AP Physics C: Electricity and Magnetism Practice Test 4 – 60 Questions with Answers
Test yourself with 60 original AP Physics C: Electricity and Magnetism practice questions covering all 6 units of the course: electric charges, fields, and Gauss’s law, electric potential, conductors and capacitors, electric circuits, magnetic fields and electromagnetism, and electromagnetic induction. Every answer includes the full working. All questions are calculus-based.
Unit 8: Electric Charges, Fields, and Gauss’s Law
Q1. Two point charges carry charges 24 μC and 18 μC and are 54 cm apart in vacuum. What is the magnitude of the electrostatic force between them?
- (A) 6.66 N
- (B) 26.6 N
- (C) 13.3 N
- (D) 3.33 N
Show Answer
Answer: C – F = kq1q2/r2 gives 13.3 N.
Q2. A point charge of 27 μC is fixed in vacuum. What is the magnitude of the electric field at a point 75 cm from the charge?
- (A) 2.16 × 105 N/C
- (B) 8.63 × 105 N/C
- (C) 4.32 × 105 N/C
- (D) 1.73 × 106 N/C
Show Answer
Answer: C – E = k|q|/r2 gives 4.32 × 105 N/C.
Q3. Two positive point charges 17 μC and 17 μC lie on the x-axis 22 cm apart. A point P lies on the x-axis 25 cm beyond the second charge, on the side away from the first. What is the magnitude of the net electric field at P?
- (A) 1.57 × 106 N/C
- (B) 3.14 × 106 N/C
- (C) 6.27 × 106 N/C
- (D) 7.84 × 105 N/C
Show Answer
Answer: B – Both fields point away from P’s sources, so E = kq1/r12 + kq2/r22 = 3.14 × 106 N/C.
Q4. An infinitely long straight wire carries a uniform linear charge density of 16 nC/m. What is the magnitude of the electric field 40 cm from the wire?
- (A) 360 N/C
- (B) 1.44 × 103 N/C
- (C) 2.88 × 103 N/C
- (D) 719 N/C
Show Answer
Answer: D – By Gauss’s law, E = 2kλ/r = 719 N/C.
Q5. A very large flat sheet carries a uniform surface charge density of 29 μC/m2. What is the magnitude of the electric field near the sheet, away from its edges?
- (A) 8.19 × 105 N/C
- (B) 3.28 × 106 N/C
- (C) 1.64 × 106 N/C
- (D) 2.46 × 106 N/C
Show Answer
Answer: C – For one sheet, E = σ/(2ε0) = 1.64 × 106 N/C.
Q6. A solid insulating sphere of radius 24 cm carries a total charge of 35 μC uniformly distributed through its volume. What is the magnitude of the electric field at a point 17 cm from its centre?
- (A) 3.87 × 106 N/C
- (B) 1.93 × 106 N/C
- (C) 7.74 × 106 N/C
- (D) 1.55 × 107 N/C
Show Answer
Answer: A – Inside, Gauss’s law gives E = kQr/R3 = 3.87 × 106 N/C.
Q7. A thin ring of radius 14 cm carries a total charge of 32 μC uniformly around its circumference. What is the magnitude of the electric field on the ring’s axis 25 cm from its centre?
- (A) 3.06 × 106 N/C
- (B) 1.53 × 106 N/C
- (C) 6.11 × 106 N/C
- (D) 7.64 × 105 N/C
Show Answer
Answer: A – Integrating around the ring, E = kQx/(R2 + x2)3/2 = 3.06 × 106 N/C.
Q8. A thin rod of length 33 cm carries a total charge of 32 nC uniformly along its length. What is the magnitude of the electric field on the rod’s axis 18 cm beyond one end?
- (A) 1.57 × 103 N/C
- (B) 6.27 × 103 N/C
- (C) 1.25 × 104 N/C
- (D) 3.13 × 103 N/C
Show Answer
Answer: D – Integrating dq contributions gives E = kQ/[d(d + L)] = 3.13 × 103 N/C.
