AP Physics C: Electricity and Magnetism Practice Test 3 – 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. A particle of mass 2 mg and charge 3 μC is placed in a uniform electric field of 4895 N/C. Ignoring gravity, what is the magnitude of its initial acceleration?
- (A) 3.67 × 103 m/s2
- (B) 1.47 × 104 m/s2
- (C) 1.84 × 103 m/s2
- (D) 7.34 × 103 m/s2
Show Answer
Answer: D – a = qE/m = 7.34 × 103 m/s2.
Q2. An electric dipole consists of charges +13 μC and -13 μC separated by 24 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) 6.54 × 104 N/C
- (B) 1.31 × 105 N/C
- (C) 2.62 × 105 N/C
- (D) 5.23 × 105 N/C
Show Answer
Answer: B – On the axis far away, E is approximately 2kp/r3 = 1.31 × 105 N/C.
Q3. A thin rod of length 48 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 13 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) ∪ kλ dx / x2
- (D) ∪ λ dx / x2
Show Answer
Answer: C – Each element contributes dE = k dq/x2 = kλ dx/x2, and the contributions add along the axis.
Q4. Two point charges carry charges 2 μC and 3 μC and are 42 cm apart in vacuum. What is the magnitude of the electrostatic force between them?
- (A) 0.153 N
- (B) 0.306 N
- (C) 0.612 N
- (D) 0.0764 N
Show Answer
Answer: B – F = kq1q2/r2 gives 0.306 N.
Q5. A point charge of 30 μC is fixed in vacuum. What is the magnitude of the electric field at a point 39 cm from the charge?
- (A) 1.77 × 106 N/C
- (B) 8.87 × 105 N/C
- (C) 3.55 × 106 N/C
- (D) 7.09 × 106 N/C
Show Answer
Answer: A – E = k|q|/r2 gives 1.77 × 106 N/C.
Q6. Two positive point charges 20 μC and 14 μC lie on the x-axis 23 cm apart. A point P lies on the x-axis 20 cm beyond the second charge, on the side away from the first. What is the magnitude of the net electric field at P?
- (A) 4.12 × 106 N/C
- (B) 2.06 × 106 N/C
- (C) 8.24 × 106 N/C
- (D) 1.03 × 106 N/C
Show Answer
Answer: A – Both fields point away from P’s sources, so E = kq1/r12 + kq2/r22 = 4.12 × 106 N/C.
Q7. An infinitely long straight wire carries a uniform linear charge density of 59 nC/m. What is the magnitude of the electric field 14 cm from the wire?
- (A) 3.79 × 103 N/C
- (B) 7.58 × 103 N/C
- (C) 1.52 × 104 N/C
- (D) 3.03 × 104 N/C
Show Answer
Answer: B – By Gauss’s law, E = 2kλ/r = 7.58 × 103 N/C.
Q8. A very large flat sheet carries a uniform surface charge density of 35 μC/m2. What is the magnitude of the electric field near the sheet, away from its edges?
- (A) 1.98 × 106 N/C
- (B) 9.89 × 105 N/C
- (C) 3.95 × 106 N/C
- (D) 4.94 × 105 N/C
Show Answer
Answer: A – For one sheet, E = σ/(2ε0) = 1.98 × 106 N/C.
Q9. A solid insulating sphere of radius 27 cm carries a total charge of 6 μC uniformly distributed through its volume. What is the magnitude of the electric field at a point 38 cm from its centre?
- (A) 1.87 × 105 N/C
- (B) 7.47 × 105 N/C
- (C) 1.49 × 106 N/C
- (D) 3.74 × 105 N/C
Show Answer
Answer: D – Outside, the sphere acts as a point charge, so E = kQ/r2 = 3.74 × 105 N/C.
Q10. A thin ring of radius 10 cm carries a total charge of 13 μC uniformly around its circumference. What is the magnitude of the electric field on the ring’s axis 36 cm from its centre?
- (A) 4.03 × 105 N/C
- (B) 1.61 × 106 N/C
- (C) 8.07 × 105 N/C
- (D) 2.02 × 105 N/C
Show Answer
Answer: C – Integrating around the ring, E = kQx/(R2 + x2)3/2 = 8.07 × 105 N/C.
Q11. A thin rod of length 23 cm carries a total charge of 25 nC uniformly along its length. What is the magnitude of the electric field on the rod’s axis 9 cm beyond one end?
- (A) 3.9 × 103 N/C
- (B) 1.56 × 104 N/C
- (C) 3.12 × 104 N/C
- (D) 7.8 × 103 N/C
Show Answer
Answer: D – Integrating dq contributions gives E = kQ/[d(d + L)] = 7.8 × 103 N/C.
