# Wright State University Lake Campus/2016-9/Phy2410/Sample exams

phc20160712T125120

This identifier represents a unique rendition of the course phc. It contains 2 versions that are identical except for numerical values and order of questions and answers in test. For more information visit Quizbank. WARNING: This rendition has been posted on Wikiversity and is therefore available to students.

### phc:T1:V1

phc20160712T125120

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

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

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

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

3) What is the speed of a transverse wave on a string if the string is 0.58 m long, clamped at both ends, and harmonic number 4 has a frequency of 543 Hz?

a) 8.86 x 101 unit
b) 1.07 x 102 unit
c) 1.3 x 102 unit
d) 1.57 x 102 unit
e) 1.91 x 102 unit

4) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
${\displaystyle Answer}$ (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) 22 + (7-s)2
d) 92 + (7-s)2
e) 92 + (2-s)2

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

6) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
${\displaystyle Answer}$ (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) 2
b) 4
c) 1/2
d) 8

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

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

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

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

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

a) 7.99 x 10-1N/C
b) 9.22 x 10-1N/C
c) 1.07 x 100N/C
d) 1.23 x 100N/C
e) 1.42 x 100N/C

11) Integrate the line integral of, ${\displaystyle {\vec {F}}=9.9xy{\hat {x}}+6.1y^{3}{\hat {y}}}$, along the y axis from y = 7 to y = 16

a) 7.86E+04
b) 8.41E+04
c) 9.00E+04
d) 9.63E+04
e) 1.03E+05

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

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

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

#### KEY:phc:T1:V1

phc20160712T125120

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

-a) 2.86 x 10-1
+b) 3.47 x 10-1
-c) 4.2 x 10-1
-d) 5.09 x 10-1
-e) 6.17 x 10-1

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

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

3) What is the speed of a transverse wave on a string if the string is 0.58 m long, clamped at both ends, and harmonic number 4 has a frequency of 543 Hz?

-a) 8.86 x 101 unit
-b) 1.07 x 102 unit
-c) 1.3 x 102 unit
+d) 1.57 x 102 unit
-e) 1.91 x 102 unit

4) A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
${\displaystyle Answer}$ (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) 22 + (9-s)2
-c) 92 + (7-s)2
-d) 22 + (7-s)2
-e) 92 + (2-s)2

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

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

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

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

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

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

-a) 7.99 x 10-1N/C
-b) 9.22 x 10-1N/C
+c) 1.07 x 100N/C
-d) 1.23 x 100N/C
-e) 1.42 x 100N/C

11) Integrate the line integral of, ${\displaystyle {\vec {F}}=9.9xy{\hat {x}}+6.1y^{3}{\hat {y}}}$, along the y axis from y = 7 to y = 16

- a) 7.86E+04
- b) 8.41E+04
- c) 9.00E+04
+ d) 9.63E+04
- e) 1.03E+05

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

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

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

### phc:T1:V2

phc20160712T125120

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

2) What is the speed of a transverse wave on a string if the string is 1.05 m long, clamped at both ends, and harmonic number 5 has a frequency of 153 Hz?

a) 5.3 x 101 unit
b) 6.43 x 101 unit
c) 7.79 x 101 unit
d) 9.43 x 101 unit
e) 1.14 x 102 unit

3) Integrate the line integral of, ${\displaystyle {\vec {F}}=6.9xy{\hat {x}}+7.4y^{3}{\hat {y}}}$, along the y axis from y = 3 to y = 18

a) 1.69E+05
b) 1.81E+05
c) 1.94E+05
d) 2.08E+05
e) 2.22E+05

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

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

5) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
${\displaystyle Answer}$ (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) 1/2
d) 8

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

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

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

a) 5.47 x 10-1N/C
b) 6.32 x 10-1N/C
c) 7.3 x 10-1N/C
d) 8.43 x 10-1N/C
e) 9.73 x 10-1N/C

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

a) s−4
b) 4−s
c) s−8
d) 4
e) 8−s

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

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

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

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 ${\displaystyle {\mathcal {C}}=}$

a) 7−s
b) 3−s
c) 3
d) s−3
e) s−7

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

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

13) 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

#### KEY:phc:T1:V2

phc20160712T125120

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

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

2) What is the speed of a transverse wave on a string if the string is 0.58 m long, clamped at both ends, and harmonic number 4 has a frequency of 543 Hz?

-a) 8.86 x 101 unit
-b) 1.07 x 102 unit
-c) 1.3 x 102 unit
+d) 1.57 x 102 unit
-e) 1.91 x 102 unit

3) Integrate the line integral of, ${\displaystyle {\vec {F}}=7.8xy{\hat {x}}+8y^{3}{\hat {y}}}$, along the y axis from y = 6 to y = 13

- a) 4.45E+04
- b) 4.76E+04
- c) 5.10E+04
+ d) 5.45E+04
- e) 5.83E+04

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

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

5) A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
${\displaystyle Answer}$ (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) 2
-b) 1/2
-c) 8
+d) 4

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

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

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

-a) 7.26 x 10-1N/C
-b) 8.38 x 10-1N/C
+c) 9.68 x 10-1N/C
-d) 1.12 x 100N/C
-e) 1.29 x 100N/C

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

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

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

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

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 ${\displaystyle {\mathcal {C}}=}$

+a) 7−s
-b) s−7
-c) s−3
-d) 3
-e) 3−s

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

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

13) 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

### phc:T2:V1

phc20160712T125120

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

a) 6.1 ohms.
b) 7 ohms.
c) 8.1 ohms.
d) 9.3 ohms.
e) 10.7 ohms.
2) What is the current through R1 and R2 in the figure shown?
a) ${\displaystyle I_{1}=10A}$ and ${\displaystyle I_{2}=16.67A}$.
b) ${\displaystyle I_{1}=0.1A}$ and ${\displaystyle I_{2}=0.1667A}$.
c) ${\displaystyle I_{1}=1A}$ and ${\displaystyle I_{2}=1.667A}$.
d) ${\displaystyle I_{1}=1A}$ and ${\displaystyle I_{2}=25A}$.

