Physics 2 · Electric Force, Field, and Potential · 14 min read · Updated 2026-05-11
Potential and Electric Potential Energy — AP Physics 2
AP Physics 2 · Electric Force, Field, and Potential · 14 min read
1. Core Definitions: Electric Potential Energy★★☆☆☆⏱ 4 min
When a charge moves through an electric field, the change in electric potential energy equals the negative of the work done by the electric force on the charge: $
Delta U = -W_E$. If the charge moves at constant kinetic energy, this change equals the work done by an external force to move the charge: $
Delta U = W_{\text{ext}}$.
For any charge $q$ moving through a potential difference $
Delta V$, the change in potential energy simplifies to the core formula:
\Delta U = q \Delta V
For a system of two point charges $q_1$ and $q_2$ separated by distance $r$, with zero potential energy set at infinite separation, the absolute potential energy of the system is:
If charges have the same sign, $U$ is positive: work must be done to bring repelling charges together from infinity. If charges have opposite signs, $U$ is negative: the system has less energy than when separated, so work must be done to pull them apart.
2. Electric Potential and Potential of Point Charge Systems★★★☆☆⏱ 4 min
Potential difference (or voltage) $
Delta V = V_f - V_i$ is the difference in potential between two points, the measurable quantity used in circuits and experiments. For a single point charge $Q$, with $V=0$ at infinity, potential at distance $r$ is:
V = \frac{kQ}{r}
A key advantage of potential over electric field is that potential is a scalar quantity. For a system of multiple point charges, the total potential at any point is just the algebraic sum of potentials from each individual charge: $V_{\text{total}} = \sum \frac{k q_i}{r_i}$. No vector components are needed—just add signed values based on the sign of each charge.
3. Electric Field, Potential, and Equipotential Surfaces★★★☆☆⏱ 4 min
Electric field and potential are closely related: the electric field points in the direction of maximum decreasing potential, and its magnitude equals the negative rate of change of potential with distance. For a uniform electric field aligned with the x-axis, this simplifies to:
E = - \frac{\Delta V}{\Delta x}
The magnitude of the field is $|E| = |\Delta V / d|$, where $d$ is the distance along the direction of the electric field between the two points.
No work is done to move a charge along an equipotential, so electric field lines are always perpendicular to equipotential surfaces. For point charges, equipotentials are concentric spheres; for uniform fields between parallel plates, they are parallel planes perpendicular to field lines.
4. Applications: Energy Conservation for Charged Particles★★★★☆⏱ 3 min
Conservation of energy applies to conservative electric fields, allowing us to calculate the kinetic energy and speed of accelerated charged particles, a common AP Physics 2 problem type.
Common Pitfalls
Why: Similar names lead students to forget the definition of potential as "per unit charge".
Why: Students know E points to lower potential and reverse subtraction to get a "reasonable" sign, leading to wrong energy changes.
Why: Students just learned electric field is a vector, so they default to vector addition for potential.
Why: The point charge formula is only defined with zero potential at infinity.
Why: Students rush and confuse the orientation of the two line types.