AP Physics C: Electricity and Magnetism Last-Minute Review (Night Before)

The exam is tomorrow. This page is 30–45 minutes of skim, not a crash course. Put your notes away after this review. Sleep is more important than reviewing a fourth time.

Essential formulas by unit

Unit 1: Electrostatics

Concept	Formula	Notes
Coulomb's law	$\vec F = k \frac{q_1 q_2}{r^2} \hat r$	$k = 8.99 \times 10^9 \, N \cdot m^2 / C^2$
Electric field	$\vec E = k \frac{q}{r^2}$ (point); $dE = k \frac{dq}{r^2}$ (continuous)	Always set up integral; don't just memorize results
Electric potential	$V = k \frac{q}{r}$ (point); $V = -\int E \, dr$ (from field)	$E = -\frac{dV}{dr}$ (1D derivative relation)
Gauss's law	$\oint \vec E \cdot d\vec A = \frac{Q_{enc}}{\epsilon_0}$	$\epsilon_0 = 8.85 \times 10^{-12} \, C^2 / (N \cdot m^2)$

Gauss's law results (memorize)

Spherical: $E = \frac{kQ}{r^2}$ (outside); $E = \frac{kQr}{R^3}$ (inside sphere of radius $R$ )
Cylindrical: $E = \frac{\lambda}{2\pi\epsilon_0 r}$ (line charge $\lambda$ )
Planar: $E = \frac{\sigma}{2\epsilon_0}$ (sheet with surface density $\sigma$ )

Unit 2: Conductors, Capacitors, Dielectrics

Concept	Formula	Notes
Capacitance	$C = \frac{Q}{V}$ (definition)	Farad = Coulomb/Volt
Parallel-plate	$C = \epsilon_0 \frac{A}{d}$	$\epsilon_0$ inside; dielectric constant $\kappa$ modifies to $C = \kappa \epsilon_0 \frac{A}{d}$
Energy	$U = \frac{1}{2}CV^2 = \frac{1}{2}\frac{Q^2}{C} = \frac{1}{2}QV$	All three forms are equivalent
Series caps	$\frac{1}{C_{tot}} = \frac{1}{C_1} + \frac{1}{C_2} + \ldots$	Opposite of resistors
Parallel caps	$C_{tot} = C_1 + C_2 + \ldots$	Same as resistors
Resistivity	$R = \rho \frac{L}{A}$	Temperature dependence: $R(T) = R_0 [1 + \alpha(T - T_0)]$ (often not tested)

Unit 3: Electric Circuits

Concept	Formula	Notes
Ohm's law	$V = IR$	Voltage drop across resistor
Kirchhoff's junction rule	$\sum I_{in} = \sum I_{out}$	Current conservation
Kirchhoff's loop rule	$\sum V = 0$ (around closed loop)	Include battery EMF, resistive drops, capacitor voltage
RC time constant	$\tau = RC$	Seconds
Charging	$Q(t) = Q_0(1 - e^{-t/\tau})$	Charge grows toward $Q_0 = CV_{battery}$
Discharging	$Q(t) = Q_0 e^{-t/\tau}$	Charge decays to zero
Current (charging)	$I(t) = I_0 e^{-t/\tau}$ where $I_0 = \frac{Q_0}{\tau} = \frac{V_{battery}}{R}$	Starts at $I_0$ , decays
Steady state	$I_{cap} = 0$ (after $t \gg \tau$ )	Capacitor acts as open circuit

Unit 4: Magnetic Fields

Concept	Formula	Notes
Lorentz force	$\vec F = q \vec v \times \vec B$	Perpendicular to both $\vec v$ and $\vec B$ ; direction via right-hand rule
Force on current	$\vec F = I \vec L \times \vec B$	$\vec L$ points in direction of current
Circular motion	$qvB = \frac{mv^2}{r}$ → $r = \frac{mv}{qB}$	Charged particle in perpendicular $B$ field
Biot-Savart	$d\vec B = \frac{\mu_0 I}{4\pi} \frac{d\vec\ell \times \hat r}{r^2}$	Setup; full integration rarely asked
Ampère's law	$\oint \vec B \cdot d\vec\ell = \mu_0 I_{enc}$	$\mu_0 = 4\pi \times 10^{-7} \, T \cdot m / A$

Ampère's law results (memorize)

Infinite wire: $B = \frac{\mu_0 I}{2\pi r}$
Solenoid: $B = \mu_0 n I$ (uniform inside, $n$ = turns/meter)
Toroid: $B(r) = \frac{\mu_0 I N}{2\pi r}$ (varies with $r$ , $N$ = total turns)

