Physics C Electricity and Magnetism Exam 2024

Section I: Multiple-Choice Questions +y B +z 1. +x A rectangular loop of wire lies in the xy-plane in a region with a uniform  magnetic field B directed in the −z -direction, as shown. In which of the following cases will an emf be induced in the loop? (A) When the loop is moving without rotating in the +y-direction (B) When the loop is moving without rotating in the +z-direction (C) When the loop is rotating about an axis along the z -axis (D) When the loop is rotating about an axis along the y -axis 2. A cylindrical wire segment with length 0.25 m and diameter 3.0 × 10−3 m dissipates energy at a rate of 6.0 × 10−4 W when a current of 0.50 A is in the wire segment. Which of the following is approximately equal to the resistivity of the wire? (A) 6.8 × 10−8 Ω ⋅ m (B) 9.0 × 10−5 Ω ⋅ m (C) 7.5 × 10−3 Ω ⋅ m (D) 840 Ω⋅ m 2024 +Q B A +Q 3. Two small spheres, each with positive charge +Q , are fixed in place at two corners of an equilateral triangle, as shown in the figure. Point A is at the other corner, and Point B is midway between the spheres. A test charge with positive charge +q is moved from Point A to Point B at a constant velocity by an external force. The work done by the external force on the moving particle is Wext, and the work done by the electrostatic forces from the spheres on the moving particle is Welec. Which of the following correctly identifies the signs of these quantities? A B C D Wext Welec Positive Positive Negative Negative Positive Negative Positive Negative (A) A (B) B (C) C (D) D 2024 +y y = +4d y = +2d Wire R 4I Wire S 2I +z y = –d 4. +x Wire T 2I Three long wires, R, S, and T, are arranged in the xy-plane parallel to each other and the x-axis at the positions shown in the figure. The direction and current in each wire are indicated. Which of the following correctly indicates the magnitude and direction of the magnetic field at the origin of the coordinate system? (A) in the −z -direction (B) in the +z-direction (C) in the −z -direction (D) in the +z-direction B 5m A +y 37° +z +x E = 1000 V/m 5. Points A and B are separated by a distance of 5 m and located in a uniform electric field of magnitude 1000 V m directed in the +y -direction, as shown in the figure. The line between Point A and Point B makes an angle of 37 to the x-axis. When a proton (of charge +e ) is moved by an external force from Point A to Point B, what is the change in electric potential energy of the proton-field system? (A) −5000 eV (B) −3000 eV (C) +3000 eV (D) +5000 eV 2024 A C B 6. C 3 C , are connected in parallel, 3 as shown. The equivalent capacitance between points A and B is Ceq . A dielectric C is inserted into the capacitor with capacitance , and the new equivalent 3 capacitance between points A and B is 2Ceq . What is the value of the dielectric constant of the dielectric? (A) 2 Two air-filled capacitors, with capacitance C and (B) 3 (C) 5 (D) 6 L L R Circuit 1 7. R R Circuit 2 An inductor with inductance L is placed in series with a resistor of resistance R , a battery of emf , and a switch that is initially open, as shown in the Circuit 1 diagram. The switch is closed at time t = 0, and Circuit 1 reaches half of its steady-state current at t = t1 . Circuit 2 is constructed by adding a resistor of resistance R in parallel with the original resistor, as shown in the Circuit 2 diagram. The switch is closed at time t = 0, and Circuit 2 reaches half of its steady-state current at t = t 2. Which of the following correctly compares t1 and t 2 , and provides a valid justification? (A) t 2 = t1, because the time for an RL circuit to reach half of its steady-state current only depends on L (B) t 2 = t1, because both the time constant and the steady-state current double in Circuit 2 compared to Circuit 1 (C) t 2 > t1, because the equivalent resistance is greater in Circuit 2 than in Circuit 1, so the time constant is greater in Circuit 2 (D) t 2 > t1, because the equivalent resistance is less in Circuit 2 than in Circuit 1, so the time constant is greater in Circuit 2 2024 Questions 8 and 9 refer to the following. A sphere of uniform charge density has a positive net charge +Q and radius RS . A small particle of positive charge +q can be moved through space both inside the sphere of uniform charge and outside the sphere. 