AP Physics C E&M Formula Sheet Cheat Sheet

Key Facts

• Coulomb’s law gives the electric force between point charges as $\vec{F} = \frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r^2}\hat{r}$.
• The electric field is force per unit positive test charge, so $\vec{E} = \frac{\vec{F}}{q}$ and for a point charge $\vec{E} = \frac{1}{4\pi\epsilon_0}\frac{q}{r^2}\hat{r}$.
• Gauss’s law relates electric flux to enclosed charge by $\oint \vec{E}\cdot d\vec{A} = \frac{Q_{\text{enc}}}{\epsilon_0}$.
• Electric potential difference is related to electric field by $\Delta V = -\int_a^b \vec{E}\cdot d\vec{\ell}$, and potential energy is $U = qV$.
• Capacitance is defined by $C = \frac{Q}{\Delta V}$, and a parallel-plate capacitor has $C = \kappa\epsilon_0\frac{A}{d}$.
• Circuit equations include Ohm’s law $V = IR$, power $P = IV = I^2R = \frac{V^2}{R}$, and capacitor charging $q(t) = C\mathcal{E}(1 - e^{-t/RC})$.
• 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 gives induced emf as $\mathcal{E} = -\frac{d\Phi_B}{dt}$, where magnetic flux is $\Phi_B = \int \vec{B}\cdot d\vec{A}$.

Vocabulary

Electric field

The electric field $\vec{E}$ is the force per unit positive test charge at a point in space.

Electric flux

Electric flux $\Phi_E = \int \vec{E}\cdot d\vec{A}$ measures how much electric field passes through a surface.

Electric potential

Electric potential $V$ is electric potential energy per unit charge, defined by $V = \frac{U}{q}$.

Capacitance

Capacitance $C$ is the ratio of stored charge to potential difference, given by $C = \frac{Q}{\Delta V}$.

Magnetic flux

Magnetic flux $\Phi_B = \int \vec{B}\cdot d\vec{A}$ measures the amount of magnetic field passing through a surface.

Induced emf

Induced emf $\mathcal{E}$ is the voltage produced by a changing magnetic flux, described by $\mathcal{E} = -\frac{d\Phi_B}{dt}$.