Quick answer: Electric potential is potential energy per unit charge, V = U/q, measured in volts. This AP Physics C worksheet on electric potential gives 20 problems from easy to hard: units of potential, point charge potential and uniform field gap. The worked answers are on a separate page, and the worksheet is a free printable PDF.
These twenty problems train you to move between field, potential and energy using calculus: integrating E to get V, differentiating V to get E, and using conductors and equipotentials. They progress from one-step recall to multi-step derivations in the style of AP Physics C: Electricity and Magnetism.
The set suits students on the AP course, first-year university physics and A Level learners ready for calculus. Work with k = 8.99 × 10⁹ N·m²/C².
Level: AP Physics C (Mechanics and E&M, calculus-based) · Curriculum: AP PC:E&M Unit 9
Problem 1 Units of potential ★★★
1. State the SI unit of electric potential in terms of joules and coulombs.2. Calculate the work an external agent must do to carry a 3.0 μC charge through a potential difference of 200 V.
Problem 2 Point charge potential ★★★
1. Calculate the potential 0.30 m from a +5.0 nC point charge, taking V = 0 at infinity.2. State the potential at 0.60 m from the same charge.
Problem 3 Uniform field gap ★★★
Aarav measures a uniform field of 1500 N/C between two parallel plates 0.020 m apart.1. Calculate the potential difference between the plates.
2. State which plate is at the higher potential if the field points from plate A to plate B.
Problem 4 Electron accelerated ★★★
Chiamaka’s school demonstration tube accelerates electrons from rest through 250 V.1. Calculate the kinetic energy gained, in joules.
2. Calculate the final speed (m = 9.11 × 10⁻³¹ kg, e = 1.60 × 10⁻¹⁹ C).
Problem 5 Inside a conductor ★★★
1. State the electric field inside a solid conductor in electrostatic equilibrium.2. Explain why the whole conductor is at one potential.
Problem 6 Reading a V–x graph ★★★
The graph shows the potential along the x-axis in a region of space.2. State the direction of E.
3. Calculate the work done by the field on a +2.0 μC charge moved from x = 0 to x = 4.0 cm.
Problem 7 Two charges, one point ★★★
Charges of +3.0 nC and −1.0 nC are 0.40 m apart.1. Calculate the potential at the midpoint.
2. Explain why you can add the two potentials without using vectors.
Problem 8 Field given by x² ★★★
Along the x-axis Ex = (600 V/m³)x², and V(0) = 0.1. Integrate to find V(x).
2. Calculate V at x = 0.30 m.
Problem 9 Field from potential ★★★
A potential varies as V(x) = 40x − 150x² (V, with x in metres).1. Derive Ex(x).
2. Calculate Ex at x = 0.10 m.
3. Find where Ex = 0.
Problem 10 Ring on its axis ★★★
A ring of radius 0.12 m carries a uniform charge of 4.0 nC.1. Calculate the potential on the axis 0.16 m from the centre.
2. Calculate Ex at that point.
Problem 11 Assembling two charges ★★★
Wanjiru brings a 2.0 μC charge from infinity to 0.50 m from a fixed 3.0 μC charge.1. Calculate the work she must do.
2. Explain the sign of your answer.
Problem 12 Charged sphere ★★★
A conducting sphere of radius 0.15 m is held at 3000 V.1. Calculate its charge.
2. Calculate the field at its surface.
3. Calculate the potential 0.45 m from the centre.
4. State V and E inside.
Problem 13 Joined spheres ★★★
The two spheres shown are joined by a thin wire and share a total charge of 80 nC.2. Calculate the charge on each sphere.
3. Calculate the common potential.
4. Compare the surface fields E₁ and E₂.
Problem 14 Spacing of equipotentials ★★★
The diagram shows three equipotential lines in a flat region.2. Calculate the average field between 40 V and 60 V.
3. Explain where the field is stronger.
4. State the direction of the field.
Problem 15 Potential near a long wire ★★★
A long straight wire carries a uniform charge of 3.0 nC per metre, so E = 2kλ/r.1. Derive the potential difference V(0.10 m) − V(0.40 m).
2. Calculate it and state which point is at higher potential.
Problem 16 Charged rod on its axis ★★★
A thin rod of length 0.50 m carries 6.0 nC uniformly. Point P lies on the rod’s line, 0.10 m beyond one end.1. Show that V = k(Q/L) ln[(L + d)/d] for distance d from the near end.
2. Calculate V at P.
Problem 17 Charged disc ★★★
A disc of radius 0.20 m carries uniform surface charge 5.0 nC/m². Its potential on the axis is V = (σ/2ε₀)(√(x² + R²) − x), ε₀ = 8.85 × 10⁻¹² C²/(N·m²).1. Calculate V at x = 0.15 m.
2. Differentiate to find Ex and calculate it at x = 0.15 m.
3. Show that V tends to kQ/x for large x.
Problem 18 Uniform charged ball ★★★
Kofi models a cloud as a uniformly charged ball of radius 0.050 m holding 10 nC, with E = kQr/R³ inside.1. Integrate to find V(r) inside, matching kQ/R at the surface.
2. Calculate V at the centre.
3. Calculate V at r = R/2.
Problem 19 Particle released near a charge ★★★
A 5.0 g bead carrying +2.0 μC is released from rest 0.10 m from a fixed +4.0 μC charge, on a frictionless insulating track.1. Calculate its speed when it reaches r = 0.50 m.
2. Calculate its speed as r → ∞.
3. Explain why the speed never exceeds the second value.
Problem 20 Spot the error ★★★
Mei says: ‘Inside a hollow charged conducting shell E = 0, so V = 0 there too.’ The shell has radius 0.25 m and charge −30 nC.1. Identify and correct her mistake.
2. Calculate the potential inside the shell.
3. Calculate the potential 0.50 m from the centre.
