Electromagnetism II 1. Salt water contains n sodium ions (Na + ) per cubic meter and n chloride ions (Cl ) per cubic meter. A battery is connected to metal rods that dip into a narrow pipe full of salt water. The cross-sectional area of the pipe is A (see Figure below). The magnitude of the drift velocity of the sodium ions is v Na, and the magnitude of the drift velocity of the chloride ions is v Cl. Assume that v Na > v Cl. (+e is the charge of a proton.) What is the magnitude of the ammeter reading (a) enav Na enav Cl (b) enav Na + enav Cl (c) enav Na (d) enav Cl (e) zero 2. In the three circuits shown below, the batteries are identical and have negligible internal resistance, and all the light bulbs are identical. Rank the light bulbs (A, B, C, D, E) in order of brightness from brightest to dimmest. (a) A > B = C > D = E (b) A > D = E > B = C (c) A = B = C > D = E (d) A = D = E > B = C (e) None of the above. 3. The capacitor in the figure below is originally charged. What does the ammeter read as a function of time after the switch is closed? (a) I = 0 always. (b) I = constant 0 1
(c) I increases, then is constant. (d) I instantly jumps up, then slowly decreases. (e) None of the above. 4. Which graph best represents the magnetic field established at the center of a coil by a steady current in the coil? (a) (b) (c) (d) (e) 5. Two thin spherical conducting shells are centered on the same point. The inner sphere has radius b and total charge q. The outer sphere has radius B and total charge Q. At a point a distance R from the common center, where b < R < B, and assuming the electric potential is zero an infinite distance away, the total potential due to the two spheres is: (a) kq/b + kq/b (b) kq/b + kq/r (c) kq/r (d) kq/r + kq/b (e) kq/r + kq/r 6. What is the magnitude of the total electric field for the two spheres at the point described in the preceding question? 2
(a) kq/b 2 + kq/b 2 (b) kq/b 2 + kq/r 2 (c) kq/r 2 (d) kq/r 2 + kq/b 2 (e) kq/r 2 + kq/r 2 7. The straight wire in the figure below is infinitely long and carries a current I. The rectangular loop carries a conventional current I in the counterclockwise direction. The net force, in SI units, on the rectangular loop is: ( (a) µ0ii c 1 2π a ) 1 b to the right ( (b) µ0ii c 1 2π a + ) 1 b to the left ( ) (c) µ0ii c 2π a + c b + 2(b a) c to the left (d) µ0ii 2π (e) 0 2(b 1) c to the right 8. A (spatially) uniform magnetic field of 0.080 T is directed into the plane of the page and perpendicular to it, as shown in the figure below. A wire loop in the plane of the page has constant area 0.010 m 2. If the magnitude of the magnetic field decreases at a constant rate of 3.0 10 4 T/s, what are the magnitude and direction of the induced emf? (a) 3.0 10 6 V clockwise (b) 3.0 10 6 V counterclockwise (c) 2.4 10 5 V counterclockwise (d) 8.0 10 4 V counterclockwise (e) 8.0 10 4 V clockwise 9. Three conducting spheres have identical diameters (see Figure below). 3
Spheres 1 and 2 are separated by a distance that is large compared to their diameter. They have equal charges and repel each other with an electrostatic force F. Sphere 3 is initially uncharged and has an insulated handle. It is touched first to sphere 1, then to sphere 2, and then removed. If spheres 1 and 2 are returned to their original separation, the force between them is: (a) 0 (b) (1/16)F (c) (1/4)F (d) (3/8)F (e) (1/2)F 10. In the figure below, conducting spheres A has radius a and sphere B has radius b. The spheres had been connected by a conducting wire which has since been removed. Both spheres are now positively charged and isolated from their surroundings. Assuming the potential an infinite distance away is zero, which of the following statements about the spheres are true: I. Sphere A is at the higher potential. II. Sphere B is at the higher potential. III. Both spheres have the same potential. IV. Sphere A has the larger charge. V. Sphere B has the larger charge. VI. Both spheres have the same charge. (a) I and IV (b) I and VI (c) II and VI (d) III and IV (e) III and V 11. Two concentric spherical shells, one with radius b and net charge +Q, and the other with radius 2b and net charge +Q, are isolated from each other (see Figure below). If R is the distance from the common center, the highest electric field magnitude E occurs: 4
(a) only at R = 0, where E is infinite. (b) anywhere R < b, where E is constant (c) immediately outside the smaller (R = b) shell. (d) immediately outside the larger (R = 2b) shell. (e) far away from the shells; E increases with distance. 12. An infinite conducting plate of thickness 0.0200 m is surrounded by a uniform field E = 400 V/m directed left to right (see the Figure below). Let the potential V 0 = 0 at a distance 0.0200 m to the right of the plate. What is V 3, the potential 0.0300 m to the left of the plate? (a) 28 V (b) 20 V (c) +12 V (d) +20 V (e) +28 V 13. As illustrated in the figure below, four point charges are fixed in a square pattern. The diagonal of the square has length 2a What are the magnitude and direction of the electric field at the center of the square? (a) kq/a 2 at 45 above the +x axis (b) kq/a 2 at 45 below the x axis (c) 3kq/a 2 at 45 above the x axis (d) 3kq/a 2 at 45 below the +x axis (e) 9kq/a 2 at 45 above the +x axis 14. A particle with charge +q and mass m travels perpendicularly to a magnetic field, and therefore moves in a circle. The circle s radius is R, and the frequency of the motion is f. What is the magnitude of the magnetic field? (a) mf q (b) 2πmf q m (c) 2πqf 5
(d) mc qr (e) mqf 2πR 15. Charge is uniformly distributed through a volume of radius a. Which graph best represents the magnitude of the electric field as a function of distance from the center of the sphere? (a) (b) (c) (d) (e) 16. An electron and a proton are placed between two oppositely charged parallel plates. Both are closer to the positive plate than the negative plate. Which of the following statements must be true? I. The force on the proton is greater than the force on the electron. II. The potential energy of the proton is greater than that of the electron. III. The potential energy of the proton and the electron is the same. (a) I only (b) II only (c) III only (d) I & II only (e) I & III only 6
17. What is the total current supplied by the power supply in the following circuit? (a) 1 A (b) 1.5 A (c) 2 A (d) 2.25 A (e) 3 18. Three bulbs, A, B, and C, are wired to a battery. A and B are wired in parallel, and this combination is wired in series with C. If A were to burn out, what would happen to the brightness of the other two bulbs? (a) B would brighten and C would stay the same. (b) Both B and C would brighten. (c) B would brighten and C would dim. (d) B would dim and C would brighten. (e) Both B and C would stay the same. 7