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.

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.