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

phc20160712T125120

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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 &beta;kQ/a2, where &beta; 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 &lambda; situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * a) 2
 * b) 9 &minus; s
 * c) 2 &minus; s
 * d) s &minus; 9
 * e) s &minus; 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 &lambda; situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal D^2 + \mathcal E^2=$$:
 * a) 22 + (9-s)2
 * b) 72 + (2-s)2
 * c) 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 $$\rho$$. 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) $$\varepsilon_0 E=  H\rho z$$
 * b)b) none of these are correct
 * c)c) $$\varepsilon_0 E=   \rho z $$
 * d)d) $$\varepsilon_0 E=  H\rho $$
 * e) $$\varepsilon_0 E = H\rho /2$$

6) A line of charge density &lambda; situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal A=$$:
 * a) 2
 * b) 4
 * c) 1/2
 * d) 8

7) A line of charge density &lambda; situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$
 * a) 3
 * b) s&minus;7
 * c) 3&minus;s
 * d) s&minus;3
 * e) 7&minus;s

8) A sphere has a uniform charge density of $$\rho$$, 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) $$ r^2\varepsilon_0 E=R^3\rho /2$$
 * c)b) $$ r^2\varepsilon_0 E=R^3\rho /3$$
 * d)d) $$ r^2\varepsilon_0 E=r^3\rho /3$$
 * e) $$ r^2\varepsilon_0 E=r^3\rho /2$$

9) A cylinder of radius, R, and height H has a uniform charge density of $$\rho$$. 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) $$\varepsilon_0 E=  H\rho $$
 * b) $$\varepsilon_0 E=   \rho z $$
 * c)c) $$\varepsilon_0 E=  H\rho z$$
 * d)e) $$\varepsilon_0 E = H\rho /2$$
 * 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, $$\vec F = 9.9xy\hat x + 6.1y^3\hat y $$, 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 &lambda; situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal F=$$:
 * a) 1/2
 * b) 3/2
 * c) 2/3
 * d) 2
 * e) 3

13) A line of charge density &lambda; situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * a) s&minus;8
 * b) s&minus;4
 * c) 4&minus;s
 * d) 8&minus;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 &beta;kQ/a2, where &beta; 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 &lambda; situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * -a) s &minus; 9
 * -b) 2 &minus; s
 * -c) s &minus; 2
 * -d) 2
 * +e) 9 &minus; 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 &lambda; situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal D^2 + \mathcal E^2=$$:
 * -a) 72 + (2-s)2
 * +b) 22 + (9-s)2
 * -c) 92 + (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 $$\rho$$. 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) $$\varepsilon_0 E = H\rho /2$$
 * -b)b) none of these are correct
 * -c)d) $$\varepsilon_0 E=  H\rho $$
 * -d)e) $$\varepsilon_0 E=  H\rho z$$
 * +e)c) $$\varepsilon_0 E=   \rho z $$

6) A line of charge density &lambda; situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal A=$$:
 * +a) 4
 * -b) 8
 * -c) 2
 * -d) 1/2

7) A line of charge density &lambda; situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$
 * +a) 7&minus;s
 * -b) s&minus;3
 * -c) 3
 * -d) s&minus;7
 * -e) 3&minus;s

8) A sphere has a uniform charge density of $$\rho$$, and a radius equal to R. What formula describes the electric field at a distance r < R?
 * -a) $$ r^2\varepsilon_0 E=r^3\rho /2$$
 * +b)d) $$ r^2\varepsilon_0 E=r^3\rho /3$$
 * -c)c) none of these are correct
 * -d)b) $$ r^2\varepsilon_0 E=R^3\rho /3$$
 * -e)e) $$ r^2\varepsilon_0 E=R^3\rho /2$$

9) A cylinder of radius, R, and height H has a uniform charge density of $$\rho$$. 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) $$\varepsilon_0 E = H\rho /2$$
 * -b) $$\varepsilon_0 E=   \rho z $$
 * -c)d) none of these are correct
 * -d)b) $$\varepsilon_0 E=  H\rho $$
 * -e)c) $$\varepsilon_0 E=  H\rho z$$

