AP Physics C: Electricity and Magnetism 3-Day Cram Plan

You have three days until the AP Physics C: Electricity and Magnetism exam. This is calculus-based — skip the algebra shortcuts and drill the integral setup, symmetry arguments, and Lenz's law reasoning that scorers actually want.

This plan assumes ~4 focused hours per day. Each day ends with a full FRQ-style practice problem.

Day 1: Electrostatics & Gauss's Law (4 hrs)

Gauss's law appears on nearly every exam. The FRQ rubric demands that you choose the right surface, cite symmetry, and write the integral.

What to review (90 min)

• Coulomb's law: $\vec F = k \frac{q_1 q_2}{r^2} \hat r$ and the electric field $E = k \frac{q}{r^2}$ from a point charge.
• Electric field from continuous charge distributions via $dE = k \frac{dq}{r^2}$. Set up the integral for a ring, then a disk.
• Electric potential: $V = -\int \vec E \cdot d\vec\ell$ from a path integral. Know that $E = -\frac{dV}{dx}$ (the derivative relationship).
• Gauss's law: $\oint \vec E \cdot d\vec A = \frac{Q_{enc}}{\epsilon_0}$ — this is the entire unit.
  • Spherical symmetry (point charge, uniformly charged sphere)
  • Cylindrical symmetry (infinite line charge, charged cylinder)
  • Planar symmetry (infinite sheet, parallel plates)
• Choose the Gaussian surface; apply $E \perp A$ to simplify the dot product; solve for $E$.

What to practice (2.5 hrs)

• 20 multiple-choice on $E$ from point/continuous distributions.
• 1 full FRQ: Gauss's law for a uniformly charged spherical shell — find $E$ inside and outside, then relate to potential.

💡 Highest leverage: Gauss's law symmetry choice decides your entire FRQ setup. Spend 10 min tonight drawing spheres, cylinders, and sheets. Know when each one applies.

⚠️ Trap: $\epsilon_0$ in SI units, not $k$. On the exam, always use $\oint \vec E \cdot d\vec A = \frac{Q_{enc}}{\epsilon_0}$, not $\frac{4\pi k Q_{enc}}{...}$.

Day 2: Conductors, Capacitors, Circuits (4 hrs)

Circuit problems and capacitor FRQs mix RC transient decay with steady-state reasoning. Master the $\tau = RC$ formula and the exponential curves.

What to review (90 min)

• Conductors in equilibrium: $E = 0$ inside, charge on surface, perpendicular field just outside.
• Capacitor basics: $C = \frac{Q}{V}$, parallel-plate $C = \epsilon_0 \frac{A}{d}$, energy $U = \frac{1}{2}CV^2 = \frac{1}{2}\frac{Q^2}{C}$.
• Series vs parallel reduction — capacitor math is opposite to resistor math.
• RC circuits: time constant $\tau = RC$; charging $Q(t) = Q_0(1 - e^{-t/\tau})$; discharging $Q(t) = Q_0 e^{-t/\tau}$.
• Kirchhoff's junction rule (current in = current out) and loop rule ($\sum V = 0$ around a closed loop, including resistive drops).
• Resistivity: $R = \rho \frac{L}{A}$ and its temperature dependence.

What to practice (2.5 hrs)

• 1 RC charging FRQ: initial condition ($Q = 0$), time constant, current as a function of time, energy in the capacitor.
• 1 circuit FRQ: multiloop with Kirchhoff's laws and a capacitor in steady state (current = 0 through the capacitor).
• 15 no-calculator MCQ on capacitor combinations and RC transient reasoning.

⚠️ Trap: In steady state (long time), current stops at a capacitor. $\frac{dQ}{dt} = 0$. Don't keep current flowing through a capacitor after $t \to \infty$.

⚠️ Trap: Charging curve is $1 - e^{-t/\tau}$ (approaches 1). Discharging is $e^{-t/\tau}$ (approaches 0). Memorize both.

Day 3: Magnetism, Induction, Full FRQ Practice (4 hrs)

Lorentz force, Ampère's law, and Faraday's law are three separate tools. Know which applies when.

What to review (90 min)

• Lorentz force on a charge: $\vec F = q \vec v \times \vec B$. Direction via right-hand rule (fingers from $\vec v$ to $\vec B$, thumb = force).
• Force on a current-carrying wire: $\vec F = I \vec L \times \vec B$, where $\vec L$ points in direction of current.
• Magnetic field from a current:
  • Biot-Savart law: $d\vec B = \frac{\mu_0 I}{4\pi} \frac{d\vec\ell \times \hat r}{r^2}$ — tough integral, but know the setup.
  • Ampère's law: $\oint \vec B \cdot d\vec\ell = \mu_0 I_{enc}$ for symmetry (infinite wire, solenoid, toroid).
• Magnetic flux: $\Phi_B = \int \vec B \cdot d\vec A$ (units: Tesla·m²).
• Faraday's law: $\varepsilon = -\frac{d\Phi_B}{dt}$ — the induced EMF opposes the change (Lenz's law).
• Motional EMF: $\varepsilon = BLv$ when a conductor slides through a perpendicular field.
• Inductors: $\varepsilon = -L \frac{dI}{dt}$; energy $U = \frac{1}{2}LI^2$; time constant $\tau = \frac{L}{R}$ for RL circuits.

What to practice (2.5 hrs — full timed set)

• 1 full FRQ on Ampère's law: find $B$ inside a cylindrical wire or solenoid using symmetry.
• 1 full FRQ on Faraday's law: changing magnetic flux through a loop, find induced EMF and current direction via Lenz's law.
• 25 mixed multiple-choice (think through each right-hand-rule choice; don't rush).

💡 Highest leverage: Lenz's law direction is not optional on FRQs. Always state: "By Lenz's law, the induced current flows [clockwise/counterclockwise] to oppose the [increasing/decreasing] flux."

⚠️ Sign trap: In Faraday's law $\varepsilon = -\frac{d\Phi_B}{dt}$, the negative sign is Lenz's law. If $\frac{d\Phi_B}{dt} > 0$ (flux increasing), then $\varepsilon < 0$ (EMF opposes the change). Don't forget the negative.

The night before

Skim our last-minute review checklist. Print the Gauss's law symmetry table and RC/RL transient template. Get 8 hours of sleep — your brain needs to lock in the right-hand-rule muscle memory.

Three key equations to internalize by muscle memory

$\text{Gauss's law:} \quad \oint \vec E \cdot d\vec A = \frac{Q_{enc}}{\epsilon_0}$

$\text{Faraday's law:} \quad \varepsilon = -\frac{d\Phi_B}{dt}$

$\text{RC time constant:} \quad \tau = RC, \quad Q(t) = Q_0 e^{-t/\tau}$

What this plan skips

You will not fully master the Biot-Savart integral or advanced dielectric properties in 3 days. If asked on the exam: cite Ampère's law instead (or Biot-Savart by name without deriving). Accept 2–4 lost points and move on. Your time is better spent mastering Gauss's law and Faraday's law.

Ready to start?

Open the AP Physics C: E&M topic library → and begin Day 1 with whichever symmetry case (sphere, cylinder, sheet) feels rustiest. Work 3–5 example problems per topic from the reference solutions. You've got this.