AP Physics C: Electricity and Magnetism Study Guide

The course is a calculus-based study of electromagnetism. It opens with electrostatics: Coulomb's law, the electric field, electric potential, and Gauss's law, where you integrate over charge distributions and use symmetry to find fields you could never sum by hand.

From there you study conductors, capacitors, and dielectrics (how charge arranges itself and stores energy), then electric circuits with resistors and capacitors, including the exponential charging and discharging governed by a differential equation. The course turns to magnetic fields — the forces on moving charges and currents, plus the Biot–Savart and Ampère laws — and finishes with electromagnetism, where Faraday's law of induction ties changing magnetic flux to induced EMF. The through-line is that each new law is another piece of the same field framework, and calculus is the tool that makes the geometry solvable.

The College Board does not publish fixed percentage weights for the Physics C units, so treat them as roughly comparable and prioritize by how much later material depends on each. The five units are:

• Electrostatics — Coulomb's law, fields, potential, and Gauss's law
• Conductors, Capacitors, Dielectrics — charge distribution and stored energy
• Electric Circuits — resistive and RC circuits, transient behavior
• Magnetic Fields — forces on charges and currents, Biot–Savart, Ampère's law
• Electromagnetism — Faraday's law, induced EMF, inductance

The practical takeaway: electrostatics is the foundation the entire course rests on — fields and potential reappear in every later unit — so make Gauss's law and potential second nature before moving on. Induction at the end is the conceptual capstone and a frequent free-response topic.

Physics C: E&M is as much a calculus and symmetry exam as a physics one. A routine that works:

1. Choose the symmetry first. Before integrating, decide whether spherical, cylindrical, or planar symmetry lets you use Gauss's or Ampère's law — that single choice turns a brutal integral into a one-line result.
2. Distinguish field from potential constantly. Field is a vector you find by integration or Gauss's law; potential is a scalar you add up. Knowing which the question wants prevents most setup errors.
3. Master the RC and RL differential equations. Charging, discharging, and induced-current transients are predictable points if you can write and solve the exponential.
4. Work in mixed sets and review with full solutions. Mixed practice forces you to pick the right law, and a complete worked explanation for a missed problem — including why a tempting wrong answer fails — teaches more than easy repetition.

• Confusing electric field and electric potential, or mishandling the relationship $E=-dV/dx$ between them.
• Forcing Gauss's law where there is no symmetry — it is always true, but only useful when the field is constant over a chosen surface.
• Direction errors with the right-hand rule for magnetic force and field, and forgetting that magnetic force does no work.
• Sign mistakes in Faraday's and Lenz's laws — the induced current opposes the change in flux, and getting that direction wrong reverses the whole answer.
• Vague free-response justifications. A correct field magnitude with no statement of direction or reasoning leaves easy points unclaimed.

Every unit below has a focused practice set with full written explanations and a rationale for every wrong choice, plus a worked-solutions page you can read straight through. Start with a unit you're shaky on, then take a mixed set across the whole subject to pressure-test your tool selection before exam day. It's free and needs no account.