x 104 volts.
c) 6.58 x 104 volts.
d) 7.97 x 104 volts.
e) 9.66 x 104 volts.

6) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal. To counter the magnetic force, a voltage is applied between two large parallel plates that are 59 mm apart. What must be the applied voltage if the magnetic field is 45μT?

a) 1.1 x 100 volts
b) 3.6 x 100 volts
c) 1.1 x 101 volts
d) 3.6 x 101 volts
e) 1.1 x 102 volts

7) A battery has an emf of 5.6 volts, and an internal resistance of 450 ${\displaystyle k\Omega }$. It is connected to a 2.7 ${\displaystyle M\Omega }$ resistor. What power is developed in the 2.7 ${\displaystyle M\Omega }$ resistor?

a) 4.88 ${\displaystyle \mu }$W.
b) 5.61 ${\displaystyle \mu }$W.
c) 6.45 ${\displaystyle \mu }$W.
d) 7.42 ${\displaystyle \mu }$W.
e) 8.53 ${\displaystyle \mu }$W.

8) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
${\displaystyle Answer}$ (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) 7−s
b) 3−s
c) 8
d) s−7
e) s−3

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,
${\displaystyle {\vec {\mathfrak {F}}}=(2.28+1.72z)\rho ^{3}{\hat {\rho }}+7.33z^{3}{\hat {z}}}$
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) 1.50E+04
b) 1.82E+04
c) 2.20E+04
d) 2.66E+04
e) 3.23E+04

10) An object is placed 10.9 cm to the left of a diverging lens with a focal length of 16.4 cm. On the side, at a distance of 6.8 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) 1.81 x 10-1 cm
b) 5.71 x 10-1 cm
c) 1.81 x 100 cm
d) 5.71 x 100 cm
e) 1.81 x 101 cm

11) A circlular capactitor of radius 3.2 m has a gap of 12 mm, and a charge of 33 μC. The capacitor is discharged through a 6 kΩ resistor. What is the decay time?

a) 1.42E-04 s
b) 1.73E-04 s
c) 2.09E-04 s
d) 2.53E-04 s
e) 3.07E-04 s

12) 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
13) 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) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=5A}$; ${\displaystyle I_{3}=3.3A}$; ${\displaystyle I_{4}=2.5A}$.
c) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=0.5A}$; ${\displaystyle I_{3}=0.33A}$; ${\displaystyle I_{4}=0.25A}$.
d) ${\displaystyle I_{1}=10A}$; ${\displaystyle I_{2}=50A}$; ${\displaystyle I_{3}=33A}$; ${\displaystyle I_{4}=25A}$..

14) The same parallel plate capacitor, with area 1.45 m2, plate separation 0.93mm, and an applied voltage of 4.45 kV. How much charge is stored?

a) 40.39 μC.
b) 46.45 μC.
c) 53.42 μC.
d) 61.43 μC.
e) 70.65 μC.

15) A 3.1 volt battery moves 40 Coulombs of charge in 0.9 hours. What is the power?

a) 2.61 x 10-2 W
b) 3.16 x 10-2 W
c) 3.83 x 10-2 W
d) 4.64 x 10-2 W
e) 5.62 x 10-2 W

### KEY:PhysicsCalc2:FE:V3

PhysicsCalc2149994633029

1) 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 (-6.4, 6.4) to the point (6.4, 6.4).

-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

2) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H_{y}}$ at the point (5.7188,7.2066) if a current of 5.7A flows through a wire that runs along the z axis?

+a) 6.13E-02 A/m
-b) 6.72E-02 A/m
-c) 7.37E-02 A/m
-d) 8.08E-02 A/m
-e) 8.86E-02 A/m

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

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

-a) 4.23 x 101degrees
-b) 4.88 x 101degrees
-c) 5.64 x 101degrees
-d) 6.51 x 101degrees
+e) 7.52 x 101degrees

5) Two orbiting satellites are orbiting at a speed of 70 km/s perpendicular to a magnetic field of 46 μT. They are connected by a cable that is 30 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) 4.48 x 104 volts.
-b) 5.43 x 104 volts.
-c) 6.58 x 104 volts.
-d) 7.97 x 104 volts.
+e) 9.66 x 104 volts.

6) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal. To counter the magnetic force, a voltage is applied between two large parallel plates that are 59 mm apart. What must be the applied voltage if the magnetic field is 45μT?

-a) 1.1 x 100 volts
-b) 3.6 x 100 volts
-c) 1.1 x 101 volts
+d) 3.6 x 101 volts
-e) 1.1 x 102 volts

7) A battery has an emf of 5.6 volts, and an internal resistance of 450 ${\displaystyle k\Omega }$. It is connected to a 2.7 ${\displaystyle M\Omega }$ resistor. What power is developed in the 2.7 ${\displaystyle M\Omega }$ resistor?

-a) 4.88 ${\displaystyle \mu }$W.
-b) 5.61 ${\displaystyle \mu }$W.
-c) 6.45 ${\displaystyle \mu }$W.
-d) 7.42 ${\displaystyle \mu }$W.
+e) 8.53 ${\displaystyle \mu }$W.

8) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
${\displaystyle Answer}$ (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) 7−s
-b) 3−s
-c) 8
-d) s−7
-e) s−3

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,
${\displaystyle {\vec {\mathfrak {F}}}=(2.28+1.72z)\rho ^{3}{\hat {\rho }}+7.33z^{3}{\hat {z}}}$
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) 1.50E+04
+b) 1.82E+04
-c) 2.20E+04
-d) 2.66E+04
-e) 3.23E+04

10) An object is placed 10.9 cm to the left of a diverging lens with a focal length of 16.4 cm. On the side, at a distance of 6.8 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) 1.81 x 10-1 cm
-b) 5.71 x 10-1 cm
-c) 1.81 x 100 cm
+d) 5.71 x 100 cm
-e) 1.81 x 101 cm

11) A circlular capactitor of radius 3.2 m has a gap of 12 mm, and a charge of 33 μC. The capacitor is discharged through a 6 kΩ resistor. What is the decay time?

+a) 1.42E-04 s
-b) 1.73E-04 s
-c) 2.09E-04 s
-d) 2.53E-04 s
-e) 3.07E-04 s

12) 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
13) 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) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=5A}$; ${\displaystyle I_{3}=3.3A}$; ${\displaystyle I_{4}=2.5A}$.
+c) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=0.5A}$; ${\displaystyle I_{3}=0.33A}$; ${\displaystyle I_{4}=0.25A}$.
-d) ${\displaystyle I_{1}=10A}$; ${\displaystyle I_{2}=50A}$; ${\displaystyle I_{3}=33A}$; ${\displaystyle I_{4}=25A}$..

14) The same parallel plate capacitor, with area 1.45 m2, plate separation 0.93mm, and an applied voltage of 4.45 kV. How much charge is stored?

-a) 40.39 μC.
-b) 46.45 μC.
-c) 53.42 μC.
+d) 61.43 μC.
-e) 70.65 μC.

15) A 3.1 volt battery moves 40 Coulombs of charge in 0.9 hours. What is the power?

-a) 2.61 x 10-2 W
-b) 3.16 x 10-2 W
+c) 3.83 x 10-2 W
-d) 4.64 x 10-2 W
-e) 5.62 x 10-2 W