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, $$\vec F = 9.9xy\hat x + 6.1y^3\hat y $$, 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 &lambda; situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal F=$$:
 * -a) 2
 * -b) 3
 * -c) 1/2
 * +d) 3/2
 * -e) 2/3

13) A line of charge density &lambda; situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * -a) 4
 * -b) s&minus;8
 * -c) s&minus;4
 * -d) 4&minus;s
 * +e) 8&minus;s

phc:T1:V2
phc20160712T125120 1) A line of charge density &lambda; situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * a) s &minus; 2
 * b) 2
 * c) 2 &minus; s
 * d) 9 &minus; s
 * e) s &minus; 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, $$\vec F = 6.9xy\hat x + 7.4y^3\hat y $$, 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 $$\rho$$, and a radius equal to R. What formula describes the electric field at a distance r < R?
 * a)b) $$ r^2\varepsilon_0 E=R^3\rho /3$$
 * b)d) $$ r^2\varepsilon_0 E=r^3\rho /3$$
 * c)e) $$ r^2\varepsilon_0 E=R^3\rho /2$$
 * d)c) none of these are correct
 * e) $$ r^2\varepsilon_0 E=r^3\rho /2$$

5) A line of charge density &lambda; situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal A=$$:
 * a) 4
 * b) 2
 * c) 1/2
 * d) 8

6) A cylinder of radius, R, and height H has a uniform charge density of $$\rho$$. 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) $$\varepsilon_0 E=   \rho z $$
 * b)d) $$\varepsilon_0 E=  H\rho $$
 * c) $$\varepsilon_0 E = H\rho /2$$
 * d)b) none of these are correct
 * e)e) $$\varepsilon_0 E=  H\rho z$$

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 &lambda; situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * a) s&minus;4
 * b) 4&minus;s
 * c) s&minus;8
 * d) 4
 * e) 8&minus;s

9) A cylinder of radius, R, and height H has a uniform charge density of $$\rho$$. 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) $$\varepsilon_0 E = H\rho /2$$
 * c)c) $$\varepsilon_0 E=  H\rho z$$
 * d)b) $$\varepsilon_0 E=  H\rho $$
 * e) $$\varepsilon_0 E=   \rho z $$

10) A line of charge density &lambda; situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal D^2 + \mathcal E^2=$$:
 * a) 92 + (2-s)2
 * b) 72 + (2-s)2
 * c) 22 + (9-s)2
 * d) 92 + (7-s)2
 * e) 22 + (7-s)2

11) A line of charge density &lambda; situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$
 * a) 7&minus;s
 * b) 3&minus;s
 * c) 3
 * d) s&minus;3
 * e) s&minus;7

12) A line of charge density &lambda; situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal F=$$:
 * a) 2/3
 * b) 1/2
 * c) 3
 * d) 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 &beta;kQ/a2, where &beta; 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 &lambda; situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * -a) 2
 * -b) s &minus; 2
 * +c) 9 &minus; s
 * -d) 2 &minus; s
 * -e) s &minus; 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, $$\vec F = 7.8xy\hat x + 8y^3\hat y $$, 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 $$\rho$$, and a radius equal to R. What formula describes the electric field at a distance r < R?
 * +a)d) $$ r^2\varepsilon_0 E=r^3\rho /3$$
 * -b) $$ r^2\varepsilon_0 E=r^3\rho /2$$
 * -c)e) $$ r^2\varepsilon_0 E=R^3\rho /2$$
 * -d)b) $$ r^2\varepsilon_0 E=R^3\rho /3$$
 * -e)c) none of these are correct

5) A line of charge density &lambda; situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal A=$$:
 * -a) 2
 * -b) 1/2
 * -c) 8
 * +d) 4