Q9. A uniform electric field of 2959 N/C passes through a flat surface of area 0.04 m2. The angle between the field and the normal to the surface is 0°. What is the electric flux through the surface?
- (A) 59.2 N·m2/C
- (B) 237 N·m2/C
- (C) 118 N·m2/C
- (D) 473 N·m2/C
Show Answer
Answer: C – Φ = EA cosθ = 118 N·m2/C.
Q10. A particle of mass 17 mg and charge 7 μC is placed in a uniform electric field of 4429 N/C. Ignoring gravity, what is the magnitude of its initial acceleration?
- (A) 912 m/s2
- (B) 3.65 × 103 m/s2
- (C) 456 m/s2
- (D) 1.82 × 103 m/s2
Show Answer
Answer: D – a = qE/m = 1.82 × 103 m/s2.
Q11. An electric dipole consists of charges +15 μC and -15 μC separated by 28 mm. Estimate the magnitude of the electric field on the dipole axis 34 cm from its centre, where the distance is much larger than the separation.
- (A) 9.61 × 104 N/C
- (B) 3.84 × 105 N/C
- (C) 7.69 × 105 N/C
- (D) 1.92 × 105 N/C
Show Answer
Answer: D – On the axis far away, E is approximately 2kp/r3 = 1.92 × 105 N/C.
Q12. A thin rod of length 31 cm carries a uniform linear charge density λ. Which integral gives the magnitude of the electric field at a point on the rod’s axis 29 cm beyond one end, where x is the distance from a charge element dq to the point?
- (A) ∪ kλ dx / x2
- (B) ∪ kλ dx / x
- (C) ∪ kλ dx / x3
- (D) ∪ λ dx / x2
Show Answer
Answer: A – Each element contributes dE = k dq/x2 = kλ dx/x2, and the contributions add along the axis.
Unit 9: Electric Potential
Q13. A thin spherical shell of radius 22 cm carries a total charge of 7 μC uniformly on its surface. What is the electric potential at a point 53 cm from its centre, with zero potential at infinity?
- (A) 1.19 × 105 V
- (B) 5.94 × 104 V
- (C) 2.37 × 105 V
- (D) 4.75 × 105 V
Show Answer
Answer: A – Outside, V = kQ/r = 1.19 × 105 V.
Q14. A particle of mass 8 μg and charge 74 nC starts from rest and accelerates through a potential drop of 642 V. What is its final speed, ignoring gravity and other forces?
- (A) 54.5 m/s
- (B) 218 m/s
- (C) 109 m/s
- (D) 27.2 m/s
Show Answer
Answer: C – qΔV = (1/2)mv2, so v = √(2qΔV/m) = 109 m/s.
Q15. Point charges 13 μC and -4 μC are fixed in vacuum. At a certain point P, the distances to the two charges are 21 cm and 28 cm respectively. What is the electric potential at P, with zero potential at infinity?
- (A) 2.14 × 105 V
- (B) 8.56 × 105 V
- (C) 4.28 × 105 V
- (D) -4.28 × 105 V
Show Answer
Answer: C – Potentials add as scalars: V = kq1/r1 + kq2/r2 = 4.28 × 105 V.
Q16. A charge is moved slowly along an equipotential surface held at 200 V, from one point to another on the same surface. How much work is done by the electric field during this move?
- (A) 200 J
- (B) 100 J
- (C) 400 J
- (D) 0 J
Show Answer
Answer: D – Moving along an equipotential means ΔV = 0, so W = qΔV = 0.
Q17. A point charge of 14 μC is fixed in vacuum, with zero potential at infinity. What is the electric potential 50 cm from the charge?
- (A) 1.26 × 105 V
- (B) 5.03 × 105 V
- (C) 2.52 × 105 V
- (D) -2.52 × 105 V
Show Answer
Answer: C – V = kq/r = 2.52 × 105 V.
Q18. A charge of 16 μC is moved slowly from a point at potential 157 V to a point at potential 407 V. How much work is done by an external agent, ignoring any change in kinetic energy?
