PHY2054 - Exam 1 - Fall 1997 - Selman Hershfield
1. Charges Q1 = -2 micro-C, Q2 = +5 micro-C, Q3 = -4 micro-C, and Q4 = -4 micro-C are arranged on a rectangle with width, w = 5cm, and height, h = 3cm, as shown in Figure 1. What is the magnitude of the force on Q4?

1. 25 N
2. 35 N
3. 45 N
4. 55 N
5. 65 N

2. For the same case as in the previous question, what is the direction of the force on Q4? Use the direction convention shown in Figure 1.

1. 76 degrees
2. 104 degrees
3. 256 degrees
4. 284 degrees
5. 346 degrees

3. A 2C charge and a 4C charge are separated by 1m. What is the magnitude of the force on the 2C charge divided by the magnitude of the force on the 4C charge? Assume that there are no other charges in the vicinity.

1. 0.25
2. 0.5
3. 1
4. 2
5. 4

4. Two identical small metal spheres have charge 30 micro-C and -20 micro-C. The metal spheres are touched together and then separated by 1 m. What is the force on the sphere which was originally 30 micro-C? (In computing the force you may treat the spheres as point charges.)

1. 0.23 N towards the other sphere
2. 0.23 N away from the other sphere
3. 0.92 N towards the other sphere
4. -0.92 N away from the other sphere
5. 5.52 N towards the other sphere

5. In Figure 2(a) a proton travels next to a charged plate with charge Q1 . In Figure (b) a proton travels around a charge Q2. Which of the following are true of Q1 and Q2?

1. Q1 > 0 and Q2 > 0
2. Q1 > 0 and Q2 < 0
3. Q1 < 0 and Q2 > 0
4. Q1 < 0 and Q2 < 0
5. none of the above

6. An electroscope is initially neutral. A positively charged rod is brought close to the electroscope without touching. With the rod in place the electroscope is then grounded. The result is displayed in Figure 3. Which of the following cases is NOT true?

1. The net charge on the electroscope in Figure 3 is negative.
2. If the rod is removed with the ground in place, the net charge on the electroscope is negative.
3. If the ground is removed with the rod in place, the net charge on the electroscope is negative.
4. If the ground is removed and then the rod is removed, the net charge on the electroscope is negative.
5. All of the above are true.

7. You have three kinds of rods: positively charged insulators, negatively charged insulators, and neutral metallic rods. Two rods choosen at random attract. Which of the following is NOT true?

1. One of the rods can be a positively charged insulator.
2. One of the rods can be a negatively charged insulator.
3. At least one of the rods must be charged.
4. Both of the rods can be charged.
5. Both of the rods can be neutral metallic rods.

8. Charges Q2 = -1C and Q3 = 1C are arranged on an equilateral triangle as shown in Figure 4. What is the direction of the electric field at point P1? Use the direction convention shown in Figure 4.

1. 0 degrees
2. 30 degrees
3. 90 degrees
4. 180 degrees
5. 330 degrees

9. Three large parallel planes shown in the Figure 5 have charge per unit area: sigma1 = -8x10-9 C/m2 , sigma2 = 3x10-9 C/m2 , and sigma3 = 5x10-9 C/m2 . What is the electric field at point P3? Use the sign convention that positive is to the right, and negative is to the left.

1. -565 V/m
2. -225 V/m
3. 0 V/m
4. 225 V/m
5. 565 V/m

10. A charge of -2 C is placed at 0 m, and a charge of 1 C is placed at 1m as shown in Figure 6. List all the regions in Figure 6 where there is a point that the electric field is zero.

1. I
2. II
3. III
4. I and II
5. II and III

11. Two charges in a plane produce the field line pattern shown in Figure 7. Which of the following is true?

1. Q1 > 0, Q2 > 0, |Q1 | > |Q2 |
2. Q1 > 0, Q2 < 0, |Q1 | > |Q2 |
3. Q1 < 0, Q2 > 0, |Q1 | > |Q2 |
4. Q1 < 0, Q2 < 0, |Q1 | < |Q2 |
5. Q1 > 0, Q2 < 0, |Q1 | < |Q2 |

12. A spherical conductor is surrounded by two conducting shells as shown in Fig. 8. The radius of the sphere is 1m. The inner radius of the middle shell is 1.5m, and the outer radius of the same shell is 2m. Finally, the inner radius of the outside shell is 2.5m, and the outer radius of the outside shell is 3m. If the electric field at r = 1.2m is 3.75 x 104 N/C pointing radially outwards, and the electric field at r = 2.3 m is 0.68 x 104 N/C pointing radially outwards, what is the net charge on the middle shell?

