AP® Physics C: Electricity and Magnetism Cheat Sheet

Last Updated: September 23, 2024

Notes

Master the essential concepts of AP Physics C: Electricity and Magnetism with this comprehensive cheat sheet, covering key formulas, laws, and circuit principles.

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Unit 1: Electrostatics

Law of Conservation of Charge:
- Charge cannot be created or destroyed, only transferred.
Conductors:
- Charge distributes evenly on the surface, does not hold inside.
- Inside has zero net charge.
Insulator:
- Charge does not distribute evenly, holds charge in one spot.
Coulomb’s Law:
- $F_e = k \frac{|q_1 q_2|}{r^2}$
- Positive $F_e$ : repel, Negative $F_e$ : attract
Electric Field:
- $E = \frac{F_e}{q}$
- $E = k \frac{q}{r^2}$ for a point charge.
Gauss’s Law:
- $\oint \vec{E} \cdot d\vec{A} = \frac{Q_{\text{enc}}}{\epsilon_0}$
Electric Potential Energy:
- $\frac{q_1 q_2}{r}$
Electric Potential:
- $V = \frac{U}{q} = k \frac{q}{r}$
Potential Difference (Voltage):
- $\Delta V = -\int \vec{E} \cdot d\vec{s}$
Equipotential Surfaces:
- Surfaces where the potential is constant, $\vec{E}$ is perpendicular to equipotential surfaces.

Unit 2: Conductors, Capacitors, & Dielectrics

Capacitance:
- $C = \frac{Q}{V}$
- Units: Farads (F)
Parallel Plate Capacitor:
- $C = \frac{\epsilon_0 A}{d}$
Capacitors in Series:
- $\frac{1}{C_{\text{eq}}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots$
Capacitors in Parallel:
- $C_{\text{eq}} = C_1 + C_2 + \cdots$
Energy Stored in Capacitor:
- $U = \frac{1}{2} CV^2$
Dielectrics:
- Increases capacitance by a factor K: C′=KC
Electric Field in Dielectrics:
- $E = \frac{E_0}{K}$
Capacitance with Dielectric:
- $C = \frac{K \epsilon_0 A}{d}$
- $U = \frac{1}{2} \frac{Q^2}{C} = \frac{1}{2} CV^2$

Unit 3: Electric Circuits

Current:
- $I = \frac{dQ}{dt}$
- $I = \frac{V}{R}$ (Ohm’s Law)
Resistance:
- $R = \frac{\rho L}{A}$
- $\rho$ = resistivity, L = length, A = area
Ohm’s Law:
- V = IR
Power:
- $P = IV = I^2 R = \frac{V^2}{R}$
Kirchhoff’s Laws:
- Junction Rule: $\sum I_{\text{in}} = \sum I_{\text{out}}$
- Loop Rule: $\sum \Delta V = 0$
Resistors in Series:
- $R_{\text{eq}} = R_1 + R_2 + \cdots$
Resistors in Parallel:
- $\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots$
RC Circuits:
- Charging: $q(t) = Q_{\text{max}} \left( 1 - e^{-t/RC} \right)$
- Discharging: $q(t) = Q_{\text{max}} e^{-t/RC}$

Unit 4: Magnetic Fields

Magnetic Force on a Moving Charge:
- $F_B = qvB \sin \theta$
- Right-hand rule: Thumb (v), Fingers (B), Palm (Force).
Magnetic Force on a Current-Carrying Wire:
- $F_B = ILB \sin \theta$
Biot-Savart Law:
- $d\vec{B} = \frac{\mu_0 I}{4 \pi} \frac{d\vec{l} \times \hat{r}}{r^2}$
Ampère’s Law:
- $\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{enc}}$
Magnetic Flux:
- $\Phi_B = \vec{B} \cdot \vec{A} = BA \cos \theta$
Torque on a Loop:
- $\tau = NIAB \sin \theta$

Unit 5: Electromagnetism

Faraday’s Law of Induction:
- $\mathcal{E} = -\frac{d\Phi_B}{dt}$
- Induced emf opposes the change in magnetic flux (Lenz’s Law).
Inductance:
- $V = L \frac{dI}{dt}$
- $L = \frac{\mu_0 N^2 A}{l}$
Inductors in Circuits:
- RL Circuit (Charging): $I(t) = \frac{\mathcal{E}}{R} \left( 1 - e^{-t/\tau} \right)$
- RL Circuit (Discharging): $I(t) = I_0 e^{-t/\tau}$
- Time constant $\tau = \frac{L}{R}$
LC Oscillations:
- $\omega_0 = \frac{1}{\sqrt{LC}}$
- $f_0 = \frac{1}{2\pi\sqrt{LC}}$
Transformers:
- $\frac{V_s}{V_p} = \frac{N_s}{N_p}$
- $\frac{I_s}{I_p} = \frac{N_p}{N_s}$

FRQ Tips

Show Your Work: Detailed steps can earn partial credit.
Use Units Consistently: Always include units in your calculations and final answers.
Apply Right-Hand Rules: Essential for magnetic force and field direction.
Label Diagrams: Clearly label all forces, fields, and relevant quantities.
Think Symmetrically: Use symmetry in charge distributions and fields to simplify problems.