3) The diameter of a copper wire is 9.2 mm, and it carries a current of 64 amps. What is the drift velocity if copper has a density of 8.8E3 kg/m3 and an atomic mass of 63.54 g/mol? (1 mol = 6.02E23 atoms, and copper has one free electron per atom.)

a) 4.91 x 10-5m/s
b) 5.95 x 10-5m/s
c) 7.2 x 10-5m/s
d) 8.73 x 10-5m/s
e) 1.06 x 10-4m/s

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

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

5) A 1.3 Farad capacitor charged with 1.9 Coulombs. What is the energy stored in the capacitor if the plates are 0.3 mm apart?

a) 0.91 J.
b) 1.05 J.
c) 1.21 J.
d) 1.39 J.
e) 1.6 J.

6) A proton is accellerated (at rest) from a plate held at 39.7 volts to a plate at zero volts. What is the final speed?

a) 3.9 x 104 m/s.
b) 5.8 x 104 m/s.
c) 8.7 x 104 m/s.
d) 1.3 x 105 m/s.
e) 2 x 105 m/s.

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

8) Why do we say the "voltage across" or "the voltage with respect to?" Why can't we just say voltage?}

a) It's an Electrical Cliche.
b) None these are correct
c) The other point could be Negative or positive.
d) Voltage is a measure of Electric Potential difference between two electrical points.

9) Three 1 ohm resistors are connected in parallel. What is the total resistance?}

a) ${\displaystyle {\frac {3}{2}}\Omega }$.
b) ${\displaystyle {\frac {2}{3}}\Omega }$.
c) ${\displaystyle {\frac {1}{3}}\Omega }$.
d) ${\displaystyle 3\Omega }$.

10) A 3.1 volt battery moves 52 Coulombs of charge in 1.7 hours. What is the power?

a) 1.79 x 10-2 W
b) 2.17 x 10-2 W
c) 2.63 x 10-2 W
d) 3.19 x 10-2 W
e) 3.87 x 10-2 W

11) A 0.5 Farad capacitor charged with 1.3 Coulombs. What is the force between the plates if they are 0.7 mm apart?

a) 1826 N.
b) 2099 N.
c) 2414 N.
d) 2776 N.
e) 3193 N.

12) An ideal 7.4 volt battery is connected to a 0.074 ohm resistor. To measure the current an ammeter with a resistance of 12${\displaystyle m\Omega }$ is used. What current does the ammeter actually read?

a) 49.2 A.
b) 56.6 A.
c) 65.1 A.
d) 74.8 A.
e) 86 A.

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

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

14) A resistor is on for 5 seconds. It consumes power at a rate of 5 watts. How many joules are used?}

a) 3 Joules
b) None of these are true
c) 5 Joules
d) 25 Joules

#### KEY:phc:T2:V1

phc20160712T125120

1) A 5.6 ohm resistor is connected in series to a pair of 7.2 ohm resistors that are in parallel. What is the net resistance?

-a) 7 ohms.
-b) 8 ohms.
+c) 9.2 ohms.
-d) 10.6 ohms.
-e) 12.2 ohms.
2) What is the current through R1 and R2 in the figure shown?
-a) ${\displaystyle I_{1}=0.1A}$ and ${\displaystyle I_{2}=0.1667A}$.
-b) ${\displaystyle I_{1}=10A}$ and ${\displaystyle I_{2}=16.67A}$.
-c) ${\displaystyle I_{1}=1A}$ and ${\displaystyle I_{2}=25A}$.
+d) ${\displaystyle I_{1}=1A}$ and ${\displaystyle I_{2}=1.667A}$.

3) The diameter of a copper wire is 3.6 mm, and it carries a current of 52 amps. What is the drift velocity if copper has a density of 8.8E3 kg/m3 and an atomic mass of 63.54 g/mol? (1 mol = 6.02E23 atoms, and copper has one free electron per atom.)

+a) 3.82 x 10-4m/s
-b) 4.63 x 10-4m/s
-c) 5.61 x 10-4m/s
-d) 6.8 x 10-4m/s
-e) 8.24 x 10-4m/s

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

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

5) A 0.5 Farad capacitor charged with 1.6 Coulombs. What is the energy stored in the capacitor if the plates are 0.7 mm apart?

-a) 2.23 J.
+b) 2.56 J.
-c) 2.94 J.
-d) 3.39 J.
-e) 3.89 J.

6) A proton is accellerated (at rest) from a plate held at 588.2 volts to a plate at zero volts. What is the final speed?

-a) 6.6 x 104 m/s.
-b) 10 x 104 m/s.
-c) 1.5 x 105 m/s.
-d) 2.2 x 105 m/s.
+e) 3.4 x 105 m/s.

7) 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) ${\displaystyle R_{1}=125V}$ and ${\displaystyle R_{2}=125V}$.
-c) ${\displaystyle R_{1}=150V}$ and ${\displaystyle R_{2}=100V}$.
-d) ${\displaystyle R_{1}=250V}$ and ${\displaystyle R_{2}=0V}$.

8) Why do we say the "voltage across" or "the voltage with respect to?" Why can't we just say voltage?}

-a) None these are correct
-b) It's an Electrical Cliche.
-c) The other point could be Negative or positive.
+d) Voltage is a measure of Electric Potential difference between two electrical points.

9) Three 1 ohm resistors are connected in parallel. What is the total resistance?}

-a) ${\displaystyle 3\Omega }$.
-b) ${\displaystyle {\frac {2}{3}}\Omega }$.
-c) ${\displaystyle {\frac {3}{2}}\Omega }$.
+d) ${\displaystyle {\frac {1}{3}}\Omega }$.

10) A 3.1 volt battery moves 52 Coulombs of charge in 1.7 hours. What is the power?