6) A cylinder of radius, R, and height H has a uniform charge density of $$\rho$$. 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) $$\varepsilon_0 E=  H\rho z$$
 * -b) $$\varepsilon_0 E = H\rho /2$$
 * -c)d) $$\varepsilon_0 E=  H\rho $$
 * -d)b) none of these are correct
 * +e)c) $$\varepsilon_0 E=   \rho z $$

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 &lambda; situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * +a) 8&minus;s
 * -b) 4&minus;s
 * -c) s&minus;4
 * -d) s&minus;8
 * -e) 4

9) A cylinder of radius, R, and height H has a uniform charge density of $$\rho$$. 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) $$\varepsilon_0 E = H\rho /2$$
 * -b)c) $$\varepsilon_0 E=  H\rho z$$
 * -c)b) $$\varepsilon_0 E=  H\rho $$
 * -d) $$\varepsilon_0 E=   \rho z $$
 * -e)d) none of these are correct

10) A line of charge density &lambda; situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal D^2 + \mathcal E^2=$$:
 * -a) 22 + (7-s)2
 * +b) 22 + (9-s)2
 * -c) 92 + (7-s)2
 * -d) 92 + (2-s)2
 * -e) 72 + (2-s)2

11) A line of charge density &lambda; situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$
 * +a) 7&minus;s
 * -b) s&minus;7
 * -c) s&minus;3
 * -d) 3
 * -e) 3&minus;s

12) A line of charge density &lambda; situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal F=$$:
 * -a) 3
 * +b) 3/2
 * -c) 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 &beta;kQ/a2, where &beta; 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)  $$I_1 = 10A$$ and $$I_2 = 16.67A$$.
 * b)  $$I_1 = 0.1A$$ and $$I_2 = 0.1667A$$.
 * c)  $$I_1 = 1A$$ and $$I_2 = 1.667A$$.
 * d) $$I_1 = 1A$$ and $$I_2 = 25A$$.

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

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) $$R_1 = 250V$$ and $$R_2 = 0V$$.
 * b) $$R_1 = 125V$$ and $$R_2 = 125V$$.
 * c) $$R_1 = 150V$$ and $$R_2 = 100V$$.
 * 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) $$\frac{3}{2}\Omega$$.
 * b) $$\frac{2}{3}\Omega$$.
 * c) $$\frac{1}{3}\Omega$$.
 * d) $$ 3\Omega$$.

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$$m\Omega$$ 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,  $$\vec\mathfrak F = (2.12+1.85z)\rho^3\hat\rho +8.88z^2\hat z $$ Let $$\hat n$$ be the outward unit normal to this cylinder and evaluate, $$\left |\oint\vec\mathfrak F\cdot\hat n dA\right|\,$$ 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)  $$I_1 = 0.1A$$ and $$I_2 = 0.1667A$$.
 * -b)  $$I_1 = 10A$$ and $$I_2 = 16.67A$$.
 * -c) $$I_1 = 1A$$ and $$I_2 = 25A$$.
 * +d)  $$I_1 = 1A$$ and $$I_2 = 1.667A$$.

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) $$\frac{10}{7}\Omega$$.
 * -b) $$\frac{7}{10}\Omega$$.
 * -c)  $$\frac{6}{10}\Omega$$.
 * -d) $$\frac{10}{6}\Omega$$.

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) $$R_1 = 125V$$ and $$R_2 = 125V$$.
 * -c) $$R_1 = 150V$$ and $$R_2 = 100V$$.
 * -d) $$R_1 = 250V$$ and $$R_2 = 0V$$.

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

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$$m\Omega$$ 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,  $$\vec\mathfrak F = (2.28+1.72z)\rho^3\hat\rho +7.33z^3\hat z $$ Let $$\hat n$$ be the outward unit normal to this cylinder and evaluate, $$\left |\oint\vec\mathfrak F\cdot\hat n dA\right|\,$$ 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) $$R_1 = 250V$$ and $$R_2 = 0V$$.
 * c) $$R_1 = 125V$$ and $$R_2 = 125V$$.
 * d) $$R_1 = 150V$$ and $$R_2 = 100V$$.