Q12. A closed surface encloses a net charge of 22 μC. What is the net electric flux through the surface?
- (A) 1.24 × 106 N·m2/C
- (B) 4.97 × 106 N·m2/C
- (C) 2.49 × 106 N·m2/C
- (D) 6.21 × 105 N·m2/C
Show Answer
Answer: C – Gauss’s law: Φ = Qenc/ε0 = 2.49 × 106 N·m2/C.
Unit 9: Electric Potential
Q13. Two point charges 13 μC and -4 μC are held 21 cm apart. What is the electric potential energy of this pair?
- (A) -2.23 J
- (B) -1.11 J
- (C) -4.45 J
- (D) 2.23 J
Show Answer
Answer: A – U = kq1q2/r = -2.23 J; the sign follows the sign of q2.
Q14. In a region, the electric potential varies with position as V(x) = 14x2 + (-28)x + 20, where V is in volts and x is in metres. What is the x-component of the electric field at x = 2.0 m?
- (A) -14 N/C
- (B) -28 N/C
- (C) -56 N/C
- (D) 28 N/C
Show Answer
Answer: B – Ex = -dV/dx = -(28x + -28); at x = 2.0 m this gives -28 N/C.
Q15. A thin ring of radius 16 cm carries a total charge of 23 μC uniformly around its circumference. What is the electric potential on the ring’s axis 38 cm from its centre, with zero potential at infinity?
- (A) 2.51 × 105 V
- (B) 1 × 106 V
- (C) 1.25 × 105 V
- (D) 5.01 × 105 V
Show Answer
Answer: D – Every element is the same distance away, so V = kQ/√(R2 + x2) = 5.01 × 105 V.
Q16. A thin spherical shell of radius 25 cm carries a total charge of 29 μC uniformly on its surface. What is the electric potential at a point 5 cm from its centre, with zero potential at infinity?
- (A) 5.21 × 105 V
- (B) 1.04 × 106 V
- (C) 2.09 × 106 V
- (D) 4.17 × 106 V
Show Answer
Answer: B – Inside a charged shell the potential is constant and equal to its surface value, V = kQ/R = 1.04 × 106 V.
Q17. A particle of mass 42 μg and charge 27 nC starts from rest and accelerates through a potential drop of 272 V. What is its final speed, ignoring gravity and other forces?
- (A) 18.7 m/s
- (B) 9.35 m/s
- (C) 37.4 m/s
- (D) 4.68 m/s
Show Answer
Answer: A – qΔV = (1/2)mv2, so v = √(2qΔV/m) = 18.7 m/s.
Q18. Point charges 10 μC and 11 μC are fixed in vacuum. At a certain point P, the distances to the two charges are 42 cm and 23 cm respectively. What is the electric potential at P, with zero potential at infinity?
- (A) 6.44 × 105 V
- (B) 3.22 × 105 V
- (C) 1.29 × 106 V
- (D) -6.44 × 105 V
Show Answer
Answer: A – Potentials add as scalars: V = kq1/r1 + kq2/r2 = 6.44 × 105 V.
Q19. A charge is moved slowly along an equipotential surface held at 270 V, from one point to another on the same surface. How much work is done by the electric field during this move?
- (A) 270 J
- (B) 135 J
- (C) 540 J
- (D) 0 J
Show Answer
Answer: D – Moving along an equipotential means ΔV = 0, so W = qΔV = 0.
Q20. A point charge of 28 μC is fixed in vacuum, with zero potential at infinity. What is the electric potential 34 cm from the charge?
- (A) 3.7 × 105 V
- (B) 1.48 × 106 V
- (C) -7.4 × 105 V
- (D) 7.4 × 105 V
Show Answer
Answer: D – V = kq/r = 7.4 × 105 V.
Q21. A charge of 16 μC is moved slowly from a point at potential 147 V to a point at potential 247 V. How much work is done by an external agent, ignoring any change in kinetic energy?
- (A) 0.0008 J
- (B) 0.0032 J
- (C) 0.0004 J
- (D) 0.0016 J
Show Answer
Answer: D – W = qΔV = 0.0016 J.
Unit 10: Conductors and Capacitors
Q22. A 12 μF capacitor is connected across a 18 V battery. What charge is stored on each plate?
- (A) 0.000108 C
- (B) 0.000432 C
- (C) 0.000864 C
- (D) 0.000216 C
Show Answer
Answer: D – Q = CV = 0.000216 C.
Q23. A spherical capacitor consists of two concentric conducting shells of radii 9 cm and 20 cm. What is its capacitance?