- (A) 0.004 J
- (B) 0.002 J
- (C) 0.008 J
- (D) 0.001 J
Show Answer
Answer: A – W = qΔV = 0.004 J.
Q19. Two point charges 11 μC and -2 μC are held 27 cm apart. What is the electric potential energy of this pair?
- (A) -0.733 J
- (B) -0.366 J
- (C) -1.47 J
- (D) 0.733 J
Show Answer
Answer: A – U = kq1q2/r = -0.733 J; the sign follows the sign of q2.
Q20. In a region, the electric potential varies with position as V(x) = 9x2 + (5)x + 20, where V is in volts and x is in metres. What is the x-component of the electric field at x = 0.5 m?
- (A) -7 N/C
- (B) -28 N/C
- (C) 14 N/C
- (D) -14 N/C
Show Answer
Answer: D – Ex = -dV/dx = -(18x + 5); at x = 0.5 m this gives -14 N/C.
Q21. A thin ring of radius 27 cm carries a total charge of 13 μC uniformly around its circumference. What is the electric potential on the ring’s axis 26 cm from its centre, with zero potential at infinity?
- (A) 1.56 × 105 V
- (B) 3.12 × 105 V
- (C) 6.24 × 105 V
- (D) 7.79 × 104 V
Show Answer
Answer: B – Every element is the same distance away, so V = kQ/√(R2 + x2) = 3.12 × 105 V.
Unit 10: Conductors and Capacitors
Q22. A parallel-plate capacitor has plates of area 160 cm2 separated by 8 mm in vacuum. What is its capacitance?
- (A) 1.77 × 10-11 F
- (B) 8.85 × 10-12 F
- (C) 3.54 × 10-11 F
- (D) 7.08 × 10-11 F
Show Answer
Answer: A – C = ε0A/d = 1.77 × 10-11 F.
Q23. An isolated parallel-plate capacitor is charged to 36 V in vacuum. The gap is then completely filled with a dielectric of constant 2.5 without changing the charge on the plates. What is the new voltage across the capacitor?
- (A) 7.2 V
- (B) 28.8 V
- (C) 57.6 V
- (D) 14.4 V
Show Answer
Answer: D – With Q fixed, V = Q/C falls by κ: V = V0/κ = 14.4 V.
Q24. Capacitors of 7 μF and 2 μF are connected in series. What is their equivalent capacitance?
- (A) 0.778 μF
- (B) 3.11 μF
- (C) 6.22 μF
- (D) 1.56 μF
Show Answer
Answer: D – 1/Ceq = 1/C1 + 1/C2, so Ceq = 1.56 μF.
Q25. Capacitors of 13 μF, 6 μF and 3 μF are connected in parallel. What is their equivalent capacitance?
- (A) 22 μF
- (B) 11 μF
- (C) 44 μF
- (D) 16.5 μF
Show Answer
Answer: A – In parallel, Ceq = C1 + C2 + C3 = 22 μF.
Q26. A 37 μF capacitor is charged to 200 V. How much energy is stored in the capacitor?
- (A) 0.74 J
- (B) 0.37 J
- (C) 1.48 J
- (D) 0.185 J
Show Answer
Answer: A – U = (1/2)CV2 = 0.74 J.
Q27. A 34 μF capacitor is connected across a 115 V battery. What charge is stored on each plate?
- (A) 0.00196 C
- (B) 0.00782 C
- (C) 0.00391 C
- (D) 0.0156 C
Show Answer
Answer: C – Q = CV = 0.00391 C.
Q28. A spherical capacitor consists of two concentric conducting shells of radii 5 cm and 15 cm. What is its capacitance?
- (A) 4.17 × 10-12 F
- (B) 8.34 × 10-12 F
- (C) 1.67 × 10-11 F
- (D) 2.09 × 10-12 F
Show Answer
Answer: B – C = 4πε0ab/(b – a) = 8.34 × 10-12 F.
Q29. The voltage across a parallel-plate capacitor is 290 V and the plate separation is 10 mm. What is the magnitude of the uniform electric field between the plates?