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

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$$m\Omega$$ 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)  $$I_1 = 1A$$ and $$I_2 = 1.667A$$.
 * b) $$I_1 = 1A$$ and $$I_2 = 25A$$.
 * c)  $$I_1 = 0.1A$$ and $$I_2 = 0.1667A$$.
 * d)  $$I_1 = 10A$$ and $$I_2 = 16.67A$$.

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

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,  $$\vec\mathfrak F = (2+1.45z)\rho^2\hat\rho +8.02z^3\hat z $$ Let $$\hat n$$ be the outward unit normal to this cylinder and evaluate, $$\left |\oint\vec\mathfrak F\cdot\hat n dA\right|\,$$ 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) $$R_1 = 125V$$ and $$R_2 = 125V$$.
 * -b) $$R_1 = 250V$$ and $$R_2 = 0V$$.
 * -c) None of these are true.
 * -d) $$R_1 = 150V$$ and $$R_2 = 100V$$.

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) $$\frac{10}{7}\Omega$$.
 * -b) $$\frac{10}{6}\Omega$$.
 * -c) $$\frac{7}{10}\Omega$$.
 * -d)  $$\frac{6}{10}\Omega$$.

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$$m\Omega$$ 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)  $$I_1 = 10A$$ and $$I_2 = 16.67A$$.
 * -b)  $$I_1 = 0.1A$$ and $$I_2 = 0.1667A$$.
 * -c) $$I_1 = 1A$$ and $$I_2 = 25A$$.
 * +d)  $$I_1 = 1A$$ and $$I_2 = 1.667A$$.

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

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,  $$\vec\mathfrak F = (2.37+2.6z)\rho^2\hat\rho +8.84z^3\hat z $$ Let $$\hat n$$ be the outward unit normal to this cylinder and evaluate, $$\left |\oint\vec\mathfrak F\cdot\hat n dA\right|\,$$ 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 &mu;T. 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 &lambda; situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * a) 5&minus;s
 * b) s&minus;4
 * c) s&minus;1
 * d) 5
 * e) 1&minus;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 &mu;T. 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 &mu;F capacitor is connected in series to a 414 k&Omega; 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 &mu;T. 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 &lambda; situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * -a) s&minus;4
 * -b) 5
 * -c) s&minus;1
 * +d) 1&minus;s
 * -e) 5&minus;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 &mu;T. 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 &mu;F capacitor is connected in series to a 414 k&Omega; 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 &mu;T. 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 &mu;T. 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 &lambda; situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * a) 5&minus;s
 * b) s&minus;1
 * c) s&minus;4
 * d) 5
 * e) 1&minus;s

12) A 65 &mu;F capacitor is connected in series to a 414 k&Omega; 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 &mu;T. 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 &mu;T. 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 &lambda; situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * -a) 5&minus;s
 * -b) s&minus;1
 * +c) 1&minus;s
 * -d) 5
 * -e) s&minus;4

12) A 65 &mu;F capacitor is connected in series to a 414 k&Omega; 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=&mu;0H, where B is magnetic field. A current of 59A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, 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) Ray drawing eye schematic01.svg
 * b) Ray_drawing_eye_schematic.svg
 * c) They have the same focal lengh.

3) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ 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=&mu;0H, where B is magnetic field. A current of 33A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, 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 &beta;kQ/a2, where &beta; 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$$\int \vec H\cdot\vec{d\ell}$$ 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 &mu;C.  The capacitor is discharged through a  7 k&Omega; 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 &mu;C.  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=&mu;0H, where B is magnetic field. A current of 81A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, 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) Ray_drawing_eye_schematic.svg
 * -b) Ray drawing eye schematic01.svg
 * -c) They have the same focal lengh.

3) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ 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=&mu;0H, where B is magnetic field. A current of 63A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, 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 &beta;kQ/a2, where &beta; 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$$\int \vec H\cdot\vec{d\ell}$$ 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=&mu;0H 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 &mu;C.  The capacitor is discharged through a  9 k&Omega; 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 &mu;C.  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=&mu;0H, where B is magnetic field. A current of 46A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, 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 &mu;C.  The capacitor is discharged through a  8 k&Omega; 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) Ray_drawing_eye_schematic.svg
 * b) Ray drawing eye schematic01.svg
 * c) They have the same focal lengh.

5) H is defined by, B=&mu;0H, where B is magnetic field. A current of 88A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, 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 &beta;kQ/a2, where &beta; 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$$\int \vec H\cdot\vec{d\ell}$$ 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 &mu;C.  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 $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ 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=&mu;0H, where B is magnetic field. A current of 81A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, 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=&mu;0H 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 &mu;C.  The capacitor is discharged through a  9 k&Omega; 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) Ray_drawing_eye_schematic.svg
 * -c) Ray drawing eye schematic01.svg

5) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, 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 &beta;kQ/a2, where &beta; 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$$\int \vec H\cdot\vec{d\ell}$$ 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 &mu;C.  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 $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ 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,  $$\vec\mathfrak F = (2.24+1.11z)\rho^3\hat\rho +8.16z^3\hat z $$ Let $$\hat n$$ be the outward unit normal to this cylinder and evaluate, $$\left |\int_{top}\vec\mathfrak F\cdot\hat n dA\right|\,$$ 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 &beta;kQ/a2, where &beta; 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=&mu;0H, where B is magnetic field. A current of 86A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, 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 &lambda; situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * a) 2
 * b) 9 &minus; s
 * c) s &minus; 2
 * d) 2 &minus; s
 * e) s &minus; 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 &mu;C.  The capacitor is discharged through a  5 k&Omega; 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) $$I_1 = 0.25A$$; $$I_2 = 0.33A$$; $$I_3 = 0.5A$$; $$I_4 = 0.1A$$.
 * b) $$I_1 = 1A$$; $$I_2 = 0.5A$$; $$I_3 = 0.33A$$; $$I_4 = 0.25A$$.
 * c) $$I_1 = 1A$$; $$I_2 = 5A$$; $$I_3 = 3.3A$$; $$I_4 = 2.5A$$.
 * d)  $$I_1 = 10A$$; $$I_2 = 50A$$; $$I_3 = 33A$$; $$I_4 = 25A$$..

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 $$\rho$$. 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) $$2R\varepsilon_0 E=  r^2\rho $$
 * b)b) $$2r\varepsilon_0 E = R^2\rho $$
 * c)e) $$2r^2\varepsilon_0 E= R^3  \rho $$
 * d)d) none of these are correct
 * e)c) $$2\varepsilon_0 E = r\rho $$

16) A 819 mF capacitor is connected in series to a 798 k&Omega; 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,  $$\vec\mathfrak F = (2.07+2.87z)\rho^2\hat\rho +9.56z^3\hat z $$ Let $$\hat n$$ be the outward unit normal to this cylinder and evaluate, $$\left |\int_{top}\vec\mathfrak F\cdot\hat n dA\right|\,$$ 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 &beta;kQ/a2, where &beta; 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=&mu;0H 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=&mu;0H, where B is magnetic field. A current of 36A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, 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 &lambda; situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * -a) 2 &minus; s
 * -b) s &minus; 2
 * +c) 9 &minus; s
 * -d) 2
 * -e) s &minus; 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 &mu;C.  The capacitor is discharged through a  6 k&Omega; 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) $$I_1 = 1A$$; $$I_2 = 0.5A$$; $$I_3 = 0.33A$$; $$I_4 = 0.25A$$.
 * -b)  $$I_1 = 10A$$; $$I_2 = 50A$$; $$I_3 = 33A$$; $$I_4 = 25A$$..
 * -c) $$I_1 = 1A$$; $$I_2 = 5A$$; $$I_3 = 3.3A$$; $$I_4 = 2.5A$$.
 * -d) $$I_1 = 0.25A$$; $$I_2 = 0.33A$$; $$I_3 = 0.5A$$; $$I_4 = 0.1A$$.