- (A) 9.1 × 10-12 F
- (B) 1.82 × 10-11 F
- (C) 3.64 × 10-11 F
- (D) 4.55 × 10-12 F
Show Answer
Answer: B – C = 4πε0ab/(b – a) = 1.82 × 10-11 F.
Q24. The voltage across a parallel-plate capacitor is 191 V and the plate separation is 5 mm. What is the magnitude of the uniform electric field between the plates?
- (A) 3.82 × 104 N/C
- (B) 1.91 × 104 N/C
- (C) 7.64 × 104 N/C
- (D) 1.53 × 105 N/C
Show Answer
Answer: A – E = V/d = 3.82 × 104 N/C.
Q25. A parallel-plate capacitor has plates of area 41 cm2 separated by 5 mm in vacuum. What is its capacitance?
- (A) 3.63 × 10-12 F
- (B) 7.26 × 10-12 F
- (C) 1.45 × 10-11 F
- (D) 2.9 × 10-11 F
Show Answer
Answer: B – C = ε0A/d = 7.26 × 10-12 F.
Q26. A parallel-plate capacitor has capacitance 45 pF in vacuum. The gap is then completely filled with a dielectric of constant 5 while the plates remain isolated. What is the new capacitance?
- (A) 112 pF
- (B) 225 pF
- (C) 450 pF
- (D) 56.2 pF
Show Answer
Answer: B – C = κC0 = 225 pF.
Q27. Capacitors of 3 μF and 10 μF are connected in series. What is their equivalent capacitance?
- (A) 1.15 μF
- (B) 2.31 μF
- (C) 4.62 μF
- (D) 9.23 μF
Show Answer
Answer: B – 1/Ceq = 1/C1 + 1/C2, so Ceq = 2.31 μF.
Q28. Capacitors of 18 μF, 9 μF and 4 μF are connected in parallel. What is their equivalent capacitance?
- (A) 15.5 μF
- (B) 62 μF
- (C) 31 μF
- (D) 23.2 μF
Show Answer
Answer: C – In parallel, Ceq = C1 + C2 + C3 = 31 μF.
Q29. A 18 μF capacitor is charged to 147 V. How much energy is stored in the capacitor?
- (A) 0.0972 J
- (B) 0.389 J
- (C) 0.194 J
- (D) 0.0486 J
Show Answer
Answer: C – U = (1/2)CV2 = 0.194 J.
Unit 11: Electric Circuits
Q30. A resistor of 82 Ω is connected across a 99 V source. How much power is dissipated in the resistor?
- (A) 59.8 W
- (B) 120 W
- (C) 239 W
- (D) 29.9 W
Show Answer
Answer: B – P = V2/R = 120 W.
Q31. A battery of emf 31 V and internal resistance 2 Ω is connected to an external resistor of 36 Ω. What is the terminal voltage of the battery?
- (A) 14.7 V
- (B) 58.7 V
- (C) 7.34 V
- (D) 29.4 V
Show Answer
Answer: D – I = emf/(R + r), and V = emf – Ir = 29.4 V.
Q32. A resistor of 40 kΩ and a capacitor of 44 μF are connected in series. What is the time constant of this RC circuit?
- (A) 0.88 s
- (B) 3.52 s
- (C) 0.44 s
- (D) 1.76 s
Show Answer
Answer: D – τ = RC = 1.76 s.
Q33. An initially uncharged capacitor is connected in series with a 38 kΩ resistor to a battery. The RC time constant is not given directly. How long after connection will the capacitor reach 90% of its maximum charge? The capacitance is 42 μF.
- (A) 1.84 s
- (B) 3.67 s
- (C) 7.35 s
- (D) 0.919 s
Show Answer
Answer: B – τ = RC = 1.6 s, and q = Qmax(1 – e-t/τ), so t = -τ ln(1 – 0.9) = 3.67 s.
Q34. A capacitor charged to 32 V discharges through a resistor. The RC time constant is 2.5 s. What is the voltage across the capacitor 2 s after discharge begins?
- (A) 7.19 V
- (B) 28.8 V
- (C) 14.4 V
- (D) 3.59 V
Show Answer
Answer: C – V = V0e-t/τ = 14.4 V.
Q35. An uncharged capacitor is connected to a 20 V battery through a resistor. The RC time constant is 0.8 s. What is the voltage across the capacitor 1.5 s after connection?
- (A) 8.47 V
- (B) 33.9 V
- (C) 4.23 V
- (D) 16.9 V
Show Answer
Answer: D – V = V0(1 – e-t/τ) = 16.9 V.
