AP Physics C: Electricity and Magnetism Practice Test 1 – 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. An infinitely long straight wire carries a uniform linear charge density of 82 nC/m. What is the magnitude of the electric field 16 cm from the wire?
- (A) 9.21 × 103 N/C
- (B) 4.61 × 103 N/C
- (C) 1.84 × 104 N/C
- (D) 3.69 × 104 N/C
Show Answer
Answer: A – By Gauss’s law, E = 2kλ/r = 9.21 × 103 N/C.
Q2. A very large flat sheet carries a uniform surface charge density of 28 μC/m2. What is the magnitude of the electric field near the sheet, away from its edges?
- (A) 1.58 × 106 N/C
- (B) 7.91 × 105 N/C
- (C) 3.16 × 106 N/C
- (D) 3.95 × 105 N/C
Show Answer
Answer: A – For one sheet, E = σ/(2ε0) = 1.58 × 106 N/C.
Q3. A solid insulating sphere of radius 26 cm carries a total charge of 11 μC uniformly distributed through its volume. What is the magnitude of the electric field at a point 53 cm from its centre?
- (A) 1.76 × 105 N/C
- (B) 7.04 × 105 N/C
- (C) 3.52 × 105 N/C
- (D) 1.41 × 106 N/C
Show Answer
Answer: C – Outside, the sphere acts as a point charge, so E = kQ/r2 = 3.52 × 105 N/C.
Q4. A thin ring of radius 24 cm carries a total charge of 12 μC uniformly around its circumference. What is the magnitude of the electric field on the ring’s axis 37 cm from its centre?
- (A) 2.33 × 105 N/C
- (B) 9.31 × 105 N/C
- (C) 1.16 × 105 N/C
- (D) 4.65 × 105 N/C
Show Answer
Answer: D – Integrating around the ring, E = kQx/(R2 + x2)3/2 = 4.65 × 105 N/C.
Q5. A thin rod of length 36 cm carries a total charge of 12 nC uniformly along its length. What is the magnitude of the electric field on the rod’s axis 11 cm beyond one end?
- (A) 2.09 × 103 N/C
- (B) 1.04 × 103 N/C
- (C) 4.17 × 103 N/C
- (D) 8.35 × 103 N/C
Show Answer
Answer: A – Integrating dq contributions gives E = kQ/[d(d + L)] = 2.09 × 103 N/C.
Q6. A closed surface encloses a net charge of 26 μC. What is the net electric flux through the surface?
- (A) 1.47 × 106 N·m2/C
- (B) 2.94 × 106 N·m2/C
- (C) 5.88 × 106 N·m2/C
- (D) 7.34 × 105 N·m2/C
Show Answer
Answer: B – Gauss’s law: Φ = Qenc/ε0 = 2.94 × 106 N·m2/C.
Q7. A particle of mass 15 mg and charge 7 μC is placed in a uniform electric field of 5302 N/C. Ignoring gravity, what is the magnitude of its initial acceleration?
- (A) 1.24 × 103 m/s2
- (B) 4.95 × 103 m/s2
- (C) 619 m/s2
- (D) 2.47 × 103 m/s2
Show Answer
Answer: D – a = qE/m = 2.47 × 103 m/s2.
Q8. An electric dipole consists of charges +16 μC and -16 μC separated by 17 mm. Estimate the magnitude of the electric field on the dipole axis 35 cm from its centre, where the distance is much larger than the separation.
- (A) 1.14 × 105 N/C
- (B) 5.7 × 104 N/C
- (C) 2.28 × 105 N/C
- (D) 4.56 × 105 N/C
Show Answer
Answer: A – On the axis far away, E is approximately 2kp/r3 = 1.14 × 105 N/C.
Q9. A thin rod of length 36 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 32 cm beyond one end, where x is the distance from a charge element dq to the point?
