AP Physics C Electricity and Magnetism Laws Cheat Sheet

A printable reference covering Gauss's law, electric potential, capacitance, circuits, magnetic fields, induction, and Maxwell's equations for grades 11-12.

Download PNG

Related Tools

Related Labs

Related Worksheets

Related Infographics

AP Physics C Electricity and Magnetism connects electric charge, fields, circuits, magnetism, and changing fields using calculus-based laws. This cheat sheet helps students organize the major laws that appear across free-response and multiple-choice problems. It is especially useful for choosing the correct integral law, sign convention, or circuit relationship under time pressure. The core ideas are that charges create electric fields, currents create magnetic fields, and changing fields can induce circulation in the other field. Gauss's law, Ampere's law, Faraday's law, and Maxwell's correction describe field behavior with symmetry and calculus. Circuits use charge conservation, energy conservation, and component laws such as $V = IR$ and $Q = CV$ .

Key Facts

Coulomb's law gives the electric force between point charges as $\vec{F} = k\frac{q_1 q_2}{r^2}\hat{r}$ , where $k = \frac{1}{4\pi \epsilon_0}$ .
The electric field is force per unit positive test charge, so $\vec{E} = \frac{\vec{F}}{q}$ and for a point charge $\vec{E} = k\frac{q}{r^2}\hat{r}$ .
Gauss's law states $\oint \vec{E}\cdot d\vec{A} = \frac{Q_{\text{enc}}}{\epsilon_0}$ , which is most useful when symmetry makes $E$ constant on the Gaussian surface.
Electric potential difference is related to electric field by $\Delta V = -\int_a^b \vec{E}\cdot d\vec{\ell}$ , and electric potential energy is $U = qV$ .
Capacitance is defined by $C = \frac{Q}{\Delta V}$ , and a parallel-plate capacitor has $C = \kappa \epsilon_0 \frac{A}{d}$ when filled with dielectric constant $\kappa$ .
Kirchhoff's junction rule is $\sum I_{\text{in}} = \sum I_{\text{out}}$ , and Kirchhoff's loop rule is $\sum \Delta V = 0$ around any closed loop.
The magnetic force on a moving charge is $\vec{F}_B = q\vec{v}\times \vec{B}$ , and the force on a current-carrying wire is $\vec{F}_B = I\vec{L}\times \vec{B}$ .
Faraday's law of induction is $\mathcal{E} = -\frac{d\Phi_B}{dt}$ , where magnetic flux is $\Phi_B = \int \vec{B}\cdot d\vec{A}$ .

Vocabulary

Electric flux: Electric flux measures how much electric field passes through a surface and is calculated by $\Phi_E = \int \vec{E}\cdot d\vec{A}$ .
Gaussian surface: A Gaussian surface is an imaginary closed surface used with Gauss's law to relate electric flux to enclosed charge.
Electric potential: Electric potential is electric potential energy per unit charge, written as $V = \frac{U}{q}$ .
Capacitance: Capacitance is a measure of how much charge a capacitor stores per potential difference, defined by $C = \frac{Q}{\Delta V}$ .
Magnetic flux: Magnetic flux measures how much magnetic field passes through a surface and is given by $\Phi_B = \\int \vec{B}\cdot d\vec{A}$ .
Induced emf: Induced emf is the voltage produced by changing magnetic flux, described by $\mathcal{E} = -\frac{d\Phi_B}{dt}$ .

Common Mistakes to Avoid

Using Gauss's law without symmetry is wrong because $\oint \vec{E}\cdot d\vec{A} = \frac{Q_{\text{enc}}}{\epsilon_0}$ is always true, but it only easily gives $E$ when the field is constant or has a simple direction on the surface.
Forgetting the negative sign in $\Delta V = -\int \vec{E}\cdot d\vec{\ell}$ is wrong because electric field points in the direction of decreasing electric potential for a positive test charge.
Treating $\vec{F}_B = q\vec{v}\times \vec{B}$ like ordinary multiplication is wrong because the magnetic force depends on direction and has magnitude $F_B = |q|vB\sin \theta$ .
Adding capacitors like resistors is wrong because capacitors in parallel add as $C_{\text{eq}} = C_1 + C_2 + \cdots$ , while capacitors in series satisfy $\frac{1}{C_{\text{eq}}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots$ .
Ignoring displacement current in Ampere-Maxwell law is wrong because changing electric flux contributes according to $\oint \vec{B}\cdot d\vec{\ell} = \mu_0 I_{\text{enc}} + \mu_0\epsilon_0\frac{d\Phi_E}{dt}$ .

Practice Questions

1 A point charge of $+3.0\ \mu\text{C}$ is located at the center of a spherical Gaussian surface of radius $0.20\ \text{m}$ . What is the electric flux through the surface?
2 A parallel-plate capacitor has plate area $2.0\times 10^{-3}\ \text{m}^2$ , plate separation $1.0\times 10^{-3}\ \text{m}$ , and dielectric constant $\kappa = 4.0$ . Find its capacitance.
3 A wire segment of length $0.50\ \text{m}$ carries current $3.0\ \text{A}$ perpendicular to a uniform magnetic field of magnitude $0.20\ \text{T}$ . What is the magnetic force magnitude?
4 Why can Gauss's law determine the electric field easily for an infinite charged plane but not for an irregularly shaped charged object?

Sign in to save