1. -10 micro-C
2. -2 micro-C
3. 2 micro-C
4. 5 micro-C
5. 10 micro-C

13. Point charges of 1C, 2C, and -3C are arranged as shown in Figure 9. What is flux through the sphere shown in Figure 9?

1. 0 V m
2. 1.13 x 1011 V m
3. 2.26 x 1011 V m
4. -3.39 x 1011 V m
5. 6.78 x 1011 V m

14. Charges Q1 = +4 micro-C, Q2 = -4 micro-C, Q3 = +5 micro-C, and Q4 = -7 micro-C are arranged on a rectangle with width, w = 5cm, and height, h = 3cm, as shown in Figure 1. What is the potential energy of this charge configuration? Use the convention that U = 0 when the charges are very far apart.

1. -18 J
2. -16 J
3. -14 J
4. -12 J
5. -10 J

15. A charge of -2 C is placed at 0 m, and a charge of 1 C is placed at 1 m. An electron is placed a x = 2 m and let go. What is the speed of the electron by the time it reaches x = 1.5 m? (The numbers below are larger than the speed of light (!) because of an unfortunate choice of parameters above. A more sophisticated analysis than we are using in this course would give a velocity less than the speed of light, c = 3 x 108 m/s even for this set of parameters.)

1. 1 x 1010 m/s
2. 2 x 1010 m/s
3. 3 x 1010 m/s
4. 4 x 1010 m/s
5. 5 x 1010 m/s

16. The point charges in Figure 10 have opposite signs, but the same magnitude. (i) Which point, P, Q, or R, has the largest electrical potential (voltage)? (ii) An electron is placed at one of the points. Which point, P, Q, or R, gives the largest potential energy for the electron?

1. (i) P, (ii) Q
2. (i) P, (ii) R
3. (i) R, (ii) P
4. (i) R, (ii) R
5. (i) P, (ii) P

17. Charges Q2 = -1 micro-C and Q3 = 2 micro-C are arranged on an equilateral triangle with sides 4 cm as shown in Figure 4. What is the electrical potential (voltage) at point P1? Use the convention that V = 0 infinitely far away from the charges.

1. -6.75x105 V
2. -2.25x105 V
3. 0 V
4. +2.25x105 V
5. +6.75x105 V

18. A charge of -2 C is placed at 0 m, and a charge of 1 C is placed at 1m as shown in Figure 6. List all the regions in Figure 6 where there is a point that the electrical potential is zero.

1. I
2. II
3. III
4. I and II
5. II and III

19. Six charges are arranged on a hexagon as shown in Figure 11. Q1 = Q2 = Q3 = +1 micro-C and Q4 = Q5 = Q6 = -1 micro-C. The charges are rotated by 60 degrees about the center ,P, of the hexagon. List all of the following quantities which change: F = the force on charge Q1 , E = the electric field at P, U = the net potential energy of the charges, and V = the electrical potential at P.

1. F, E, U, V
2. F, E
3. U, V
4. E, V
5. none change

20. A capacitor has charge 2 micro-C and voltage 3 V. What is the change in the potential energy, PEf - PEi, of a -5 micro-C charge which is moved from the positive plate to the negative plate?

1. -15 x 10-6 J
2. -3 x 10-6 J
3. +3 x 10-6 J
4. +10 x 10-6 J
5. +15 x 10-6 J

1. Answer = (4) 55 N
2. Answer = (3) 256 degrees
4. Answer = (2) 0.23 N away from the other sphere
5. Answer = (2) Q1 > 0 and Q2 < 0
6. Answer = (2) If the rod is removed with the ground in place, the net charge on the electroscope is negative.
7. Answer = (5) Both of the rods can be neutral metallic rods.
8. Answer = (1) 0 degrees
9. Answer = (1) -565 V/m