- (A) ∪ kλ dx / x
- (B) ∪ kλ dx / x3
- (C) ∪ λ dx / x2
- (D) ∪ kλ dx / x2
Show Answer
Answer: D – Each element contributes dE = k dq/x2 = kλ dx/x2, and the contributions add along the axis.
Q10. Two point charges carry charges 14 μC and 22 μC and are 23 cm apart in vacuum. What is the magnitude of the electrostatic force between them?
- (A) 26.2 N
- (B) 52.3 N
- (C) 105 N
- (D) 13.1 N
Show Answer
Answer: B – F = kq1q2/r2 gives 52.3 N.
Q11. A point charge of 10 μC is fixed in vacuum. What is the magnitude of the electric field at a point 36 cm from the charge?
- (A) 6.94 × 105 N/C
- (B) 3.47 × 105 N/C
- (C) 1.39 × 106 N/C
- (D) 2.77 × 106 N/C
Show Answer
Answer: A – E = k|q|/r2 gives 6.94 × 105 N/C.
Q12. Two positive point charges 5 μC and 10 μC lie on the x-axis 44 cm apart. A point P lies on the x-axis 22 cm beyond the second charge, on the side away from the first. What is the magnitude of the net electric field at P?
- (A) 1.96 × 106 N/C
- (B) 9.8 × 105 N/C
- (C) 3.92 × 106 N/C
- (D) 4.9 × 105 N/C
Show Answer
Answer: A – Both fields point away from P’s sources, so E = kq1/r12 + kq2/r22 = 1.96 × 106 N/C.
Unit 9: Electric Potential
Q13. A thin spherical shell of radius 32 cm carries a total charge of 15 μC uniformly on its surface. What is the electric potential at a point 44 cm from its centre, with zero potential at infinity?
- (A) 1.53 × 105 V
- (B) 6.13 × 105 V
- (C) 3.06 × 105 V
- (D) 1.23 × 106 V
Show Answer
Answer: C – Outside, V = kQ/r = 3.06 × 105 V.
Q14. A particle of mass 58 μg and charge 169 nC starts from rest and accelerates through a potential drop of 748 V. What is its final speed, ignoring gravity and other forces?
- (A) 66 m/s
- (B) 33 m/s
- (C) 132 m/s
- (D) 16.5 m/s
Show Answer
Answer: A – qΔV = (1/2)mv2, so v = √(2qΔV/m) = 66 m/s.
Q15. Point charges 17 μC and -19 μC are fixed in vacuum. At a certain point P, the distances to the two charges are 23 cm and 25 cm respectively. What is the electric potential at P, with zero potential at infinity?
- (A) -9.38 × 103 V
- (B) -3.75 × 104 V
- (C) 1.88 × 104 V
- (D) -1.88 × 104 V
Show Answer
Answer: D – Potentials add as scalars: V = kq1/r1 + kq2/r2 = -1.88 × 104 V.
Q16. A charge is moved slowly along an equipotential surface held at 159 V, from one point to another on the same surface. How much work is done by the electric field during this move?
- (A) 159 J
- (B) 79.5 J
- (C) 318 J
- (D) 0 J
Show Answer
Answer: D – Moving along an equipotential means ΔV = 0, so W = qΔV = 0.
Q17. A point charge of -21 μC is fixed in vacuum, with zero potential at infinity. What is the electric potential 32 cm from the charge?
- (A) -2.95 × 105 V
- (B) -1.18 × 106 V
- (C) -5.9 × 105 V
- (D) 5.9 × 105 V
Show Answer
Answer: C – V = kq/r = -5.9 × 105 V.
Q18. A charge of 12 μC is moved slowly from a point at potential 200 V to a point at potential 450 V. How much work is done by an external agent, ignoring any change in kinetic energy?
- (A) 0.0015 J
- (B) 0.003 J
- (C) 0.006 J
- (D) 0.00075 J
Show Answer
Answer: B – W = qΔV = 0.003 J.
