AP Physics C: Electricity and Magnetism

The Physics C: E&M equation sheet, annotated for 2026

Transcribed from the equations table of the official AP Physics C: Electricity and Magnetism Course and Exam Description (Effective Fall 2024). College Board provides this sheet on both sections of the exam, so nothing here needs memorizing; knowing when each equation applies is the skill the exam actually tests. The geometry and math reference tables printed alongside the equations are not reproduced here.

For the units these equations belong to, see the Physics C: E&M course hub.

Constants and Conversion Factors

k = \frac{1}{4\pi\varepsilon_0} = 9.0 \times 10^9\ (\text{N} \cdot \text{m}^2)/\text{C}^2

Coulomb constant

\varepsilon_0 = 8.85 \times 10^{-12}\ \text{C}^2/(\text{N} \cdot \text{m}^2)

Vacuum permittivity

\mu_0 = 4\pi \times 10^{-7}\ (\text{T} \cdot \text{m})/\text{A}

Vacuum permeability

m_p = 1.67 \times 10^{-27}\ \text{kg}

Proton mass

m_n = 1.67 \times 10^{-27}\ \text{kg}

Neutron mass

m_e = 9.11 \times 10^{-31}\ \text{kg}

Electron mass

e = 1.60 \times 10^{-19}\ \text{C}

Elementary charge

1\ \text{eV} = 1.60 \times 10^{-19}\ \text{J}

1 electron volt

c = 3.00 \times 10^8\ \text{m/s}

Speed of light

1\ \text{u} = 1.66 \times 10^{-27}\ \text{kg} = 931\ \text{MeV}/c^2

1 unified atomic mass unit

G = 6.67 \times 10^{-11}\ \text{m}^3/(\text{kg} \cdot \text{s}^2) = 6.67 \times 10^{-11}\ \text{N} \cdot \text{m}^2/\text{kg}^2

Universal gravitational constant

g = 9.8\ \text{m/s}^2

Magnitude of the acceleration due to gravity at Earth's surface

g = 9.8\ \text{N/kg}

Magnitude of the gravitational field strength at Earth's surface

Electricity and Magnetism

\left| \vec{F}_E \right| = \frac{1}{4\pi\varepsilon_0} \frac{|q_1 q_2|}{r^2} = k \frac{|q_1 q_2|}{r^2}