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 $$\rho$$. 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) $$2r\varepsilon_0 E = R^2\rho $$
 * -b)e) $$2r^2\varepsilon_0 E= R^3  \rho $$
 * -c)d) none of these are correct
 * -d) $$2R\varepsilon_0 E=  r^2\rho $$
 * +e)c) $$2\varepsilon_0 E = r\rho $$

16) A 819 mF capacitor is connected in series to a 798 k&Omega; 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,  $$\vec\mathfrak F = (2.28+1.72z)\rho^3\hat\rho +7.33z^3\hat z $$ Let $$\hat n$$ be the outward unit normal to this cylinder and evaluate, $$\left |\int_{top}\vec\mathfrak F\cdot\hat n dA\right|\,$$ 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 k&Omega; 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 &beta;kQ/a2, where &beta; 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 &mu;C.  The capacitor is discharged through a  9 k&Omega; 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=&mu;0H, where B is magnetic field. A current of 48A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, 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 $$\rho$$. 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) $$2r\varepsilon_0 E = R^2\rho $$
 * b) $$2R\varepsilon_0 E=  r^2\rho $$
 * c)c) $$2\varepsilon_0 E = r\rho $$
 * d)d) none of these are correct
 * e)e) $$2r^2\varepsilon_0 E= R^3  \rho $$

15) A line of charge density &lambda; situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * a) 2 &minus; s
 * b) 9 &minus; s
 * c) s &minus; 9
 * d) 2
 * e) s &minus; 2

16) What is the current through R1, R2, R3, and R4 in the figure shown?
 * a) $$I_1 = 1A$$; $$I_2 = 0.5A$$; $$I_3 = 0.33A$$; $$I_4 = 0.25A$$.
 * b)  $$I_1 = 10A$$; $$I_2 = 50A$$; $$I_3 = 33A$$; $$I_4 = 25A$$..
 * c) $$I_1 = 0.25A$$; $$I_2 = 0.33A$$; $$I_3 = 0.5A$$; $$I_4 = 0.1A$$.
 * d) $$I_1 = 1A$$; $$I_2 = 5A$$; $$I_3 = 3.3A$$; $$I_4 = 2.5A$$.

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,  $$\vec\mathfrak F = (1.89+1.31z)\rho^3\hat\rho +8.35z^2\hat z $$ Let $$\hat n$$ be the outward unit normal to this cylinder and evaluate, $$\left |\int_{top}\vec\mathfrak F\cdot\hat n dA\right|\,$$ 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 k&Omega; 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 &beta;kQ/a2, where &beta; 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 &mu;C.  The capacitor is discharged through a  7 k&Omega; 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=&mu;0H, where B is magnetic field. A current of 36A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, 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 $$\rho$$. 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) $$2r^2\varepsilon_0 E= R^3  \rho $$
 * -c) $$2R\varepsilon_0 E=  r^2\rho $$
 * -d)b) $$2r\varepsilon_0 E = R^2\rho $$
 * +e)c) $$2\varepsilon_0 E = r\rho $$

15) A line of charge density &lambda; situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * -a) s &minus; 2
 * -b) 2 &minus; s
 * -c) 2
 * -d) s &minus; 9
 * +e) 9 &minus; s

16) What is the current through R1, R2, R3, and R4 in the figure shown?
 * -a)  $$I_1 = 10A$$; $$I_2 = 50A$$; $$I_3 = 33A$$; $$I_4 = 25A$$..
 * -b) $$I_1 = 1A$$; $$I_2 = 5A$$; $$I_3 = 3.3A$$; $$I_4 = 2.5A$$.
 * +c) $$I_1 = 1A$$; $$I_2 = 0.5A$$; $$I_3 = 0.33A$$; $$I_4 = 0.25A$$.
 * -d) $$I_1 = 0.25A$$; $$I_2 = 0.33A$$; $$I_3 = 0.5A$$; $$I_4 = 0.1A$$.