Q19. Two point charges 5 μC and 14 μC are held 54 cm apart. What is the electric potential energy of this pair?
- (A) 0.583 J
- (B) 1.17 J
- (C) 2.33 J
- (D) -1.17 J
Show Answer
Answer: B – U = kq1q2/r = 1.17 J; the sign follows the sign of q2.
Q20. In a region, the electric potential varies with position as V(x) = 15x2 + (-27)x + 20, where V is in volts and x is in metres. What is the x-component of the electric field at x = 2.5 m?
- (A) -24 N/C
- (B) -96 N/C
- (C) -48 N/C
- (D) 48 N/C
Show Answer
Answer: C – Ex = -dV/dx = -(30x + -27); at x = 2.5 m this gives -48 N/C.
Q21. A thin ring of radius 23 cm carries a total charge of 19 μC uniformly around its circumference. What is the electric potential on the ring’s axis 20 cm from its centre, with zero potential at infinity?
- (A) 5.6 × 105 V
- (B) 2.8 × 105 V
- (C) 1.12 × 106 V
- (D) 1.4 × 105 V
Show Answer
Answer: A – Every element is the same distance away, so V = kQ/√(R2 + x2) = 5.6 × 105 V.
Unit 10: Conductors and Capacitors
Q22. The voltage across a parallel-plate capacitor is 207 V and the plate separation is 4 mm. What is the magnitude of the uniform electric field between the plates?
- (A) 2.59 × 104 N/C
- (B) 1.04 × 105 N/C
- (C) 2.07 × 105 N/C
- (D) 5.18 × 104 N/C
Show Answer
Answer: D – E = V/d = 5.18 × 104 N/C.
Q23. A parallel-plate capacitor has plates of area 194 cm2 separated by 1 mm in vacuum. What is its capacitance?
- (A) 8.58 × 10-11 F
- (B) 1.72 × 10-10 F
- (C) 3.43 × 10-10 F
- (D) 6.87 × 10-10 F
Show Answer
Answer: B – C = ε0A/d = 1.72 × 10-10 F.
Q24. An isolated parallel-plate capacitor is charged to 33 V in vacuum. The gap is then completely filled with a dielectric of constant 4 without changing the charge on the plates. What is the new voltage across the capacitor?
- (A) 4.12 V
- (B) 16.5 V
- (C) 8.25 V
- (D) 33 V
Show Answer
Answer: C – With Q fixed, V = Q/C falls by κ: V = V0/κ = 8.25 V.
Q25. Capacitors of 9 μF and 7 μF are connected in series. What is their equivalent capacitance?
- (A) 1.97 μF
- (B) 7.88 μF
- (C) 3.94 μF
- (D) 15.8 μF
Show Answer
Answer: C – 1/Ceq = 1/C1 + 1/C2, so Ceq = 3.94 μF.
Q26. Capacitors of 6 μF, 13 μF and 9 μF are connected in parallel. What is their equivalent capacitance?
- (A) 14 μF
- (B) 56 μF
- (C) 21 μF
- (D) 28 μF
Show Answer
Answer: D – In parallel, Ceq = C1 + C2 + C3 = 28 μF.
Q27. A 36 μF capacitor is charged to 62 V. How much energy is stored in the capacitor?
- (A) 0.0346 J
- (B) 0.138 J
- (C) 0.0692 J
- (D) 0.0173 J
Show Answer
Answer: C – U = (1/2)CV2 = 0.0692 J.
Q28. A 34 μF capacitor is connected across a 55 V battery. What charge is stored on each plate?
- (A) 0.000935 C
- (B) 0.00374 C
- (C) 0.00748 C
- (D) 0.00187 C
Show Answer
Answer: D – Q = CV = 0.00187 C.
Q29. A spherical capacitor consists of two concentric conducting shells of radii 15 cm and 22 cm. What is its capacitance?
