# (D) Blv/R Counterclockwise

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1 1. There is a counterclockwise current I in a circular loop of wire situated in an external magnetic field directed out of the page as shown above. The effect of the forces that act on this current is to make the loop (A) expand in size (B) contract in size (C) rotate about an axis perpendicular to the page (D) rotate about an axis in the plane of the page (E) accelerate into the page 2. The figure above shows a rectangular loop of wire of width l and resistance R. One end of the loop is in a uniform magnetic field of strength B at right angles to the plane of the loop. The loop is pulled to the right at a constant speed v. What are the magnitude and direction of the induced current in the loop? Magnitude Direction (A) BlvR Clockwise (B) BlvR Counterclockwise (C) Blv/R Clockwise (D) Blv/R Counterclockwise (E) 0 Undefined 3. In each of the following situations, a bar magnet is aligned along the axis of a conducting loop. The magnet and the loop move with the indicated velocities. In which situation will the bar magnet NOT induce a current in the conducting loop?

2 4. Which of the paths above represents the path of an electron traveling without any loss of energy through a uniform magnetic field directed into the page? (A) A (B) B (C) C (D) D (E) E 5. Two capacitors are connected in parallel as shown above. A voltage V is applied to the pair. What is the ratio of charge stored on C 1 to the charge stored on C 2, when C 1 = 1.5C 2? (A) 4/9 (B) 2/3 (C) 1 (D) 3/2 (E) 9/4 6. Two long, parallel wires, fixed in space, carry currents I 1 and I 2. The force of attraction has magnitude F. What currents will give an attractive force of magnitude 4F? (A) 2I 1 and ½I 2 ( B) I 1 and ¼I 2 (C) ½I 1 and ½I 2 (D) 2I 1 and 2I 2 (E) 4I 1 and 4I 2 7. A square loop of copper wire is initially placed perpendicular to the lines of a constant magnetic field of 5 x 10-3 tesla. The area enclosed by the loop is 0.2 square meter. The loop is then turned through an angle of 90 so that the plane of the loop is parallel to the field lines. The turn takes 0.1 second. The average emf induced in the loop during the turn is (A) 1.0 x 10-4 V (B) 2.5 x 10-3 V (C) 0.01 V (D) 100 V (E) 400 V 8. The five resistors shown below have the lengths and cross-sectional areas indicated and are made of material with the same resistivity. Which resistor has the least resistance?

3 9. Two circular coils are situated perpendicular to the z-axis as shown above. There is a current in the primary coil. All of the following procedures will induce a current in the secondary coil EXCEPT (A) rotating the secondary coil about the z-axis (B) rotating the secondary coil about a diameter (C) moving the secondary coil closer to the primary coil (D) varying the current in the primary coil (E) decreasing the cross-sectional area of the secondary coil 10. A wire in the plane of the page carries a current directed toward the top of the page as shown above. If the wire is located in a uniform magnetic field B directed out of the page, the force on the wire resulting from the magnetic field is (A) directed into the page (B) directed out of the page (C) directed to the right (D) directed to the left (E) zero 11. A magnetic field B that is decreasing with time is directed out of the page and passes through a loop of wire in the plane of the page, as shown above. Which of the following is true of the induced current in the wire loop? (A) counterclockwise in direction. (B) It is clockwise in direction. (C) It is directed into the page. (D) It is directed out of the page. (E) It is zero in magnitude. 12. A positive charge of 10-6 coulomb is placed on an insulated solid conducting sphere. Which of the following is true? (A) The charge resides uniformly throughout the sphere. (B) The electric field inside the sphere is constant in magnitude, but not zero. (C) The electric field surrounding the sphere increases with increasing distance from the sphere. (D) An insulated metal object acquires a net positive charge when brought near to, but not in contact with, the sphere. (E) When a second conducting sphere is connected by a conducting wire to the first sphere, charge is transferred until the electric potentials of the two spheres are equal.

4 13. Which of the following will cause the electrical resistance of certain materials known as superconductors to suddenly decrease to essentially zero? (A) Increasing the voltage applied to the material beyond a certain threshold voltage (B) Increasing the pressure applied to the material beyond a certain threshold pressure (C) Cooling the material below a certain threshold temperature (D) Stretching the material to a wire of sufficiently small diameter (E) Placing the material in a sufficiently large magnetic field 14. The direction of the magnetic field at point R caused by the current I in the wire shown above is (A) to the left (B) to the right (C) toward the wire (D) into the page (E) out of the page 15. Two long, parallel wires are separated by a distance d, as shown above. One wire carries a steady current I into the plane of the page while the other wire carries a steady current I out of the page. At what points in the plane of the page and outside the wires, besides points at infinity, is the magnetic field due to the currents zero? (A) Only at point P (B) At all points on the line SS' (C) At all points on the line connecting the two wires (D) At all points on a circle of radius 2d centered on point P (E) At no points 16. A wire of constant length is moving in a constant magnetic field, as shown above. The wire and the velocity vector are perpendicular to each other and are both perpendicular to the field. Which of the following graphs best represents the potential difference E between the ends of the wire as a function of velocity?