Q36. A current of 1 A flows in a wire of cross-sectional area 1 mm2. The free-electron density is 10 × 1028 m-3. What is the drift speed of the electrons?
- (A) 3.13 × 10-5 m/s
- (B) 0.000125 m/s
- (C) 6.25 × 10-5 m/s
- (D) 0.00025 m/s
Show Answer
Answer: C – vd = I/(neA) = 6.25 × 10-5 m/s.
Q37. Resistors of 25 Ω and 85 Ω are connected in series across a 14 V battery. What is the voltage across the 85 Ω resistor?
- (A) 5.41 V
- (B) 21.6 V
- (C) 10.8 V
- (D) 2.7 V
Show Answer
Answer: C – V2 = emf × R2/(R1 + R2) = 10.8 V.
Q38. A current of 0.5 A flows uniformly through a wire of cross-sectional area 0.5 mm2. What is the current density in the wire?
- (A) 5 × 105 A/m2
- (B) 2 × 106 A/m2
- (C) 2.5 × 105 A/m2
- (D) 1 × 106 A/m2
Show Answer
Answer: D – J = I/A = 1 × 106 A/m2.
Q39. A wire of resistivity 16.0 × 10-8 Ω·m has length 2 m and cross-sectional area 0.8 mm2. What is its resistance?
- (A) 0.2 Ω
- (B) 0.8 Ω
- (C) 0.4 Ω
- (D) 0.1 Ω
Show Answer
Answer: C – R = ρL/A = 0.4 Ω.
Q40. Resistors of 14 Ω, 13 Ω and 48 Ω are connected in series. What is their equivalent resistance?
- (A) 37.5 Ω
- (B) 150 Ω
- (C) 75 Ω
- (D) 56.2 Ω
Show Answer
Answer: C – In series, Req = R1 + R2 + R3 = 75 Ω.
Q41. Resistors of 25 Ω and 50 Ω are connected in parallel. What is their equivalent resistance?
- (A) 16.7 Ω
- (B) 8.33 Ω
- (C) 33.3 Ω
- (D) 25 Ω
Show Answer
Answer: A – 1/Req = 1/R1 + 1/R2, so Req = 16.7 Ω.
Unit 12: Magnetic Fields and Electromagnetism
Q42. A long solid cylindrical wire of radius 11 cm carries a current of 20 A uniformly distributed over its cross-section. What is the magnitude of the magnetic field inside the wire at a distance 8 cm from its axis?
- (A) 1.32 × 10-5 T
- (B) 2.64 × 10-5 T
- (C) 5.29 × 10-5 T
- (D) 0.000106 T
Show Answer
Answer: B – By Ampere’s law inside, B = μ0Ir/(2πR2) = 2.64 × 10-5 T.
Q43. A long straight wire carries a current of 21 A. What is the magnitude of the magnetic field 3 cm from the wire?
- (A) 0.00014 T
- (B) 7 × 10-5 T
- (C) 0.00028 T
- (D) 0.00056 T
Show Answer
Answer: A – B = μ0I/(2πr) = 0.00014 T.
Q44. A circular loop of radius 13 cm has 5 turns and carries a current of 6 A. What is the magnitude of the magnetic field at the centre of the loop?
- (A) 0.000145 T
- (B) 7.25 × 10-5 T
- (C) 0.00029 T
- (D) 3.62 × 10-5 T
Show Answer
Answer: A – B = μ0NI/(2R) = 0.000145 T.
Q45. A solenoid of length 22 cm has 278 turns and carries a current of 2 A. What is the magnitude of the magnetic field inside the solenoid, away from its ends?
- (A) 0.00159 T
- (B) 0.00635 T
- (C) 0.0127 T
- (D) 0.00318 T
Show Answer
Answer: D – B = μ0nI, with n = 1.26 × 103 turns/m, giving 0.00318 T.
Q46. A straight wire of length 27 cm carries a current of 17 A in a uniform magnetic field of 74 mT. The angle between the wire and the field is 60°. What is the magnitude of the magnetic force on the wire?
- (A) 0.147 N
- (B) 0.588 N
- (C) 0.0735 N
- (D) 0.294 N
Show Answer
Answer: D – F = ILB sinθ = 0.294 N.
Q47. 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 55 mT. What is the radius of its circular path?
- (A) 0.038 m
- (B) 0.019 m
- (C) 0.0759 m
- (D) 0.152 m
Show Answer
Answer: A – r = mv/(qB) = 0.038 m.
Q48. An electron (mass 9.11 × 10-31 kg, charge 1.60 × 10-19 C) moves perpendicular to a uniform magnetic field of 16 mT. What is the period of its circular motion?