- (A) 2.62 × 10-11 F
- (B) 5.24 × 10-11 F
- (C) 1.05 × 10-10 F
- (D) 1.31 × 10-11 F
Show Answer
Answer: B – C = 4πε0ab/(b – a) = 5.24 × 10-11 F.
Unit 11: Electric Circuits
Q30. A current of 4 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) 0.000147 m/s
- (B) 0.000588 m/s
- (C) 0.00118 m/s
- (D) 0.000294 m/s
Show Answer
Answer: D – vd = I/(neA) = 0.000294 m/s.
Q31. Resistors of 72 Ω and 53 Ω are connected in series across a 30 V battery. What is the voltage across the 53 Ω resistor?
- (A) 6.36 V
- (B) 12.7 V
- (C) 25.4 V
- (D) 3.18 V
Show Answer
Answer: B – V2 = emf × R2/(R1 + R2) = 12.7 V.
Q32. A current of 2 A flows uniformly through a wire of cross-sectional area 2 mm2. What is the current density in the wire?
- (A) 5 × 105 A/m2
- (B) 1 × 106 A/m2
- (C) 2 × 106 A/m2
- (D) 2.5 × 105 A/m2
Show Answer
Answer: B – J = I/A = 1 × 106 A/m2.
Q33. A wire of resistivity 2.8 × 10-8 Ω·m has length 1 m and cross-sectional area 0.5 mm2. What is its resistance?
- (A) 0.028 Ω
- (B) 0.112 Ω
- (C) 0.056 Ω
- (D) 0.014 Ω
Show Answer
Answer: C – R = ρL/A = 0.056 Ω.
Q34. Resistors of 108 Ω, 119 Ω and 80 Ω are connected in series. What is their equivalent resistance?
- (A) 154 Ω
- (B) 614 Ω
- (C) 230 Ω
- (D) 307 Ω
Show Answer
Answer: D – In series, Req = R1 + R2 + R3 = 307 Ω.
Q35. Resistors of 30 Ω and 20 Ω are connected in parallel. What is their equivalent resistance?
- (A) 6 Ω
- (B) 24 Ω
- (C) 12 Ω
- (D) 48 Ω
Show Answer
Answer: C – 1/Req = 1/R1 + 1/R2, so Req = 12 Ω.
Q36. A resistor of 22 Ω is connected across a 114 V source. How much power is dissipated in the resistor?
- (A) 295 W
- (B) 1.18 × 103 W
- (C) 148 W
- (D) 591 W
Show Answer
Answer: D – P = V2/R = 591 W.
Q37. A battery of emf 13 V and internal resistance 2 Ω is connected to an external resistor of 30 Ω. What is the terminal voltage of the battery?
- (A) 6.09 V
- (B) 12.2 V
- (C) 24.4 V
- (D) 3.05 V
Show Answer
Answer: B – I = emf/(R + r), and V = emf – Ir = 12.2 V.
Q38. A resistor of 44 kΩ and a capacitor of 81 μF are connected in series. What is the time constant of this RC circuit?
- (A) 3.56 s
- (B) 1.78 s
- (C) 7.13 s
- (D) 0.891 s
Show Answer
Answer: A – τ = RC = 3.56 s.
Q39. An initially uncharged capacitor is connected in series with a 29 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 115 μF.
- (A) 2.31 s
- (B) 1.16 s
- (C) 4.62 s
- (D) 0.578 s
Show Answer
Answer: A – τ = RC = 3.33 s, and q = Qmax(1 – e-t/τ), so t = -τ ln(1 – 0.5) = 2.31 s.
Q40. A capacitor charged to 86 V discharges through a resistor. The RC time constant is 2 s. What is the voltage across the capacitor 1 s after discharge begins?
- (A) 52.2 V
- (B) 26.1 V
- (C) 104 V
- (D) 13 V
Show Answer
Answer: A – V = V0e-t/τ = 52.2 V.
