AP Physics C: Electricity and Magnetism 7-Day Study Plan

You have seven days to solidify all five units of AP Physics C: E&M. This plan spreads the five units across Days 1–5, then devotes Days 6–7 to full FRQ practice and a mock exam review.

Each day requires 3–4 hours of focused work. Do not skip review blocks; the derivative and integral setups are where most rubric points live.

Daily breakdown

Day-by-day detail

Day 1: Electrostatics foundations (3.5 hrs)

Review (60 min):

• Coulomb's law: $\vec F = k \frac{q_1 q_2}{r^2} \hat r$, electric field $E = k \frac{q}{r^2}$.
• Continuous distributions: $dE = k \frac{dq}{r^2}$. Drill the ring and disk setups (integrate along axis).
• Superposition and vector addition of $\vec E$ fields.

Practice (2.5 hrs):

• 25 MCQ on Coulomb's law, point charges, and field lines.
• 3 worked problems: ring of charge, uniformly charged rod, disk of charge (find $E$ at center and on axis).

💡 Key insight: For continuous distributions, always set up the integral; don't memorize results.

Day 2: Gauss's law deep dive + Potential (4 hrs)

Review (90 min):

• Gauss's law: $\oint \vec E \cdot d\vec A = \frac{Q_{enc}}{\epsilon_0}$. Recognize when symmetry lets you pull $E$ out of the integral.
• Three symmetry cases:
  • Spherical: $E \cdot 4\pi r^2 = \frac{Q_{enc}}{\epsilon_0}$ → $E(r) = \frac{kQ_{enc}}{r^2}$ or $\frac{Q_{enc}}{4\pi\epsilon_0 r^2}$.
  • Cylindrical: $E \cdot 2\pi r L = \frac{\lambda L}{\epsilon_0}$ → $E(r) = \frac{\lambda}{2\pi\epsilon_0 r}$.
  • Planar: $E \cdot 2A = \frac{\sigma A}{\epsilon_0}$ → $E = \frac{\sigma}{2\epsilon_0}$.
• Electric potential: $V(r) = k \frac{q}{r}$ for a point charge; $E = -\frac{dV}{dr}$ (1D) or $\vec E = -\nabla V$ (3D).
• Relating potential to Gauss's law via $V = -\int E \, dr$ along a path.

Practice (2.5 hrs):

• 20 MCQ on Gauss's law and potential.
• 5 short-answer sketches: draw the Gaussian surface, write the law, solve for $E$.
• 1 full FRQ: "A conducting sphere of radius $R$ holds total charge $Q$. Using Gauss's law, find the electric field $E(r)$ for $r < R$ and $r > R$. Relate to electric potential. If an electron is placed at the surface, what is the potential energy?"

Day 3: Capacitors & Conductors (3.5 hrs)

Review (90 min):

• Conductors in electrostatic equilibrium: $E = 0$ inside, charge on surface, $\vec E \perp$ surface.
• Capacitance: $C = \frac{Q}{V}$ (definition), parallel-plate $C = \epsilon_0 \frac{A}{d}$, cylindrical, spherical.
• Energy stored: $U = \frac{1}{2}CV^2 = \frac{1}{2}\frac{Q^2}{C} = \frac{1}{2}QV$.
• Series capacitors: $\frac{1}{C_{tot}} = \frac{1}{C_1} + \frac{1}{C_2} + \ldots$ (reciprocal sum).
• Parallel capacitors: $C_{tot} = C_1 + C_2 + \ldots$ (direct sum).
• Dielectrics: $C = \kappa \epsilon_0 \frac{A}{d}$ (dielectric constant $\kappa$), reduced $E$ inside.

Practice (2.5 hrs):

• 20 MCQ on capacitors, combinations, energy.
• 10 circuit reduction problems (mix series, parallel, and series-parallel).

⚠️ Trap: Capacitors in series have the same charge $Q$ on each plate, but different voltages. Don't confuse with resistors (which split current, not charge).

Day 4: Circuits & RC Dynamics (4 hrs)

Review (90 min):

• Resistivity: $R = \rho \frac{L}{A}$.
• Kirchhoff's junction rule: $\sum I_{in} = \sum I_{out}$.
• Kirchhoff's loop rule: $\sum V = 0$ around any closed loop (including resistive drops $V = -IR$).
• RC charging: $Q(t) = Q_0(1 - e^{-t/\tau})$, $I(t) = \frac{Q_0}{\tau} e^{-t/\tau}$, $\tau = RC$.
• RC discharging: $Q(t) = Q_0 e^{-t/\tau}$, $I(t) = -\frac{Q_0}{\tau} e^{-t/\tau}$.
• Steady state: current through a capacitor $= 0$ (open circuit).

