AP Physics C: Electricity and Magnetism, AP exams

Unit 9: Electric Potential

Unit 9 develops the energy view of electrostatics. Electric potential energy and potential are defined by integrating field along a path, and field is recovered by differentiating potential. Because potential is a scalar, it is often the faster route to a field for complicated distributions.

Position: 2 of 6 units
Topics covered: 5 topics in this guide

What is covered

Topics inside this unit.

These topics describe the scope students most often review for this part of AP Physics C: Electricity and Magnetism. Treat them as a study checklist rather than an exhaustive list of what a single exam form can sample.

Electric potential energy: Work done by the electric force, and the energy of assembling a configuration of charges.
Electric potential: Potential as energy per unit charge, and its computation for point charges and distributions.
Potential from field and field from potential: Integrating the field along a path to obtain potential, and differentiating potential to recover the field.
Equipotential surfaces: Reading equipotential maps, their perpendicular relationship to field lines, and the spacing that indicates field strength.
Conservation of electric energy: Tracking energy for charges moving in a field, and combining electric with mechanical energy.

Study tips

How to practice Electric Potential.

Section-specific guidance that follows from how this material is usually tested.

Compute potential first for complicated distributions, then differentiate; it is usually far less algebra than a vector integral.
Practice sketching equipotentials alongside field lines for standard configurations.
Keep the sign of work and potential energy straight by naming the charge sign and the direction of motion explicitly.

Where this fits

Unit 9: Electric Potential is 2 of 6 units in the AP Physics C: Electricity and Magnetism guide. Use the full guide to balance it against everything else you have to review.

Back to the AP Physics C: Electricity and Magnetism guide Official exam information

Sample Electric Potential questions

Practice questions, not yet expert-reviewed

Original practice questions written to the published framework for this section. No expert has reviewed them, and they are not taken from any official exam. Try each one before you open the answer.

Question 1Foundational
What is the electric potential at a point 0.30 m from an isolated point charge of +6.0 x 10^-9 C, taking the potential to be zero infinitely far away and using k = 9.0 x 10^9 N m^2/C^2?
1. A54 V
2. B90 V
3. C180 V
4. D600 V
Show answer
Answer: C. 180 V
Potential from a point charge is V = kq/r = (9.0 x 10^9)(6.0 x 10^-9)/0.30 = 180 V. The 600 V choice divides by r^2, which is the recipe for the field rather than the potential.
Key insight: Potential falls off as 1/r while field falls off as 1/r^2, a difference that comes straight from integrating the field.
Question 2Intermediate
A charge of -2.0 x 10^-6 C is moved slowly from a location where the potential is 0 V to a location where the potential is +50 V, starting and ending at rest. What is the work done by the external agent that moves it?
1. A-1.0 x 10^-4 J
2. B-4.0 x 10^-8 J
3. CZero
4. D+1.0 x 10^-4 J
Show answer
Answer: A. -1.0 x 10^-4 J
With no change in kinetic energy the external work equals the change in potential energy, q(change in V) = (-2.0 x 10^-6)(50) = -1.0 x 10^-4 J. The sign is negative because a negative charge is naturally attracted toward higher potential, so the agent must hold it back rather than push it.
Key insight: Negative charges have low potential energy where the potential is high, which flips the sign of the work.
Question 3Intermediate
In a certain region the electric potential varies as V(x) = 6x^2, with V in volts and x in meters. What is the x-component of the electric field at x = 2.0 m?
1. A-24 V/m
2. B-12 V/m
3. C+12 V/m
4. D+24 V/m
Show answer
Answer: A. -24 V/m
The field is the negative gradient of the potential: E_x = -dV/dx = -12x, so at x = 2.0 m it is -24 V/m. The +24 V/m choice omits the minus sign, which is what makes the field point from high potential toward low potential.
Key insight: Field points downhill on the potential landscape, which is exactly what the negative sign in E = -dV/dx encodes.
Question 4Foundational
A charged particle is moved along a path that stays entirely on one equipotential surface. How much work does the electric force do on the particle during that motion?
1. A0 J
2. BThe work equals qV, where V is the value of the potential
3. CThe work equals -qV, where V is the value of the potential
4. DThe work depends on the length of the path taken
Show answer
Answer: A. 0 J
Work by the electric force is -q times the change in potential, and on a single equipotential surface that change is zero no matter how long the path is. This is also why field lines always meet equipotential surfaces at right angles: a force perpendicular to the motion does no work.
Key insight: The electric force is conservative, so its work depends only on the endpoints, never on the route.
Question 5Advanced
Three identical point charges q are brought from infinity and fixed at the corners of an equilateral triangle whose sides have length a. In terms of k, q, and a, what is the total electric potential energy of the final configuration?
1. Akq^2/a
2. B3kq^2/a
3. C3kq^2/a^2
4. D6kq^2/a
Show answer
Answer: B. 3kq^2/a
Potential energy is summed over pairs, and three charges form exactly three pairs, each contributing kq^2/a, for a total of 3kq^2/a. The 6kq^2/a choice counts every pair twice, and 3kq^2/a^2 uses the force expression rather than the energy expression.
Key insight: Assembly energy is a sum over distinct pairs, so n charges contribute n(n-1)/2 terms.

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Unit 9: Electric Potential