Q41. An uncharged capacitor is connected to a 33 V battery through a resistor. The RC time constant is 2 s. What is the voltage across the capacitor 1.5 s after connection?
- (A) 17.4 V
- (B) 8.71 V
- (C) 34.8 V
- (D) 4.35 V
Show Answer
Answer: A – V = V0(1 – e-t/τ) = 17.4 V.
Unit 12: Magnetic Fields and Electromagnetism
Q42. A solenoid of length 57 cm has 314 turns and carries a current of 4 A. What is the magnitude of the magnetic field inside the solenoid, away from its ends?
- (A) 0.00138 T
- (B) 0.00277 T
- (C) 0.00554 T
- (D) 0.0111 T
Show Answer
Answer: B – B = μ0nI, with n = 551 turns/m, giving 0.00277 T.
Q43. A straight wire of length 23 cm carries a current of 17 A in a uniform magnetic field of 75 mT. The angle between the wire and the field is 30°. What is the magnitude of the magnetic force on the wire?
- (A) 0.0733 N
- (B) 0.293 N
- (C) 0.147 N
- (D) 0.0367 N
Show Answer
Answer: C – F = ILB sinθ = 0.147 N.
Q44. A proton (mass 1.67 × 10-27 kg, charge 1.60 × 10-19 C) moves at 2 × 105 m/s perpendicular to a uniform magnetic field of 39 mT. What is the radius of its circular path?
- (A) 0.0535 m
- (B) 0.0268 m
- (C) 0.107 m
- (D) 0.214 m
Show Answer
Answer: A – r = mv/(qB) = 0.0535 m.
Q45. An electron (mass 9.11 × 10-31 kg, charge 1.60 × 10-19 C) moves perpendicular to a uniform magnetic field of 37 mT. What is the period of its circular motion?
- (A) 4.83 × 10-10 s
- (B) 9.67 × 10-10 s
- (C) 1.93 × 10-9 s
- (D) 2.42 × 10-10 s
Show Answer
Answer: B – T = 2πm/(qB) = 9.67 × 10-10 s.
Q46. Two long parallel wires 23 cm apart carry currents of 10 A and 10 A in the same direction. What is the magnitude of the magnetic force per unit length on either wire?
- (A) 4.35 × 10-5 N/m
- (B) 8.7 × 10-5 N/m
- (C) 0.000174 N/m
- (D) 0.000348 N/m
Show Answer
Answer: B – F/L = μ0I1I2/(2πd) = 8.7 × 10-5 N/m.
Q47. A rectangular loop of area 92 cm2 has 1 turns and carries a current of 5 A in a uniform magnetic field of 63 mT. The angle between the loop’s normal and the field is 30°. What is the magnitude of the torque on the loop?
- (A) 0.00145 N·m
- (B) 0.000724 N·m
- (C) 0.0029 N·m
- (D) 0.000362 N·m
Show Answer
Answer: A – τ = NIAB sinθ = 0.00145 N·m.
Q48. A long solid cylindrical wire of radius 15 cm carries a current of 24 A uniformly distributed over its cross-section. What is the magnitude of the magnetic field inside the wire at a distance 10 cm from its axis?
- (A) 1.07 × 10-5 T
- (B) 4.27 × 10-5 T
- (C) 8.53 × 10-5 T
- (D) 2.13 × 10-5 T
Show Answer
Answer: D – By Ampere’s law inside, B = μ0Ir/(2πR2) = 2.13 × 10-5 T.
Q49. A long straight wire carries a current of 18 A. What is the magnitude of the magnetic field 5 cm from the wire?
- (A) 3.6 × 10-5 T
- (B) 0.000144 T
- (C) 7.2 × 10-5 T
- (D) 0.000288 T
Show Answer
Answer: C – B = μ0I/(2πr) = 7.2 × 10-5 T.
