AP® Physics C: Electricity and Magnetism Cheat Sheet

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}$$F_e = k \frac{|q_1 q_2|}{r^2}$

  • Positive $F_e$$F_e$​: repel, Negative $F_e$$F_e$​: attract

• Electric Field:

  • $E = \frac{F_e}{q}$$E = \frac{F_e}{q}$

  • $E = k \frac{q}{r^2}$$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}$$\oint \vec{E} \cdot d\vec{A} = \frac{Q_{\text{enc}}}{\epsilon_0}$

• Electric Potential Energy:

  • $\frac{q_1 q_2}{r}$$\frac{q_1 q_2}{r}$

• Electric Potential:

  • $V = \frac{U}{q} = k \frac{q}{r}$$V = \frac{U}{q} = k \frac{q}{r}$

• Potential Difference (Voltage):

  • $\Delta V = -\int \vec{E} \cdot d\vec{s}$$\Delta V = -\int \vec{E} \cdot d\vec{s}$

• Equipotential Surfaces:

  • Surfaces where the potential is constant, $\vec{E}$$\vec{E}$ is perpendicular to equipotential surfaces.

Unit 2: Conductors, Capacitors, & Dielectrics

• Capacitance:

  • $C = \frac{Q}{V}$$C = \frac{Q}{V}$

  • Units: Farads (F)

• Parallel Plate Capacitor:

  • $C = \frac{\epsilon_0 A}{d}$$C = \frac{\epsilon_0 A}{d}$

• Capacitors in Series:

  • $\frac{1}{C_{\text{eq}}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots$$\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$$C_{\text{eq}} = C_1 + C_2 + \cdots$

• Energy Stored in Capacitor:

  • $U = \frac{1}{2} CV^2$$U = \frac{1}{2} CV^2$

• Dielectrics:

  • Increases capacitance by a factor K: C′=KC

• Electric Field in Dielectrics:

  • $E = \frac{E_0}{K}$$E = \frac{E_0}{K}$

• Capacitance with Dielectric:

  • $C = \frac{K \epsilon_0 A}{d}$$C = \frac{K \epsilon_0 A}{d}$

  • $U = \frac{1}{2} \frac{Q^2}{C} = \frac{1}{2} CV^2$$U = \frac{1}{2} \frac{Q^2}{C} = \frac{1}{2} CV^2$

Unit 3: Electric Circuits

• Current:

  • $I = \frac{dQ}{dt}$$I = \frac{dQ}{dt}$

  • $I = \frac{V}{R}$$I = \frac{V}{R}$​ (Ohm’s Law)

• Resistance:

  • $R = \frac{\rho L}{A}$$R = \frac{\rho L}{A}$

  • $\rho$$\rho$ = resistivity, L = length, A = area

• Ohm’s Law:

  • V = IR

• Power:

  • $P = IV = I^2 R = \frac{V^2}{R}$$P = IV = I^2 R = \frac{V^2}{R}$

• Kirchhoff's Laws:

  • Junction Rule: $\sum I_{\text{in}} = \sum I_{\text{out}}$$\sum I_{\text{in}} = \sum I_{\text{out}}$

  • Loop Rule: $\sum \Delta V = 0$$\sum \Delta V = 0$

• Resistors in Series:

  • $R_{\text{eq}} = R_1 + R_2 + \cdots$$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$$\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)$$q(t) = Q_{\text{max}} \left( 1 - e^{-t/RC} \right)$

  • Discharging: $q(t) = Q_{\text{max}} e^{-t/RC}$$q(t) = Q_{\text{max}} e^{-t/RC}$

Unit 4: Magnetic Fields

• Magnetic Force on a Moving Charge:

  • $F_B = qvB \sin \theta$$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$$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}$$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}}$$\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{enc}}$

• Magnetic Flux:

  • $\Phi_B = \vec{B} \cdot \vec{A} = BA \cos \theta$$\Phi_B = \vec{B} \cdot \vec{A} = BA \cos \theta$

• Torque on a Loop:

  • $\tau = NIAB \sin \theta$$\tau = NIAB \sin \theta$

Unit 5: Electromagnetism

• Faraday's Law of Induction:

  • $\mathcal{E} = -\frac{d\Phi_B}{dt}$$\mathcal{E} = -\frac{d\Phi_B}{dt}$

  • Induced emf opposes the change in magnetic flux (Lenz's Law).

• Inductance:

  • $V = L \frac{dI}{dt}$$V = L \frac{dI}{dt}$

  • $L = \frac{\mu_0 N^2 A}{l}$$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)$$I(t) = \frac{\mathcal{E}}{R} \left( 1 - e^{-t/\tau} \right)$

  • RL Circuit (Discharging): $I(t) = I_0 e^{-t/\tau}$$I(t) = I_0 e^{-t/\tau}$

  • Time constant $\tau = \frac{L}{R}$$\tau = \frac{L}{R}$

• LC Oscillations:

  • $\omega_0 = \frac{1}{\sqrt{LC}}$$\omega_0 = \frac{1}{\sqrt{LC}}$

  • $f_0 = \frac{1}{2\pi\sqrt{LC}}$$f_0 = \frac{1}{2\pi\sqrt{LC}}$

• Transformers:

  • $\frac{V_s}{V_p} = \frac{N_s}{N_p}$$\frac{V_s}{V_p} = \frac{N_s}{N_p}$

  • $\frac{I_s}{I_p} = \frac{N_p}{N_s}$$\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.