-a) 1.79 x 10-2 W
-b) 2.17 x 10-2 W
+c) 2.63 x 10-2 W
-d) 3.19 x 10-2 W
-e) 3.87 x 10-2 W

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

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

12) An ideal 7.5 volt battery is connected to a 0.084 ohm resistor. To measure the current an ammeter with a resistance of 14${\displaystyle m\Omega }$ is used. What current does the ammeter actually read?

-a) 43.8 A.
-b) 50.3 A.
-c) 57.9 A.
-d) 66.5 A.
+e) 76.5 A.

13) 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

14) A resistor is on for 5 seconds. It consumes power at a rate of 5 watts. How many joules are used?}

+a) 25 Joules
-b) None of these are true
-c) 3 Joules
-d) 5 Joules

### phc:T2:V2

phc20160712T125120

1) 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) ${\displaystyle R_{1}=250V}$ and ${\displaystyle R_{2}=0V}$.
c) ${\displaystyle R_{1}=125V}$ and ${\displaystyle R_{2}=125V}$.
d) ${\displaystyle R_{1}=150V}$ and ${\displaystyle R_{2}=100V}$.

2) A 1.2 Farad capacitor charged with 1.6 Coulombs. What is the energy stored in the capacitor if the plates are 0.4 mm apart?

a) 0.81 J.
b) 0.93 J.
c) 1.07 J.
d) 1.23 J.
e) 1.41 J.

3) A 5.8 ohm resistor is connected in series to a pair of 2.8 ohm resistors that are in parallel. What is the net resistance?

a) 7.2 ohms.
b) 8.3 ohms.
c) 9.5 ohms.
d) 11 ohms.
e) 12.6 ohms.

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

5) A 0.5 Farad capacitor charged with 1.6 Coulombs. What is the force between the plates if they are 0.7 mm apart?

a) 3180 N.
b) 3657 N.
c) 4206 N.
d) 4837 N.
e) 5562 N.

6) A proton is accellerated (at rest) from a plate held at 767.8 volts to a plate at zero volts. What is the final speed?

a) 1.1 x 105 m/s.
b) 1.7 x 105 m/s.
c) 2.6 x 105 m/s.
d) 3.8 x 105 m/s.
e) 5.8 x 105 m/s.

7) An ideal 7.3 volt battery is connected to a 0.071 ohm resistor. To measure the current an ammeter with a resistance of 27${\displaystyle m\Omega }$ is used. What current does the ammeter actually read?

a) 49 A.
b) 56.3 A.
c) 64.8 A.
d) 74.5 A.
e) 85.7 A.

8) 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

9) Why do we say the "voltage across" or "the voltage with respect to?" Why can't we just say voltage?}

a) Voltage is a measure of Electric Potential difference between two electrical points.
b) It's an Electrical Cliche.
c) The other point could be Negative or positive.
d) None these are correct
10) What is the current through R1 and R2 in the figure shown?
a) ${\displaystyle I_{1}=1A}$ and ${\displaystyle I_{2}=1.667A}$.
b) ${\displaystyle I_{1}=1A}$ and ${\displaystyle I_{2}=25A}$.
c) ${\displaystyle I_{1}=0.1A}$ and ${\displaystyle I_{2}=0.1667A}$.
d) ${\displaystyle I_{1}=10A}$ and ${\displaystyle I_{2}=16.67A}$.

11) A resistor is on for 5 seconds. It consumes power at a rate of 5 watts. How many joules are used?}

a) None of these are true
b) 5 Joules
c) 3 Joules
d) 25 Joules

12) Three 1 ohm resistors are connected in parallel. What is the total resistance?}

a) ${\displaystyle {\frac {3}{2}}\Omega }$.
b) ${\displaystyle 3\Omega }$.
c) ${\displaystyle {\frac {1}{3}}\Omega }$.
d) ${\displaystyle {\frac {2}{3}}\Omega }$.

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

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

14) 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,
${\displaystyle {\vec {\mathfrak {F}}}=(2+1.45z)\rho ^{2}{\hat {\rho }}+8.02z^{3}{\hat {z}}}$
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) 1.13E+03
b) 1.37E+03
c) 1.66E+03
d) 2.01E+03
e) 2.44E+03

#### KEY:phc:T2:V2

phc20160712T125120

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

2) A 1.3 Farad capacitor charged with 1.9 Coulombs. What is the energy stored in the capacitor if the plates are 0.3 mm apart?

-a) 0.91 J.
-b) 1.05 J.
-c) 1.21 J.
+d) 1.39 J.
-e) 1.6 J.

3) A 6.6 ohm resistor is connected in series to a pair of 6.4 ohm resistors that are in parallel. What is the net resistance?

-a) 6.4 ohms.
-b) 7.4 ohms.
-c) 8.5 ohms.
+d) 9.8 ohms.
-e) 11.3 ohms.

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

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

5) A 0.5 Farad capacitor charged with 1.6 Coulombs. What is the force between the plates if they are 0.7 mm apart?

-a) 3180 N.
+b) 3657 N.
-c) 4206 N.
-d) 4837 N.
-e) 5562 N.

6) A proton is accellerated (at rest) from a plate held at 4.7 volts to a plate at zero volts. What is the final speed?

-a) 5.9 x 103 m/s.
-b) 8.9 x 103 m/s.
-c) 1.3 x 104 m/s.
-d) 2 x 104 m/s.
+e) 3 x 104 m/s.

7) An ideal 6 volt battery is connected to a 0.06 ohm resistor. To measure the current an ammeter with a resistance of 25${\displaystyle m\Omega }$ is used. What current does the ammeter actually read?

+a) 70.6 A.
-b) 81.2 A.
-c) 93.4 A.
-d) 107.4 A.
-e) 123.5 A.

8) A 3.9 volt battery moves 90 Coulombs of charge in 2.2 hours. What is the power?