Q50. A circular loop of radius 13 cm has 50 turns and carries a current of 2 A. What is the magnitude of the magnetic field at the centre of the loop?
- (A) 0.000242 T
- (B) 0.000967 T
- (C) 0.000121 T
- (D) 0.000483 T
Show Answer
Answer: D – B = μ0NI/(2R) = 0.000483 T.
Unit 13: Electromagnetic Induction
Q51. An emf of 2 V is induced in a circular loop of resistance 20 Ω. What is the induced current in the loop?
- (A) 0.05 A
- (B) 0.2 A
- (C) 0.1 A
- (D) 0.025 A
Show Answer
Answer: C – I = emf/R = 0.1 A.
Q52. A solenoid has 1200 turns, a cross-sectional area of 67 cm2 and a length of 80 cm. What is its self-inductance?
- (A) 0.00758 H
- (B) 0.0152 H
- (C) 0.0303 H
- (D) 0.00379 H
Show Answer
Answer: B – L = μ0N2A/l = 0.0152 H.
Q53. An inductor of 55 mH carries a current of 4 A. How much energy is stored in its magnetic field?
- (A) 0.22 J
- (B) 0.44 J
- (C) 0.88 J
- (D) 1.76 J
Show Answer
Answer: B – U = (1/2)LI2 = 0.44 J.
Q54. An inductor of 153 mH is connected in series with a resistor of 49 Ω. What is the time constant of this LR circuit?
- (A) 0.00156 s
- (B) 0.00624 s
- (C) 0.00312 s
- (D) 0.000781 s
Show Answer
Answer: C – τ = L/R = 0.00312 s.
Q55. An LR circuit with time constant 1 s is connected to a 25 V battery through a 27 Ω resistor. What is the current 1.5 s after the switch is closed, starting from zero current?
- (A) 0.36 A
- (B) 1.44 A
- (C) 0.719 A
- (D) 0.18 A
Show Answer
Answer: C – I = (V/R)(1 – e-t/τ) = 0.719 A.
Q56. An inductor carrying an initial current of 1 A is disconnected from its battery and discharges through a resistor. The LR time constant is 2 s. What is the current 1 s after discharge begins?
- (A) 0.303 A
- (B) 1.21 A
- (C) 2.43 A
- (D) 0.607 A
Show Answer
Answer: D – I = I0e-t/τ = 0.607 A.
Q57. An LC circuit consists of an inductor of 102 mH and a capacitor of 7 μF. What is the frequency of oscillation of the circuit?
- (A) 94.2 Hz
- (B) 377 Hz
- (C) 47.1 Hz
- (D) 188 Hz
Show Answer
Answer: D – f = 1/(2π√(LC)) = 188 Hz.
Q58. A flat loop of area 110 cm2 is placed in a uniform magnetic field of 91 mT. The angle between the field and the normal to the loop is 60°. What is the magnetic flux through the loop?
- (A) 0.00025 Wb
- (B) 0.000501 Wb
- (C) 0.001 Wb
- (D) 0.000125 Wb
Show Answer
Answer: B – Φ = BA cosθ = 0.000501 Wb.
Q59. A coil of 200 turns and area 63 cm2 is perpendicular to a magnetic field that increases uniformly from 46 mT to 120 mT in 55 ms. What is the magnitude of the induced emf in the coil?
- (A) 0.848 V
- (B) 3.39 V
- (C) 1.7 V
- (D) 0.424 V
Show Answer
Answer: C – emf = N|ΔΦ/Δt| = 1.7 V.
Q60. A conducting rod of length 20 cm moves at 1 m/s perpendicular to a uniform magnetic field of 105 mT, with its length perpendicular to both the velocity and the field. What is the motional emf between its ends?
- (A) 0.021 V
- (B) 0.0105 V
- (C) 0.042 V
- (D) 0.084 V
Show Answer
Answer: A – emf = BLv = 0.021 V.
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