- (A) 1.45 × 104 N/C
- (B) 2.9 × 104 N/C
- (C) 5.8 × 104 N/C
- (D) 1.16 × 105 N/C
Show Answer
Answer: B – E = V/d = 2.9 × 104 N/C.
Unit 11: Electric Circuits
Q30. An initially uncharged capacitor is connected in series with a 37 kΩ resistor to a battery. The RC time constant is not given directly. How long after connection will the capacitor reach 50% of its maximum charge? The capacitance is 18 μF.
- (A) 0.231 s
- (B) 0.462 s
- (C) 0.923 s
- (D) 0.115 s
Show Answer
Answer: B – τ = RC = 0.666 s, and q = Qmax(1 – e-t/τ), so t = -τ ln(1 – 0.5) = 0.462 s.
Q31. A capacitor charged to 88 V discharges through a resistor. The RC time constant is 4 s. What is the voltage across the capacitor 2 s after discharge begins?
- (A) 26.7 V
- (B) 107 V
- (C) 13.3 V
- (D) 53.4 V
Show Answer
Answer: D – V = V0e-t/τ = 53.4 V.
Q32. An uncharged capacitor is connected to a 37 V battery through a resistor. The RC time constant is 0.8 s. What is the voltage across the capacitor 1 s after connection?
- (A) 13.2 V
- (B) 52.8 V
- (C) 6.6 V
- (D) 26.4 V
Show Answer
Answer: D – V = V0(1 – e-t/τ) = 26.4 V.
Q33. A current of 1 A flows in a wire of cross-sectional area 1 mm2. The free-electron density is 8.5 × 1028 m-3. What is the drift speed of the electrons?
- (A) 7.35 × 10-5 m/s
- (B) 3.68 × 10-5 m/s
- (C) 0.000147 m/s
- (D) 0.000294 m/s
Show Answer
Answer: A – vd = I/(neA) = 7.35 × 10-5 m/s.
Q34. Resistors of 13 Ω and 16 Ω are connected in series across a 47 V battery. What is the voltage across the 16 Ω resistor?
- (A) 13 V
- (B) 25.9 V
- (C) 51.9 V
- (D) 6.48 V
Show Answer
Answer: B – V2 = emf × R2/(R1 + R2) = 25.9 V.
Q35. A current of 1 A flows uniformly through a wire of cross-sectional area 2 mm2. What is the current density in the wire?
- (A) 2.5 × 105 A/m2
- (B) 5 × 105 A/m2
- (C) 1 × 106 A/m2
- (D) 1.25 × 105 A/m2
Show Answer
Answer: B – J = I/A = 5 × 105 A/m2.
Q36. A wire of resistivity 5.6 × 10-8 Ω·m has length 1 m and cross-sectional area 0.2 mm2. What is its resistance?
- (A) 0.14 Ω
- (B) 0.56 Ω
- (C) 0.28 Ω
- (D) 0.07 Ω
Show Answer
Answer: C – R = ρL/A = 0.28 Ω.
Q37. Resistors of 19 Ω, 120 Ω and 44 Ω are connected in series. What is their equivalent resistance?
- (A) 91.5 Ω
- (B) 366 Ω
- (C) 137 Ω
- (D) 183 Ω
Show Answer
Answer: D – In series, Req = R1 + R2 + R3 = 183 Ω.
Q38. Resistors of 40 Ω and 30 Ω are connected in parallel. What is their equivalent resistance?
- (A) 8.57 Ω
- (B) 34.3 Ω
- (C) 17.1 Ω
- (D) 68.6 Ω
Show Answer
Answer: C – 1/Req = 1/R1 + 1/R2, so Req = 17.1 Ω.
Q39. A resistor of 40 Ω is connected across a 88 V source. How much power is dissipated in the resistor?
- (A) 96.8 W
- (B) 194 W
- (C) 387 W
- (D) 48.4 W
Show Answer
Answer: B – P = V2/R = 194 W.