+a) 4.43 x 10-2 W
-b) 5.37 x 10-2 W
-c) 6.51 x 10-2 W
-d) 7.88 x 10-2 W
-e) 9.55 x 10-2 W

9) Why do we say the "voltage across" or "the voltage with respect to?" Why can't we just say voltage?}

+a) Voltage is a measure of Electric Potential difference between two electrical points.
-b) The other point could be Negative or positive.
-c) It's an Electrical Cliche.
-d) None these are correct
10) What is the current through R1 and R2 in the figure shown?
-a) ${\displaystyle I_{1}=10A}$ and ${\displaystyle I_{2}=16.67A}$.
-b) ${\displaystyle I_{1}=0.1A}$ and ${\displaystyle I_{2}=0.1667A}$.
-c) ${\displaystyle I_{1}=1A}$ and ${\displaystyle I_{2}=25A}$.
+d) ${\displaystyle I_{1}=1A}$ and ${\displaystyle I_{2}=1.667A}$.

11) A resistor is on for 5 seconds. It consumes power at a rate of 5 watts. How many joules are used?}

-a) 3 Joules
+b) 25 Joules
-c) None of these are true
-d) 5 Joules

12) Three 1 ohm resistors are connected in parallel. What is the total resistance?}

-a) ${\displaystyle {\frac {3}{2}}\Omega }$.
-b) ${\displaystyle 3\Omega }$.
+c) ${\displaystyle {\frac {1}{3}}\Omega }$.
-d) ${\displaystyle {\frac {2}{3}}\Omega }$.

13) The diameter of a copper wire is 1.9 mm, and it carries a current of 33 amps. What is the drift velocity if copper has a density of 8.8E3 kg/m3 and an atomic mass of 63.54 g/mol? (1 mol = 6.02E23 atoms, and copper has one free electron per atom.)

-a) 5.93 x 10-4m/s
-b) 7.19 x 10-4m/s
+c) 8.71 x 10-4m/s
-d) 1.06 x 10-3m/s
-e) 1.28 x 10-3m/s

14) A cylinder of radius, r=3, 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,
${\displaystyle {\vec {\mathfrak {F}}}=(2.37+2.6z)\rho ^{2}{\hat {\rho }}+8.84z^{3}{\hat {z}}}$
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) 4.63E+03
+b) 5.61E+03
-c) 6.79E+03
-d) 8.23E+03
-e) 9.97E+03

### phc:T3:V1

phc20160712T125120

1) 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.

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

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

3) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
${\displaystyle Answer}$ (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) 5−s
b) s−4
c) s−1
d) 5
e) 1−s

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

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

5) When light passes from glass to air

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

6) The focal point is where

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

7) An object is placed 3.55 cm to the left of a converging lens with a focal length of 6.8 cm. How far is the image from the lens?

a) 4.18 x 100 cm
b) 7.43 x 100 cm
c) 1.32 x 101 cm
d) 2.35 x 101 cm
e) 4.18 x 101 cm

8) An important principle that allows fiber optics to work is

a) total external refraction
b) the invariance of the speed of light
c) partial internal absorption
d) the Doppler shift
e) total internal reflection

9) 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.

10) 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
11) 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 farsighted person might see a distant object
c) how a nearsighted person might see an object that is too close for comfort
d) how a nearsighted person might see a distant object

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:phc:T3:V1

phc20160712T125120

1) Two orbiting satellites are orbiting at a speed of 52 km/s perpendicular to a magnetic field of 41 μT. They are connected by a cable that is 33 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) 4.79 x 104 volts.
-b) 5.81 x 104 volts.
+c) 7.04 x 104 volts.
-d) 8.52 x 104 volts.
-e) 1.03 x 105 volts.

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

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

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

-a) s−4
-b) 5
-c) s−1
+d) 1−s
-e) 5−s

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

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

5) When light passes from glass to air

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

6) The focal point is where

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

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

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

8) An important principle that allows fiber optics to work is

-a) partial internal absorption
-b) the Doppler shift
-c) total external refraction
-d) the invariance of the speed of light
+e) total internal reflection

9) 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.

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

+a) 2.77 x 10-1 cm
-b) 3.32 x 10-1 cm
-c) 3.99 x 10-1 cm
-d) 4.78 x 10-1 cm
-e) 5.74 x 10-1 cm
11) Shown is a corrective lens by a person who needs glasses. This ray diagram illustrates
-a) how a farsighted person might see a distant object
-b) how a farsighted person might see an object that is too close for comfort
-c) how a nearsighted person might see an object that is too close for comfort
+d) how a nearsighted person might see a distant object

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.

### phc:T3:V2

phc20160712T125120

1) The focal point is where

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

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

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

3) When light passes from glass to air

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

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

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

5) An important principle that allows fiber optics to work is

a) total external refraction
b) the invariance of the speed of light
c) partial internal absorption
d) the Doppler shift
e) total internal reflection

6) An object of height 0.68 cm is placed 140 cm behind a diverging lens with a focal length of 87 cm. What is the height of the image?

a) 1.26 x 10-1 cm
b) 1.51 x 10-1 cm
c) 1.81 x 10-1 cm
d) 2.17 x 10-1 cm
e) 2.61 x 10-1 cm

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

a) 5.14 x 10-5 Volts
b) 1.62 x 10-4 Volts
c) 5.14 x 10-4 Volts
d) 1.62 x 10-3 Volts
e) 5.14 x 10-3 Volts
9) Shown is a corrective lens by a person who needs glasses. This ray diagram illustrates
a) how a farsighted person might see a distant object
b) how a farsighted person might see an object that is too close for comfort
c) how a nearsighted person might see a distant object
d) how a nearsighted person might see an object that is too close for comfort

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

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

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

a) 5−s
b) s−1
c) s−4
d) 5
e) 1−s

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:phc:T3:V2

phc20160712T125120

1) The focal point is where

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

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

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

3) When light passes from glass to air

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

4) Two orbiting satellites are orbiting at a speed of 66 km/s perpendicular to a magnetic field of 64 μT. They are connected by a cable that is 37 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) 1.29 x 105 volts.
+b) 1.56 x 105 volts.
-c) 1.89 x 105 volts.
-d) 2.29 x 105 volts.
-e) 2.78 x 105 volts.