8. The particle of charge +q is initially located a distance 2 RS from the center of the sphere and then moved to the sphere’s center. Which of the following correctly describes the change in the electric potential energy of the particle-sphere system, U PS , when the particle is moved, and provides a valid justification? (A) U PS 0. The electric field due to the sphere’s charge does positive work on the positively charged particle. (B) U PS 0. The motion of the positively charged particle is opposite to the direction of the electric field due to the sphere’s charge. (C) U PS 0. The electric field due to the sphere’s charge is zero at the center of the sphere. (D) U PS 0. As the positively charged particle is moved, positive work done outside the sphere is canceled by negative work of equal magnitude that is done inside the sphere. 9. With the particle held in place at the center of the charged spherical region, what is the magnitude of the net electric field due to both the particle and the sphere at a distance RS from the sphere’s center? (A) (B) (C) (D) 2024 10. A junction in a circuit consists of three wires connected together. Which of the following diagrams could indicate the directions and magnitudes of the currents in the three wires? (A) 2 A 3 A 5A (B) 2 A 3A 5A (C) 2 A 3A 5A (D) 2 A 3 A 5A Bz (T) +y B 0.4 0.2 +z +x O –0.2 3 6 9 12 Time (s) –0.4 Figure 1 Figure 2 11. A metal wire of resistance 10 Ω is bent into a circular loop of radius 0.10 m and  placed in a uniform magnetic field B, as shown in Figure 1. The z -component Bz of the magnetic field is shown as a function of time in Figure 2, where positive indicates that the magnetic field is directed out of the plane of the figure. Which of the following correctly indicates the magnitude and direction of the current induced in the loop at time t = 6.0 s? A B C D Magnitude 3.8 mA 3.8 mA 0.42 mA 0.42 mA Direction Clockwise Counterclockwise Clockwise Counterclockwise (A) A (B) B (C) C (D) D 2024 +z a a a O +x +y 12. A Gaussian surface, in the shape of a cube of side length a, is oriented with one corner at the origin O, as shown in the figure. The cubical surface is in a region with charges (not shown) where the resulting electric field is described by , where b is a positive constant. What is the total electric flux through the surface of the cube? (A) Zero (B) ba3 (C) 2ba3 (D) 6ba3 2024 Segment 2 B Segment 1 13. A semicircular loop with a clockwise current is placed in a uniform magnetic  field that is directed into the page, as shown in the figure. F1 is the net force  on Segment 1, which is the straight portion of the loop. F2 is the net force on Segment 2, which is the curved portion of the loop. Which of the following   correctly indicates the directions and relative magnitudes of F1 and F2 ?  Direction of F1 A Toward the bottom of the figure B Toward the bottom of the figure C Toward the top of the figure D Toward the top of the figure  Direction of F2 Toward the top of the figure Toward the top of the figure Toward the bottom of the figure Toward the bottom of the figure Magnitudes F1 = F2 F1 < F2 F1 = F2 F1 < F2 (A) A (B) B (C) C (D) D r r I R Figure 1 3R I 2 Figure 2 14. When a nonideal battery is connected to a resistor with resistance R , as shown in Figure 1, the current in the circuit is I. When the same nonideal battery is connected to a resistor with resistance 3R, as shown in Figure 2, the current in I the circuit is . What is the internal resistance r of the battery? 2 R (A) 4 R (B) 2 (C) R (D) 2R 2024 –3Q A +4Q B C D 15. Two small spheres are arranged along a line and have charges of −3Q and +4Q , as shown in the figure. The tick marks on the axis are equally spaced. At which of the labeled tick marks does the electric field have the greatest magnitude? (A) A (B) B (C) C (D) D 2024