Q40. A battery of emf 16 V and internal resistance 1 Ω is connected to an external resistor of 11 Ω. What is the current in the circuit?
- (A) 1.33 A
- (B) 0.667 A
- (C) 2.67 A
- (D) 5.33 A
Show Answer
Answer: A – I = emf/(R + r) = 1.33 A.
Q41. A resistor of 26 kΩ and a capacitor of 10 μF are connected in series. What is the time constant of this RC circuit?
- (A) 0.13 s
- (B) 0.52 s
- (C) 0.065 s
- (D) 0.26 s
Show Answer
Answer: D – τ = RC = 0.26 s.
Unit 12: Magnetic Fields and Electromagnetism
Q42. A solenoid of length 61 cm has 631 turns and carries a current of 4 A. What is the magnitude of the magnetic field inside the solenoid, away from its ends?
- (A) 0.0026 T
- (B) 0.0104 T
- (C) 0.0052 T
- (D) 0.0208 T
Show Answer
Answer: C – B = μ0nI, with n = 1.03 × 103 turns/m, giving 0.0052 T.
Q43. A straight wire of length 68 cm carries a current of 4 A in a uniform magnetic field of 55 mT. The angle between the wire and the field is 90°. What is the magnitude of the magnetic force on the wire?
- (A) 0.15 N
- (B) 0.0748 N
- (C) 0.299 N
- (D) 0.0374 N
Show Answer
Answer: A – F = ILB sinθ = 0.15 N.
Q44. A proton (mass 1.67 × 10-27 kg, charge 1.60 × 10-19 C) moves at 3 × 105 m/s perpendicular to a uniform magnetic field of 11 mT. What is the radius of its circular path?
- (A) 0.142 m
- (B) 0.285 m
- (C) 0.569 m
- (D) 1.14 m
Show Answer
Answer: B – r = mv/(qB) = 0.285 m.
Q45. An electron (mass 9.11 × 10-31 kg, charge 1.60 × 10-19 C) moves perpendicular to a uniform magnetic field of 48 mT. What is the period of its circular motion?
- (A) 3.73 × 10-10 s
- (B) 1.49 × 10-9 s
- (C) 7.45 × 10-10 s
- (D) 1.86 × 10-10 s
Show Answer
Answer: C – T = 2πm/(qB) = 7.45 × 10-10 s.
Q46. Two long parallel wires 19 cm apart carry currents of 7 A and 12 A in the same direction. What is the magnitude of the magnetic force per unit length on either wire?
- (A) 8.84 × 10-5 N/m
- (B) 4.42 × 10-5 N/m
- (C) 0.000177 N/m
- (D) 0.000354 N/m
Show Answer
Answer: A – F/L = μ0I1I2/(2πd) = 8.84 × 10-5 N/m.
Q47. A rectangular loop of area 149 cm2 has 1 turns and carries a current of 3 A in a uniform magnetic field of 25 mT. The angle between the loop’s normal and the field is 60°. What is the magnitude of the torque on the loop?
- (A) 0.000968 N·m
- (B) 0.000484 N·m
- (C) 0.00194 N·m
- (D) 0.000242 N·m
Show Answer
Answer: A – τ = NIAB sinθ = 0.000968 N·m.
Q48. A long solid cylindrical wire of radius 16 cm carries a current of 7 A uniformly distributed over its cross-section. What is the magnitude of the magnetic field inside the wire at a distance 13 cm from its axis?
- (A) 3.55 × 10-6 T
- (B) 7.11 × 10-6 T
- (C) 1.42 × 10-5 T
- (D) 2.84 × 10-5 T
Show Answer
Answer: B – By Ampere’s law inside, B = μ0Ir/(2πR2) = 7.11 × 10-6 T.
Q49. A long straight wire carries a current of 10 A. What is the magnitude of the magnetic field 11 cm from the wire?
- (A) 9.09 × 10-6 T
- (B) 3.64 × 10-5 T
- (C) 7.27 × 10-5 T
- (D) 1.82 × 10-5 T
Show Answer
Answer: D – B = μ0I/(2πr) = 1.82 × 10-5 T.