5) An important principle that allows fiber optics to work is

-a) partial internal absorption
-b) the Doppler shift
-c) total external refraction
+d) total internal reflection
-e) the invariance of the speed of light

6) An object of height 0.68 cm is placed 140 cm behind a diverging lens with a focal length of 87 cm. What is the height of the image?

-a) 1.26 x 10-1 cm
-b) 1.51 x 10-1 cm
-c) 1.81 x 10-1 cm
-d) 2.17 x 10-1 cm
+e) 2.61 x 10-1 cm

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

-a) 5.14 x 10-5 Volts
+b) 1.62 x 10-4 Volts
-c) 5.14 x 10-4 Volts
-d) 1.62 x 10-3 Volts
-e) 5.14 x 10-3 Volts
9) Shown is a corrective lens by a person who needs glasses. This ray diagram illustrates
+a) how a nearsighted person might see a distant object
-b) how a farsighted person might see an object that is too close for comfort
-c) how a nearsighted person might see an object that is too close for comfort
-d) how a farsighted person might see a distant object

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

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

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

-a) 5−s
-b) s−1
+c) 1−s
-d) 5
-e) s−4

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.

### phc:T4:V1

phc20160712T125120

1) H is defined by, B=μ0H, where B is magnetic field. A current of 59A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (0,7.2) to the point (7.2,7.2).

a) 7.38E+00 amps
b) 8.09E+00 amps
c) 8.87E+00 amps
d) 9.72E+00 amps
e) 1.07E+01 amps

2) Which lens has the shorter focal length?

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

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

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

4) H is defined by, B=μ0H, where B is magnetic field. A current of 33A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (-6.6, 6.6) to the point (6.6, 6.6).

a) 5.71E+00 amps
b) 6.26E+00 amps
c) 6.86E+00 amps
d) 7.52E+00 amps
e) 8.25E+00 amps

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

a) 2.86 x 10-1 unit
b) 3.47 x 10-1 unit
c) 4.2 x 10-1 unit
d) 5.09 x 10-1 unit
e) 6.17 x 10-1 unit

6) A very long and thin solenoid has 1295 turns and is 138 meters long. The wire carrys a current of 8.1A. If this solenoid is sufficiently thin, what is the line integral of${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$ along an on-axis path that starts 22 meters from the center and stops 90 meters from the center?

a) 2.97E+03 A
b) 3.26E+03 A
c) 3.57E+03 A
d) 3.92E+03 A
e) 4.30E+03 A

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

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

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

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

9) A very long and thin solenoid has 2066 turns and is 156 meters long. The wire carrys a current of 7.6A. What is the magnetic field in the center?

a) 8.75E-05 Tesla
b) 9.59E-05 Tesla
c) 1.05E-04 Tesla
d) 1.15E-04 Tesla
e) 1.26E-04 Tesla

10) 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

11) A circlular capactitor of radius 4.2 m has a gap of 18 mm, and a charge of 97 μC. The capacitor is discharged through a 7 kΩ resistor. What is the decay time?

a) 1.91E-04 s
b) 2.31E-04 s
c) 2.80E-04 s
d) 3.39E-04 s
e) 4.11E-04 s

12) A circlular capactitor of radius 4.6 m has a gap of 12 mm, and a charge of 55 μC. What is the electric field between the plates?

a) 6.37E+04 N/C (or V/m)
b) 7.71E+04 N/C (or V/m)
c) 9.34E+04 N/C (or V/m)
d) 1.13E+05 N/C (or V/m)
e) 1.37E+05 N/C (or V/m)

#### KEY:phc:T4:V1

phc20160712T125120

1) H is defined by, B=μ0H, where B is magnetic field. A current of 81A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (0,7.9) to the point (7.9,7.9).

-a) 7.68E+00 amps
-b) 8.42E+00 amps
-c) 9.23E+00 amps
+d) 1.01E+01 amps
-e) 1.11E+01 amps

2) Which lens has the shorter focal length?

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

3) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H_{y}}$ at the point (1.5944,4.101) if a current of 6.9A flows through a wire that runs along the z axis?

-a) 6.86E-02 A/m
-b) 7.52E-02 A/m
-c) 8.25E-02 A/m
+d) 9.04E-02 A/m
-e) 9.92E-02 A/m

4) H is defined by, B=μ0H, where B is magnetic field. A current of 63A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (-9.3, 9.3) to the point (9.3, 9.3).

-a) 1.19E+01 amps
-b) 1.31E+01 amps
-c) 1.44E+01 amps
+d) 1.58E+01 amps
-e) 1.73E+01 amps

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

-a) 1.95 x 10-1 unit
-b) 2.36 x 10-1 unit
-c) 2.86 x 10-1 unit
+d) 3.47 x 10-1 unit
-e) 4.2 x 10-1 unit

6) A very long and thin solenoid has 2774 turns and is 154 meters long. The wire carrys a current of 9.1A. If this solenoid is sufficiently thin, what is the line integral of${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$ along an on-axis path that starts 38 meters from the center and stops 94 meters from the center?

-a) 4.42E+03 A
-b) 4.85E+03 A
-c) 5.32E+03 A
-d) 5.83E+03 A
+e) 6.39E+03 A

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

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

8) An object of height 0.67 cm is placed 106 cm behind a diverging lens with a focal length of 61 cm. What is the height of the image?

-a) 1.18 x 10-1 cm
-b) 1.42 x 10-1 cm
-c) 1.7 x 10-1 cm
-d) 2.04 x 10-1 cm
+e) 2.45 x 10-1 cm

9) A very long and thin solenoid has 1070 turns and is 122 meters long. The wire carrys a current of 8.4A. What is the magnetic field in the center?