Practice (2.5 hrs):

• 20 MCQ on Kirchhoff's laws and circuit analysis.
• 8 multiloop problems (use Kirchhoff to set up the system).
• 1 full FRQ: "A capacitor of $C = 100 \, \mu F$ is charged through a resistor $R = 5000 \, \Omega$. (a) Find the time constant. (b) Write $Q(t)$ during charging. (c) Find the current at $t = 0$ and $t = \tau$. (d) In steady state (long time), what is the energy stored in the capacitor?"

Day 5: Magnetism & Ampère's Law (4 hrs)

Review (90 min):

• Lorentz force: $\vec F = q \vec v \times \vec B$ (direction: right-hand rule, fingers from $\vec v$ to $\vec B$, thumb = $\vec F$).
• Force on a current: $\vec F = I \vec L \times \vec B$ (where $\vec L$ = length vector in direction of current).
• Biot-Savart law: $d\vec B = \frac{\mu_0 I}{4\pi} \frac{d\vec\ell \times \hat r}{r^2}$ — setup, not always full integration.
• Ampère's law: $\oint \vec B \cdot d\vec\ell = \mu_0 I_{enc}$ for symmetric geometries.
  • Infinite wire: $B = \frac{\mu_0 I}{2\pi r}$.
  • Solenoid: $B = \mu_0 n I$ (uniform inside, zero outside).
  • Toroid: $B = \frac{\mu_0 I N}{2\pi r}$ (varies with $r$).

Practice (2.5 hrs):

• 25 MCQ on Lorentz force, Ampère's law, Biot-Savart.
• 5 right-hand-rule problems (confirm force & field directions).
• 1 full FRQ: "A long solenoid with $n = 1000$ turns per meter carries current $I = 2 \, A$. Using Ampère's law, find the magnetic field magnitude inside. If a proton enters perpendicular to $\vec B$ with speed $v = 10^5 \, m/s$, find the Lorentz force magnitude and the radius of its circular path."

Day 6: Electromagnetic Induction & RL Circuits (4 hrs)

Review (90 min):

• Magnetic flux: $\Phi_B = \int \vec B \cdot d\vec A = BA\cos\theta$ (for uniform $B$).
• Faraday's law: $\varepsilon = -\frac{d\Phi_B}{dt}$ (the negative sign is Lenz's law).
• Lenz's law: Induced current opposes the change in flux (either magnitude or direction).
• Motional EMF: $\varepsilon = BLv$ when a rod slides perpendicular through $\vec B$.
• Inductors: $\varepsilon = -L \frac{dI}{dt}$, energy $U = \frac{1}{2}LI^2$, time constant $\tau = \frac{L}{R}$.
• RL charging: $I(t) = I_0(1 - e^{-t/\tau})$. RL discharging: $I(t) = I_0 e^{-t/\tau}$.

Practice (2.5 hrs):

• 20 MCQ on Faraday's law, RL circuits, motional EMF.
• 6 Lenz's law direction problems (state whether induced current is clockwise or counterclockwise, and why).
• 1 full FRQ: "A rectangular loop of area $A = 0.1 \, m^2$ is placed in a uniform magnetic field $B = 2 \, T$ perpendicular to the loop. The field decreases linearly to zero over time $\Delta t = 0.5 \, s$. (a) Find the induced EMF. (b) If the loop has resistance $R = 10 \, \Omega$, find the induced current. (c) By Lenz's law, state the direction of the induced current."

Day 7: Full Mock Exam (90 min timed)

Administer 35 multiple-choice questions + 3 free-response questions in 90 minutes (realistic exam conditions).

After the mock, review:

• Tally your score (108 points total). See the last-minute review for score boundaries.
• Identify which unit(s) you scored lowest on. Revisit one worked example per weak unit.
• Sleep 8 hours before exam day.

Need help drilling a specific topic?

Browse our AP Physics C: E&M topic library → for deeper explanations, derivations, and additional worked examples.

FRQ practice guide? See the 3 FRQ archetypes → with fully worked solutions.