5 17. The product 2 amperes x 2 volts x 2 seconds is equal to (A) 8 coulombs (B) 8 newtons (C) 8 joules (D) 8 calories (E) 8 newton-amperes 18. A square loop of wire of resistance R and side a is oriented with its plane perpendicular to a magnetic field B, as shown above. What must be the rate of change of the magnetic field in order to produce a current I in the loop? (A) IR/a 2 (B) Ia 2 /R (C) Ia/R (D) Ra/I (E) IRa 19. A rectangular wire loop is at rest in a uniform magnetic field B of magnitude 2 T that is directed out of the page. The loop measures 5 cm by 8 cm, and the plane of the loop is perpendicular to the field, as shown above. The total magnetic flux through the loop is (A) zero (B) 2 x 10-3 T-m 2 (C) 8 x 10-3 T-m 2 (D) 2 x 10-1 T-m 2 (E) 8 x 10-1 T- m 20. A certain coffeepot draws 4.0 A of current when it is operated on 120 V household lines. If electrical energy costs 10 cents per kilowatt-hour, how much does it cost to operate the coffeepot for 2 hours? (A) 2.4 cents (B) 4.8 cents (C) 8.0 cents (D) 9.6 cents (E) 16 cents 21. An electron is in a uniform magnetic field B that is directed out of the plane of the page, as shown above. When the electron is moving in the plane of the page in the direction indicated by the arrow, the force on the electron is directed (A) toward the right (B) out of the page (C) into the page (D) toward the top of the page (E) toward the bottom of the page

6 x x x x B x x x x x x x x spring x x x x 22. A metal spring has its ends attached so that if forms a circle. It is placed in a uniform magnetic field, as shown above. Which of the following will not cause a current to be induced in the spring? (A) Changing the magnitude of the magnetic field (B) Increasing the diameter of the circle by stretching the spring (C) Rotating the spring about a diameter (D) Moving the spring parallel to the magnetic field (E) Moving the spring in and out of the magnetic field Questions A magnetic field of 0.1T forces a proton beam of 1.5 ma to move in a circle of radius 0.1 m. The plane of the circle is perpendicular to the magnetic field. 23. Of the following, which is the best estimate of the work done by the magnetic field on the protons during one complete orbit of the circle? (A) 0 J (B) J (C) 10-5 J (D) 10 2 J (E) J 24. Of the following, which is the best estimate of the speed of a proton in the beam as it moves in the circle? (A) 10-2 m/s (B) 10 3 m/s (C) 10 6 m/s (D) 10 8 m/s (E) m/s 25. A single circular loop of wire in the plane of the page is perpendicular to a uniform magnetic field B directed out of the page, as shown above. If the magnitude of the magnetic field is decreasing, then the induced current in the wire is (A) directed upward out of the paper (B) directed downward into the paper (C) clockwise around the loop (D) counterclockwise around the loop (E) zero (no current is induced)

7 Questions Two concentric circular loops of radii b and 2b, made of the same type of wire, lie in the plane of the page, as shown above. 26. The resistance of the wire loop of radius b is R. What is the resistance of the wire loop of radius 2b? (A) R/4 (B) R/2 (C) R (D) 2R (E) 4R 27. A uniform magnetic field B that is perpendicular to the plane of the page now passes through the loops, as shown above. The field is confined to a region of radius a, where a < b, and is changing at a constant rate. The induced emf in the wire loop of radius b is. What is the induced emf in the wire loop of radius 2b? (A) Zero (B) /2 (C) (D) 2 (E) Two parallel wires, each carrying a current I, repel each other with a force F. If both currents are doubled, the force of repulsion is a. 2F b. 2 2 F c. 4F d. 4 2 F e. 8F 29. The operating efficiency of a 0.5 A, 120 V electric motor that lifts a 9 kg mass against gravity at an average velocity of 0.5 m/s is most nearly a. 7% b. 13% c. 25% d. 53% e. 75 % 30. An electron e and a proton p are simultaneously released from rest in a uniform electric field E, as shown above. Assume that the particles are sufficiently far apart so that the only force acting on each particle after it is released is that due to the electric field. At a later time when the particles are still in the field, the electron and the proton will have the same a. direction of motion b. speed c. displacement d. magnitude of acceleration e. magnitude of force acting on them

8 31. Two conducting wire loops move near a very long, straight conducting wire that carries a current I. When the loops are in the positions shown above, they are moving in the directions shown with the same constant speed v. Assume that the loops are far enough apart that they do not affect each other. Which of the following is true about the induced electric currents, if any, in the loops? Loop l Loop 2 a. No current No current b. No current Counterclockwise direction c. Clockwise direction No current d. Clockwise direction Clockwise direction e. Counterclockwise direction Clockwise direction 32. A wire loop is rotated in a uniform magnetic field about an axis perpendicular to the field. as shown above. How many times is the induced current in the loop reversed if the loop makes 3 complete revolutions from the position shown? a. One b. Two c. Three d. Six e. Twelve 33. The diagram above shows electric field lines in an isolated region of space containing two small charged spheres, Y and Z Which of the following statements is true? a. The charge on Y is negative and the charge on Z is positive. b. The strength of the electric field is the same everywhere. c. The electric field is strongest midway between Y and Z. d. A small negatively charged object placed at point X would tend to move toward the right. e. Both charged spheres Y and Z carry charge of the same sign. 34. As shown above, a positively charged particle moves to the right without deflection through a pair of charged plates. Between the plates are a uniform electric field E of magnitude 6.0 N/C and a uniform magnetic field B of magnitude 2.0 T, directed as shown in the figure. The speed of the particle is nearly a m/s b m/s c. 3.0 m/s d. 12 m/s e. 18 m/s

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