-a) 7.02E-05 Tesla
-b) 7.70E-05 Tesla
-c) 8.44E-05 Tesla
+d) 9.26E-05 Tesla
-e) 1.02E-04 Tesla
10) A torus is centered around the x-y plane, with major radius, a = 3.24 m, and minor radius, r = 1.35m. A wire carrying 4.9A is uniformly wrapped with 731 turns. If B=μ0H is the magnetic field, what is H inside the torus, at a point on the xy plane that is 0.81m from the outermost edge of the torus?
+a) 1.11E+02 amps per meter
-b) 1.20E+02 amps per meter
-c) 1.30E+02 amps per meter
-d) 1.40E+02 amps per meter
-e) 1.51E+02 amps per meter

11) A circlular capactitor of radius 3.3 m has a gap of 14 mm, and a charge of 43 μC. The capacitor is discharged through a 9 kΩ resistor. What is the decay time?

+a) 1.95E-04 s
-b) 2.36E-04 s
-c) 2.86E-04 s
-d) 3.46E-04 s
-e) 4.20E-04 s

12) A circlular capactitor of radius 3.4 m has a gap of 7 mm, and a charge of 95 μC. What is the electric field between the plates?

-a) 2.44E+05 N/C (or V/m)
+b) 2.95E+05 N/C (or V/m)
-c) 3.58E+05 N/C (or V/m)
-d) 4.34E+05 N/C (or V/m)
-e) 5.25E+05 N/C (or V/m)

### phc:T4:V2

phc20160712T125120

1) H is defined by, B=μ0H, where B is magnetic field. A current of 46A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (0,7.9) to the point (7.9,7.9).

a) 5.24E+00 amps
b) 5.75E+00 amps
c) 6.30E+00 amps
d) 6.91E+00 amps
e) 7.58E+00 amps

2) What is the sum of 0.8 apples plus 18 apples?

a) 1.56E+01 apples
b) 1.71E+01 apples
c) 1.88E+01 apples
d) 2.06E+01 apples
e) 2.26E+01 apples

3) A circlular capactitor of radius 4.1 m has a gap of 11 mm, and a charge of 51 μC. The capacitor is discharged through a 8 kΩ resistor. What is the decay time?

a) 3.40E-04 s
b) 4.12E-04 s
c) 4.99E-04 s
d) 6.05E-04 s
e) 7.33E-04 s

4) Which lens has the shorter focal length?

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

5) 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 (-8.1, 8.1) to the point (8.1, 8.1).

a) 2.01E+01 amps
b) 2.20E+01 amps
c) 2.41E+01 amps
d) 2.64E+01 amps
e) 2.90E+01 amps

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

a) 1.95 x 10-1 unit
b) 2.36 x 10-1 unit
c) 2.86 x 10-1 unit
d) 3.47 x 10-1 unit
e) 4.2 x 10-1 unit

7) A very long and thin solenoid has 1259 turns and is 156 meters long. The wire carrys a current of 8.9A. If this solenoid is sufficiently thin, what is the line integral of${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$ along an on-axis path that starts 35 meters from the center and stops 90 meters from the center?

a) 2.82E+03 A
b) 3.09E+03 A
c) 3.39E+03 A
d) 3.71E+03 A
e) 4.07E+03 A

8) 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

9) A circlular capactitor of radius 3.7 m has a gap of 8 mm, and a charge of 89 μC. What is the electric field between the plates?

a) 1.93E+05 N/C (or V/m)
b) 2.34E+05 N/C (or V/m)
c) 2.83E+05 N/C (or V/m)
d) 3.43E+05 N/C (or V/m)
e) 4.16E+05 N/C (or V/m)

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

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

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

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

12) 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

#### KEY:phc:T4:V2

phc20160712T125120

1) H is defined by, B=μ0H, where B is magnetic field. A current of 81A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (0,7.9) to the point (7.9,7.9).

-a) 7.68E+00 amps
-b) 8.42E+00 amps
-c) 9.23E+00 amps
+d) 1.01E+01 amps
-e) 1.11E+01 amps
2) A torus is centered around the x-y plane, with major radius, a = 3.24 m, and minor radius, r = 1.35m. A wire carrying 4.9A is uniformly wrapped with 731 turns. If B=μ0H is the magnetic field, what is H inside the torus, at a point on the xy plane that is 0.81m from the outermost edge of the torus?
+a) 1.11E+02 amps per meter
-b) 1.20E+02 amps per meter
-c) 1.30E+02 amps per meter
-d) 1.40E+02 amps per meter
-e) 1.51E+02 amps per meter

3) A circlular capactitor of radius 3.4 m has a gap of 8 mm, and a charge of 64 μC. The capacitor is discharged through a 9 kΩ resistor. What is the decay time?

+a) 3.62E-04 s
-b) 4.38E-04 s
-c) 5.31E-04 s
-d) 6.43E-04 s
-e) 7.79E-04 s

4) Which lens has the shorter focal length?

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

5) 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 (-5.7, 5.7) to the point (5.7, 5.7).

-a) 1.54E+01 amps
-b) 1.69E+01 amps
+c) 1.85E+01 amps
-d) 2.03E+01 amps
-e) 2.22E+01 amps

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

-a) 1.61 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

7) A very long and thin solenoid has 2219 turns and is 134 meters long. The wire carrys a current of 7.6A. If this solenoid is sufficiently thin, what is the line integral of${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$ along an on-axis path that starts 44 meters from the center and stops 86 meters from the center?

-a) 2.41E+03 A
-b) 2.64E+03 A
+c) 2.89E+03 A
-d) 3.17E+03 A
-e) 3.48E+03 A

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

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

9) A circlular capactitor of radius 3.3 m has a gap of 14 mm, and a charge of 11 μC. What is the electric field between the plates?

-a) 2.04E+04 N/C (or V/m)
-b) 2.47E+04 N/C (or V/m)
-c) 3.00E+04 N/C (or V/m)
+d) 3.63E+04 N/C (or V/m)
-e) 4.40E+04 N/C (or V/m)

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

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

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

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

12) If ${\displaystyle H=B/\mu _{0}}$, where ${\displaystyle B}$ is magnetic field, what is ${\displaystyle H_{y}}$ at the point (2.0898,3.6432) if a current of 4.9A flows through a wire that runs along the z axis?

