Capacitors and Dielectrics (AP Physics C: E&M) Cheat Sheet

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

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Capacitance:$C = Q/V$. Ability to store charge. SI unit: farad (F).

Farad:SI unit of capacitance. $1$ F $= 1$ C/V.

Dielectric:Insulating material that increases capacitance when placed between plates.

Dielectric Constant:$\kappa$: ratio $C/C_0$. Always $\geq 1$.

Permittivity:$\varepsilon = \kappa\varepsilon_0$. Material response to $\vec{E}$.

Energy Density:$u = \tfrac{1}{2}\varepsilon_0 E^2$. J/m$^3$.

Dielectric Strength:Max $E$ before breakdown. V/m.

Polarization:$\vec{P}$: dipole moment per volume. Creates bound charges.

Electric Displacement:$\vec{D} = \varepsilon_0\vec{E} + \vec{P}$. Gauss: $\oint\vec{D}\cdot d\vec{A} = Q_\text{free}$.

Bound Charge:Surface charge from molecular polarization.

Free Charge:Mobile charges on conductor plates.

Breakdown Voltage:Voltage at which dielectric fails.

Series Combination:End-to-end. Same $Q$. $1/C_{eq} = \sum 1/C_i$.

Parallel Combination:Side-by-side. Same $V$. $C_{eq} = \sum C_i$.

Isolated Capacitor:Disconnected from battery. $Q$ fixed.

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