Q50. A circular loop of radius 8 cm has 10 turns and carries a current of 5 A. What is the magnitude of the magnetic field at the centre of the loop?
- (A) 0.000393 T
- (B) 0.000196 T
- (C) 0.000785 T
- (D) 9.82 × 10-5 T
Show Answer
Answer: A – B = μ0NI/(2R) = 0.000393 T.
Unit 13: Electromagnetic Induction
Q51. A conducting rod of length 37 cm moves at 4 m/s perpendicular to a uniform magnetic field of 83 mT, with its length perpendicular to both the velocity and the field. What is the motional emf between its ends?
- (A) 0.0614 V
- (B) 0.246 V
- (C) 0.123 V
- (D) 0.491 V
Show Answer
Answer: C – emf = BLv = 0.123 V.
Q52. An emf of 2 V is induced in a coil of resistance 2 Ω. What is the induced current in the loop?
- (A) 0.5 A
- (B) 1 A
- (C) 2 A
- (D) 0.25 A
Show Answer
Answer: B – I = emf/R = 1 A.
Q53. A solenoid has 1221 turns, a cross-sectional area of 12 cm2 and a length of 26 cm. What is its self-inductance?
- (A) 0.00432 H
- (B) 0.0173 H
- (C) 0.00865 H
- (D) 0.00216 H
Show Answer
Answer: C – L = μ0N2A/l = 0.00865 H.
Q54. An inductor of 151 mH carries a current of 5 A. How much energy is stored in its magnetic field?
- (A) 0.944 J
- (B) 1.89 J
- (C) 3.77 J
- (D) 7.55 J
Show Answer
Answer: B – U = (1/2)LI2 = 1.89 J.
Q55. An inductor of 24 mH is connected in series with a resistor of 43 Ω. What is the time constant of this LR circuit?
- (A) 0.000279 s
- (B) 0.000558 s
- (C) 0.00112 s
- (D) 0.00014 s
Show Answer
Answer: B – τ = L/R = 0.000558 s.
Q56. An LR circuit with time constant 0.5 s is connected to a 40 V battery through a 14 Ω resistor. What is the current 0.5 s after the switch is closed, starting from zero current?
- (A) 0.903 A
- (B) 3.61 A
- (C) 0.452 A
- (D) 1.81 A
Show Answer
Answer: D – I = (V/R)(1 – e-t/τ) = 1.81 A.
Q57. An inductor carrying an initial current of 4 A is disconnected from its battery and discharges through a resistor. The LR time constant is 1.5 s. What is the current 0.5 s after discharge begins?
- (A) 1.43 A
- (B) 2.87 A
- (C) 5.73 A
- (D) 11.5 A
Show Answer
Answer: B – I = I0e-t/τ = 2.87 A.
Q58. An LC circuit consists of an inductor of 40 mH and a capacitor of 91 μF. What is the period of oscillation of the circuit?
- (A) 0.00599 s
- (B) 0.012 s
- (C) 0.024 s
- (D) 0.048 s
Show Answer
Answer: B – T = 2π√(LC) = 0.012 s.
Q59. A flat loop of area 45 cm2 is placed in a uniform magnetic field of 109 mT. The angle between the field and the normal to the loop is 0°. What is the magnetic flux through the loop?
- (A) 0.000245 Wb
- (B) 0.000981 Wb
- (C) 0.000123 Wb
- (D) 0.000491 Wb
Show Answer
Answer: D – Φ = BA cosθ = 0.000491 Wb.
Q60. A coil of 250 turns and area 25 cm2 is perpendicular to a magnetic field that increases uniformly from 37 mT to 95 mT in 104 ms. What is the magnitude of the induced emf in the coil?
- (A) 0.174 V
- (B) 0.697 V
- (C) 0.349 V
- (D) 0.0871 V
Show Answer
Answer: C – emf = N|ΔΦ/Δt| = 0.349 V.
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