-a) 6.39E-02 A/m
-b) 7.01E-02 A/m
-c) 7.68E-02 A/m
-d) 8.43E-02 A/m
+e) 9.24E-02 A/m

### phc:FE:V1

phc20160712T125120

1) 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

2) A power supply delivers 145 watts of power to a 132 ohm resistor. What was the applied voltage?

a) 6.42 x 101 volts
b) 7.78 x 101 volts
c) 9.43 x 101 volts
d) 1.14 x 102 volts
e) 1.38 x 102 volts

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

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

5) What is the sum of 6.6 apples plus 33 apples?

a) 3.61E+01 apples
b) 3.96E+01 apples
c) 4.34E+01 apples
d) 4.76E+01 apples
e) 5.22E+01 apples

6) H is defined by, B=μ0H, where B is magnetic field. A current of 86A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (0,5) to the point (5,5).

a) 7.44E+00 amps
b) 8.15E+00 amps
c) 8.94E+00 amps
d) 9.80E+00 amps
e) 1.08E+01 amps

7) How fast is a 2648 eV electron moving?

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

8) A 0.8 Farad capacitor charged with 1.7 Coulombs. What is the energy stored in the capacitor if the plates are 0.5 mm apart?

a) 1.81 J.
b) 2.08 J.
c) 2.39 J.
d) 2.75 J.
e) 3.16 J.

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

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

10) An loop of wire with 31 turns has a radius of 0.9 meters, and is oriented with its axis parallel to a magetic field of 0.83 Tesla. What is the induced voltage if this field is reduced to 35% of its original value in 1.7 seconds?

a) 2.07 x 101 volts
b) 2.5 x 101 volts
c) 3.03 x 101 volts
d) 3.67 x 101 volts
e) 4.45 x 101 volts

11) A circlular capactitor of radius 4.9 m has a gap of 13 mm, and a charge of 35 μC. The capacitor is discharged through a 5 kΩ resistor. What is the decay time?

a) 2.57E-04 s
b) 3.11E-04 s
c) 3.77E-04 s
d) 4.57E-04 s
e) 5.53E-04 s

12) Two 6.2 ohm resistors are connected in parallel. This combination is then connected in series to a 2.6 ohm resistor. What is the net resistance?

a) 3.7 ohms.
b) 4.3 ohms.
c) 5 ohms.
d) 5.7 ohms.
e) 6.6 ohms.
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) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=0.5A}$; ${\displaystyle I_{3}=0.33A}$; ${\displaystyle I_{4}=0.25A}$.
c) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=5A}$; ${\displaystyle I_{3}=3.3A}$; ${\displaystyle I_{4}=2.5A}$.
d) ${\displaystyle I_{1}=10A}$; ${\displaystyle I_{2}=50A}$; ${\displaystyle I_{3}=33A}$; ${\displaystyle I_{4}=25A}$..

14) 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

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

16) A 819 mF capacitor is connected in series to a 798 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 8.27 x 105 s.
b) 2.61 x 106 s.
c) 8.27 x 106 s.
d) 2.61 x 107 s.
e) 8.27 x 107 s.

#### KEY:phc:FE:V1

phc20160712T125120

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,
${\displaystyle {\vec {\mathfrak {F}}}=(2.07+2.87z)\rho ^{2}{\hat {\rho }}+9.56z^{3}{\hat {z}}}$
Let ${\displaystyle {\hat {n}}}$ be the outward unit normal to this cylinder and evaluate ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

-a) 7.933E+02
+b) 9.611E+02
-c) 1.164E+03
-d) 1.411E+03
-e) 1.709E+03

2) A power supply delivers 145 watts of power to a 132 ohm resistor. What was the applied voltage?

-a) 6.42 x 101 volts
-b) 7.78 x 101 volts
-c) 9.43 x 101 volts
-d) 1.14 x 102 volts
+e) 1.38 x 102 volts

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) =( 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

4) An object is placed 6.55 cm to the left of a converging lens with a focal length of 5.4 cm. How far is the image from the lens?

-a) 3.08 x 100 cm
-b) 5.47 x 100 cm
-c) 9.73 x 100 cm
-d) 1.73 x 101 cm
+e) 3.08 x 101 cm
5) A torus is centered around the x-y plane, with major radius, a = 6.48 m, and minor radius, r = 2.16m. A wire carrying 5A is uniformly wrapped with 930 turns. If B=μ0H is the magnetic field, what is H inside the torus, at a point on the xy plane that is 0.54m from the outermost edge of the torus?
-a) 5.31E+01 amps per meter
-b) 5.73E+01 amps per meter
-c) 6.19E+01 amps per meter
-d) 6.68E+01 amps per meter
+e) 7.21E+01 amps per meter

6) 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

7) 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.

8) A 0.8 Farad capacitor charged with 1.7 Coulombs. What is the energy stored in the capacitor if the plates are 0.5 mm apart?

+a) 1.81 J.
-b) 2.08 J.
-c) 2.39 J.
-d) 2.75 J.
-e) 3.16 J.

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

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

10) An loop of wire with 92 turns has a radius of 0.39 meters, and is oriented with its axis parallel to a magetic field of 0.97 Tesla. What is the induced voltage if this field is reduced to 16% of its original value in 1.4 seconds?

+a) 2.56 x 101 volts
-b) 3.1 x 101 volts
-c) 3.76 x 101 volts
-d) 4.55 x 101 volts
-e) 5.51 x 101 volts

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) Two 6.2 ohm resistors are connected in parallel. This combination is then connected in series to a 2.6 ohm resistor. What is the net resistance?

-a) 3.7 ohms.
-b) 4.3 ohms.
-c) 5 ohms.
+d) 5.7 ohms.
-e) 6.6 ohms.
13) 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) ${\displaystyle I_{1}=0.25A}$; ${\displaystyle I_{2}=0.33A}$; ${\displaystyle I_{3}=0.5A}$; ${\displaystyle I_{4}=0.1A}$.