\vec{E} = \frac{\vec{F}_E}{q}

\vec{E} = \frac{1}{4\pi\varepsilon_0} \int \frac{dq}{r^2} \hat{r}

\Phi_E = \int \vec{E} \cdot d\vec{A}

\oint \vec{E} \cdot d\vec{A} = \frac{q_{\text{enc}}}{\varepsilon_0}

Q_{\text{total}} = \int \rho(r)\, dV

U_E = \frac{1}{4\pi\varepsilon_0} \frac{q_1 q_2}{r}

V = \frac{1}{4\pi\varepsilon_0} \int \frac{dq}{r}

\Delta V = -\int_a^b \vec{E} \cdot d\vec{r}

E_x = -\frac{dV}{dx}

\Delta U_E = q \Delta V

C = \frac{Q}{\Delta V}

C = \frac{\kappa \varepsilon_0 A}{d}

U_C = \frac{1}{2} Q \Delta V

\kappa = \frac{\varepsilon}{\varepsilon_0}

I = \frac{dq}{dt}

I = \int \vec{J} \cdot d\vec{A}

\vec{E} = \rho \vec{J}

R = \frac{\rho \ell}{A}

I = \frac{\Delta V}{R}

P = I \Delta V

R_{\text{eq,s}} = \sum_i R_i

\frac{1}{R_{\text{eq,p}}} = \sum_i \frac{1}{R_i}

\frac{1}{C_{\text{eq,s}}} = \sum_i \frac{1}{C_i}

C_{\text{eq,p}} = \sum_i C_i

\tau = R_{\text{eq}} C_{\text{eq}}

\oint \vec{B} \cdot d\vec{A} = 0

\vec{F}_B = q\, \vec{v} \times \vec{B}

d\vec{B} = \frac{\mu_0}{4\pi} \frac{I\, d\vec{\ell} \times \hat{r}}{r^2}

\vec{F}_B = \int I\, d\vec{\ell} \times \vec{B}

\oint \vec{B} \cdot d\vec{\ell} = \mu_0 I_{\text{enc}}

B_{\text{sol}} = \mu_0 n I

\Phi_B = \int \vec{B} \cdot d\vec{A}

\mathcal{E} = \oint \vec{E} \cdot d\vec{\ell} = -\frac{d\Phi_B}{dt}

emf, printed as script E on the official sheet

\left| \mathcal{E}_{\text{sol}} \right| = N \left| \frac{d\Phi_B}{dt} \right|

L_{\text{sol}} = \frac{\mu_{\text{core}} N^2 A}{\ell}

U_L = \frac{1}{2} L I^2

\mathcal{E} = -L \frac{dI}{dt}

\tau = \frac{L}{R_{\text{eq}}}

\omega_{LC} = \frac{1}{\sqrt{LC}}

Mechanics

v_x = v_{x0} + a_x t

x = x_0 + v_{x0} t + \frac{1}{2} a_x t^2

v_x^2 = v_{x0}^2 + 2 a_x (x - x_0)

\Delta x = \int v_x(t)\, dt

\Delta v_x = \int a_x(t)\, dt

\vec{x}_{\text{cm}} = \frac{\sum m_i \vec{x}_i}{\sum m_i}

\vec{r}_{\text{cm}} = \frac{\int \vec{r}\, dm}{\int dm}

\lambda = \frac{d}{d\ell} m(\ell)

\vec{a}_{\text{sys}} = \frac{\sum \vec{F}}{m_{\text{sys}}} = \frac{\vec{F}_{\text{net}}}{m_{\text{sys}}}

\left| \vec{F}_g \right| = \frac{G m_1 m_2}{r^2}

\left| \vec{F}_f \right| \leq \left| \mu \vec{F}_N \right|

\vec{F}_s = -k \Delta \vec{x}

a_c = \frac{v^2}{r} = r \omega^2

T = \frac{1}{f}

K = \frac{1}{2} m v^2

W = \int_a^b \vec{F} \cdot d\vec{r}

\Delta K = \sum W_i = \sum F_{\parallel, i}\, d_i

\Delta U = -\int_a^b \vec{F}_{\text{cf}}(r) \cdot d\vec{r}

F_x = -\frac{dU(x)}{dx}

U_s = \frac{1}{2} k (\Delta x)^2

U_G = -\frac{G m_1 m_2}{r}

\Delta U_g = m g \Delta y

P_{\text{avg}} = \frac{W}{\Delta t} = \frac{\Delta E}{\Delta t}

P_{\text{inst}} = \frac{dW}{dt}

\vec{p} = m \vec{v}

\vec{F}_{\text{net}} = \frac{d\vec{p}}{dt}

\vec{J} = \int_{t_1}^{t_2} \vec{F}_{\text{net}}(t)\, dt = \Delta \vec{p}

\vec{v}_{\text{cm}} = \frac{\sum \vec{p}_i}{\sum m_i} = \frac{\sum m_i \vec{v}_i}{\sum m_i}

\omega = \frac{d\theta}{dt}

\alpha = \frac{d\omega}{dt}

\omega = \omega_0 + \alpha t

\theta = \theta_0 + \omega_0 t + \frac{1}{2} \alpha t^2

\omega^2 = \omega_0^2 + 2 \alpha (\theta - \theta_0)

v = r \omega

a_T = r \alpha

\vec{\tau} = \vec{r} \times \vec{F}

I_{\text{tot}} = \sum I_i = \sum m_i r_i^2

I = \int r^2\, dm

I' = I_{\text{cm}} + M d^2

\alpha_{\text{sys}} = \frac{\sum \tau}{I_{\text{sys}}} = \frac{\tau_{\text{net}}}{I_{\text{sys}}}

K_{\text{rot}} = \frac{1}{2} I \omega^2

W = \int \tau \cdot d\theta

\vec{L} = \vec{r} \times \vec{p} = I \vec{\omega}

\Delta L = \int \tau\, dt

\Delta x_{\text{cm}} = r \Delta\theta

T = \frac{2\pi}{\omega} = \frac{1}{f}

T_s = 2\pi \sqrt{\frac{m}{k}}

T_p = 2\pi \sqrt{\frac{\ell}{g}}

T_{\text{phys}} = 2\pi \sqrt{\frac{I}{m g d}}

x = x_{\text{max}} \cos(\omega t + \phi)

The other sheets

AP Physics 1: Algebra-Based52 constants and equations, grouped as printed.AP Physics 2: Algebra-Based129 constants and equations, grouped as printed.AP Physics C: Mechanics53 constants and equations, grouped as printed.Physics C: E&M: the course, unit by unitUnits, weightings, topics, exam format, and the May 2025 score results.