Electrostatics (AP Physics C: E&M) Cheat Sheet

The core ideas of Electrostatics (AP Physics C: E&M) distilled into a single, scannable reference — perfect for review or quick lookup.

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Quick Reference

Coulombs Law

The force between two point charges is = k|q_1 q_2|/r^2$ where = 1/(4piarepsilon_0) approx 8.99 imes 10^9$ N m$^2$/C$^2$. Attractive for unlike charges, repulsive for like. Superposition holds.

Electric Field

$ec{E} = ec{F}/q_0$. Point charge: = kQ/r^2$. Continuous: integrate = k,dq/r^2$.

Gausss Law

$oint ec{E} cdot dec{A} = Q_{ ext{enc}}/arepsilon_0$. Best with spherical, cylindrical, or planar symmetry.

Electric Potential

= -int_infty^r ec{E}cdot dec{l}$. Point charge: = kQ/r$. Scalar.

Potential Energy

Two charges: = kq_1q_2/r$. { ext{field}} = -Delta U = -qDelta V$.

Superposition

Net field = vector sum; net potential = scalar sum.

Conductors in Equilibrium

$ec{E}=0$ inside, charge on surface, equipotential, just outside: =sigma/arepsilon_0$.

E-V Relationship

$ec{E}=- abla V$. $Delta V=-intec{E}cdot dec{l}$. Equipotentials perpendicular to field lines.

Key Terms at a Glance

Coulomb (C):SI charge unit. Electron: $-1.6\times10^{-19}$ C.

Permittivity:$\varepsilon_0\approx8.854\times10^{-12}$ C$^2$/(Nm$^2$).

Electric Flux:$\Phi_E=\int\vec{E}\cdot d\vec{A}$. Units: Nm$^2$/C.

Gaussian Surface:Imaginary closed surface for Gauss's law.

Equipotential:Constant $V$ surface. $\perp$ to $\vec{E}$.

Electric Dipole:$\pm q$ separated by $d$. $\vec{p}=q\vec{d}$.

Surface Charge Density:$\sigma=dQ/dA$. C/m$^2$.

Linear Charge Density:$\lambda=dQ/dl$. C/m.

Volume Charge Density:$\rho=dQ/dV$. C/m$^3$.

Electrostatic Equilibrium:$\vec{E}=0$ in conductors. Charge on surfaces.

Shielding:Conductor blocks external fields. Faraday cage.

Point Charge:$E\propto1/r^2$, $V\propto1/r$.

Test Charge:Infinitesimal $q_0$: $\vec{E}=\vec{F}/q_0$.

Potential Difference:$\Delta V=-\int\vec{E}\cdot d\vec{l}$. Units: V.

Superposition:Total = sum of individual contributions.

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