14) 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

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

16) A 819 mF capacitor is connected in series to a 798 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

-a) 8.27 x 105 s.
+b) 2.61 x 106 s.
-c) 8.27 x 106 s.
-d) 2.61 x 107 s.
-e) 8.27 x 107 s.

### phc:FE:V2

phc20160712T125120

1) 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

2) 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

3) 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 ,
${\displaystyle \left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,}$
over the top surface of the cylinder.

a) 2.597E+03
b) 3.147E+03
c) 3.812E+03
d) 4.619E+03
e) 5.596E+03

4) A 819 mF capacitor is connected in series to a 798 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

a) 8.27 x 105 s.
b) 2.61 x 106 s.
c) 8.27 x 106 s.
d) 2.61 x 107 s.
e) 8.27 x 107 s.

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

a) 1.09 x 10-3 unit
b) 1.33 x 10-3 unit
c) 1.61 x 10-3 unit
d) 1.95 x 10-3 unit
e) 2.36 x 10-3 unit

6) A 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

7) 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.

8) A 0.5 Farad capacitor charged with 1.3 Coulombs. What is the energy stored in the capacitor if the plates are 0.7 mm apart?

a) 1.28 J.
b) 1.47 J.
c) 1.69 J.
d) 1.94 J.
e) 2.24 J.

9) Two 6.6 ohm resistors are connected in parallel. This combination is then connected in series to a 3.4 ohm resistor. What is the net resistance?

a) 4.4 ohms.
b) 5.1 ohms.
c) 5.8 ohms.
d) 6.7 ohms.
e) 7.7 ohms.

10) An object is placed 3.15 cm to the left of a converging lens with a focal length of 6.7 cm. How far is the image from the lens?

a) 3.34 x 100 cm
b) 5.95 x 100 cm
c) 1.06 x 101 cm
d) 1.88 x 101 cm
e) 3.34 x 101 cm

11) H is defined by, B=μ0H, where B is magnetic field. A current of 48A 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 (8.4,8.4).

a) 5.47E+00 amps
b) 6.00E+00 amps
c) 6.58E+00 amps
d) 7.21E+00 amps
e) 7.91E+00 amps

12) An loop of wire with 31 turns has a radius of 0.9 meters, and is oriented with its axis parallel to a magetic field of 0.83 Tesla. What is the induced voltage if this field is reduced to 35% of its original value in 1.7 seconds?

a) 2.07 x 101 volts
b) 2.5 x 101 volts
c) 3.03 x 101 volts
d) 3.67 x 101 volts
e) 4.45 x 101 volts

13) 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

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

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

a) 2 − s
b) 9 − s
c) s − 9
d) 2
e) s − 2
16) 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) ${\displaystyle I_{1}=0.25A}$; ${\displaystyle I_{2}=0.33A}$; ${\displaystyle I_{3}=0.5A}$; ${\displaystyle I_{4}=0.1A}$.
d) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=5A}$; ${\displaystyle I_{3}=3.3A}$; ${\displaystyle I_{4}=2.5A}$.

#### KEY:phc:FE:V2

phc20160712T125120

1) A power supply delivers 169 watts of power to a 219 ohm resistor. What was the applied voltage?

-a) 8.93 x 101 volts
-b) 1.08 x 102 volts
-c) 1.31 x 102 volts
-d) 1.59 x 102 volts
+e) 1.92 x 102 volts

2) 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

3) 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,
${\displaystyle {\vec {\mathfrak {F}}}=(1.89+1.31z)\rho ^{3}{\hat {\rho }}+8.35z^{2}{\hat {z}}}$
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) 5.311E+02
-b) 6.434E+02
-c) 7.795E+02
+d) 9.444E+02
-e) 1.144E+03

4) A 819 mF capacitor is connected in series to a 798 kΩ resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)

-a) 8.27 x 105 s.
+b) 2.61 x 106 s.
-c) 8.27 x 106 s.
-d) 2.61 x 107 s.
-e) 8.27 x 107 s.

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

+a) 1.61 x 10-3 unit
-b) 1.95 x 10-3 unit
-c) 2.36 x 10-3 unit
-d) 2.86 x 10-3 unit
-e) 3.46 x 10-3 unit

6) 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

7) How fast is a 2663 eV electron moving?

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

8) A 1.3 Farad capacitor charged with 1.9 Coulombs. What is the energy stored in the capacitor if the plates are 0.3 mm apart?

-a) 0.91 J.
-b) 1.05 J.
-c) 1.21 J.
+d) 1.39 J.
-e) 1.6 J.

9) Two 7.8 ohm resistors are connected in parallel. This combination is then connected in series to a 5.4 ohm resistor. What is the net resistance?

+a) 9.3 ohms.
-b) 10.7 ohms.
-c) 12.3 ohms.
-d) 14.1 ohms.
-e) 16.3 ohms.

10) An object is placed 6.55 cm to the left of a converging lens with a focal length of 5.4 cm. How far is the image from the lens?

-a) 3.08 x 100 cm
-b) 5.47 x 100 cm
-c) 9.73 x 100 cm
-d) 1.73 x 101 cm
+e) 3.08 x 101 cm

11) 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

12) 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

13) 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

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

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

-a) s − 2
-b) 2 − s
-c) 2
-d) s − 9
+e) 9 − s
16) 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) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=5A}$; ${\displaystyle I_{3}=3.3A}$; ${\displaystyle I_{4}=2.5A}$.
+c) ${\displaystyle I_{1}=1A}$; ${\displaystyle I_{2}=0.5A}$; ${\displaystyle I_{3}=0.33A}$; ${\displaystyle I_{4}=0.25A}$.
-d) ${\displaystyle I_{1}=0.25A}$; ${\displaystyle I_{2}=0.33A}$; ${\displaystyle I_{3}=0.5A}$; ${\displaystyle I_{4}=0.1A}$.