- (A) 1.12 × 10-9 s
- (B) 4.47 × 10-9 s
- (C) 5.59 × 10-10 s
- (D) 2.24 × 10-9 s
Show Answer
Answer: D – T = 2πm/(qB) = 2.24 × 10-9 s.
Q49. Two long parallel wires 6 cm apart carry currents of 11 A and 19 A in the same direction. What is the magnitude of the magnetic force per unit length on either wire?
- (A) 0.000348 N/m
- (B) 0.000697 N/m
- (C) 0.00139 N/m
- (D) 0.00279 N/m
Show Answer
Answer: B – F/L = μ0I1I2/(2πd) = 0.000697 N/m.
Q50. A rectangular loop of area 20 cm2 has 1 turns and carries a current of 1 A in a uniform magnetic field of 36 mT. The angle between the loop’s normal and the field is 60°. What is the magnitude of the torque on the loop?
- (A) 3.12 × 10-5 N·m
- (B) 0.000125 N·m
- (C) 6.24 × 10-5 N·m
- (D) 1.56 × 10-5 N·m
Show Answer
Answer: C – τ = NIAB sinθ = 6.24 × 10-5 N·m.
Unit 13: Electromagnetic Induction
Q51. An LC circuit consists of an inductor of 26 mH and a capacitor of 49 μF. What is the frequency of oscillation of the circuit?
- (A) 70.5 Hz
- (B) 141 Hz
- (C) 282 Hz
- (D) 35.3 Hz
Show Answer
Answer: B – f = 1/(2π√(LC)) = 141 Hz.
Q52. A flat loop of area 139 cm2 is placed in a uniform magnetic field of 120 mT. The angle between the field and the normal to the loop is 60°. What is the magnetic flux through the loop?
- (A) 0.000834 Wb
- (B) 0.000417 Wb
- (C) 0.00167 Wb
- (D) 0.000209 Wb
Show Answer
Answer: A – Φ = BA cosθ = 0.000834 Wb.
Q53. A coil of 250 turns and area 30 cm2 is perpendicular to a magnetic field that increases uniformly from 17 mT to 71 mT in 104 ms. What is the magnitude of the induced emf in the coil?
- (A) 0.389 V
- (B) 0.195 V
- (C) 0.779 V
- (D) 0.0974 V
Show Answer
Answer: A – emf = N|ΔΦ/Δt| = 0.389 V.
Q54. A conducting rod of length 29 cm moves at 4 m/s perpendicular to a uniform magnetic field of 47 mT, with its length perpendicular to both the velocity and the field. What is the motional emf between its ends?
- (A) 0.0273 V
- (B) 0.109 V
- (C) 0.0545 V
- (D) 0.218 V
Show Answer
Answer: C – emf = BLv = 0.0545 V.
Q55. An emf of 4 V is induced in a rectangular loop of resistance 5 Ω. What is the induced current in the loop?
- (A) 0.8 A
- (B) 0.4 A
- (C) 1.6 A
- (D) 0.2 A
Show Answer
Answer: A – I = emf/R = 0.8 A.
Q56. A solenoid has 812 turns, a cross-sectional area of 50 cm2 and a length of 54 cm. What is its self-inductance?
- (A) 0.00384 H
- (B) 0.00767 H
- (C) 0.0153 H
- (D) 0.00192 H
Show Answer
Answer: B – L = μ0N2A/l = 0.00767 H.
Q57. An inductor of 189 mH carries a current of 2 A. How much energy is stored in its magnetic field?
- (A) 0.189 J
- (B) 0.756 J
- (C) 0.378 J
- (D) 1.51 J
Show Answer
Answer: C – U = (1/2)LI2 = 0.378 J.
Q58. An inductor of 179 mH is connected in series with a resistor of 5 Ω. What is the time constant of this LR circuit?
- (A) 0.0358 s
- (B) 0.0179 s
- (C) 0.0716 s
- (D) 0.00895 s
Show Answer
Answer: A – τ = L/R = 0.0358 s.
Q59. An LR circuit with time constant 0.5 s is connected to a 46 V battery through a 31 Ω resistor. What is the current 1 s after the switch is closed, starting from zero current?
- (A) 0.642 A
- (B) 2.57 A
- (C) 1.28 A
- (D) 0.321 A
Show Answer
Answer: C – I = (V/R)(1 – e-t/τ) = 1.28 A.
Q60. An inductor carrying an initial current of 4 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) 1.21 A
- (B) 4.85 A
- (C) 2.43 A
- (D) 9.7 A
Show Answer
Answer: C – I = I0e-t/τ = 2.43 A.
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