Unit 5: Electromagnetic Induction

Concept	Formula	Notes
Magnetic flux	$\Phi_B = \int \vec B \cdot d\vec A = BA\cos\theta$ (uniform $B$ )	Tesla·m²
Faraday's law	$\varepsilon = -\frac{d\Phi_B}{dt}$	Negative sign is Lenz's law. Always cite Lenz for direction.
Motional EMF	$\varepsilon = BLv$	Rod of length $L$ sliding perpendicular to $B$ at velocity $v$
Induced current	$I = \frac{\\|\varepsilon\\|}{R}$	Use magnitude; direction from Lenz's law
Inductor	$\varepsilon = -L \frac{dI}{dt}$	$L$ in Henries (H)
Inductor energy	$U = \frac{1}{2}LI^2$	Magnetic energy stored
RL time constant	$\tau = \frac{L}{R}$	Different from RC ( $\tau = RC$ for RC)
RL charging	$I(t) = I_0(1 - e^{-t/\tau})$	Current grows toward $I_0 = \mathcal{E}/R$
RL discharging	$I(t) = I_0 e^{-t/\tau}$	Current decays to zero

Theorems & laws (memorize the wording for FRQs)

Law	Statement	When it applies
Gauss's law for $E$	$\oint \vec E \cdot d\vec A = \frac{Q_{enc}}{\epsilon_0}$	Always true; use when charge symmetry allows simplification
Lenz's law	Induced current opposes the change in magnetic flux	Part of Faraday's law; always cite when asked for current direction
Ampère's law	$\oint \vec B \cdot d\vec\ell = \mu_0 I_{enc}$	Use for symmetric current distributions (wire, solenoid, toroid)

Symmetry summary for Gauss's law & Ampère's law

You must state which symmetry you're using. The rubric wants to see: "By spherical symmetry, the electric field is radial and constant on a sphere of radius $r$ ."

Symmetry	Gaussian/Amperian shape	Why it works	When to use
Spherical	Sphere	Charge/current at center; all directions equivalent	Point charge, uniformly charged sphere, center of symmetric sphere
Cylindrical	Cylinder (axis aligned with wire/field direction)	Charge/current along infinite line; direction and distance from axis matter	Infinite wire, uniformly charged cylinder, coaxial cable
Planar	Pillbox (two parallel faces perpendicular to plane)	Infinite sheet of charge; field perpendicular to sheet on both sides	Infinite sheet, parallel-plate capacitor

RC & RL transient curves (skim these tonight)

RC charging: $Q(t) = Q_0(1 - e^{-t/\tau})$ , $I(t) = I_0 e^{-t/\tau}$

$Q$ starts at 0, approaches $Q_0$ asymptotically.
$I$ starts at $I_0 = V/R$ , decays to 0.
After $t = 5\tau$ , capacitor is >99% charged.

RC discharging: $Q(t) = Q_0 e^{-t/\tau}$ , $I(t) = -I_0 e^{-t/\tau}$

$Q$ starts at $Q_0$ , approaches 0.
$I$ starts at $-I_0$ (reverse direction), approaches 0.

RL charging: $I(t) = I_0(1 - e^{-t/\tau})$ , $\tau = L/R$

$I$ starts at 0, approaches $I_0 = \mathcal{E}/R$ .
Voltage across inductor: $V_L = -L\frac{dI}{dt}$ , large at $t=0$ , approaches 0.

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

$I$ starts at $I_0$ , decays to 0.
Inductor opposes sudden current change; releases energy.

Top 10 exam traps

Gauss's law symmetry: You must state which surface (spherical, cylindrical, planar). Rubric demands it.
Capacitors in series: They have same charge, different voltage. Use $\frac{1}{C} = \sum \frac{1}{C_i}$ . (Not like resistors!)
Steady state: In a DC circuit with a capacitor after $t \gg \tau$ , the current through the capacitor is $0$ , not the voltage across.
RC vs RL: $\tau = RC$ (charge decay), $\tau = L/R$ (current decay). Don't mix.
Lenz's law direction: The negative sign in $\varepsilon = -\frac{d\Phi_B}{dt}$ is Lenz. Always cite: "By Lenz's law, the induced current is [clockwise/counterclockwise] to oppose the [increasing/decreasing] flux."
Right-hand rule: For Lorentz force $\vec F = q\vec v \times \vec B$ : fingers point from $\vec v$ to $\vec B$ , thumb points in direction of $\vec F$ (for positive $q$ ). For negative charge, reverse.
Ampère's law for non-symmetric geometries: Don't use Ampère's law if $B$ varies over your loop. Use Biot-Savart instead (or just accept you can't solve it easily).
Units: Always check units at the end. Volts, Amperes, Tesla, Coulombs, Farad, Henry — if your answer has wrong units, recalculate.
Charge on parallel plates: On a parallel-plate capacitor, the charge distributes only on the inner surfaces (those facing each other), not the outer surfaces. If a question asks for $E$ between plates, use $E = \frac{\sigma}{\epsilon_0}$ where $\sigma$ is that surface charge density.
Forgetting negative on Faraday: $\varepsilon = -\frac{d\Phi_B}{dt}$ , not $+\frac{d\Phi_B}{dt}$ . The minus sign is critical for phase and direction.

Score boundaries (recent years)

Out of 108 total points (35 MCQ at ~1.5 pts each + 3 FRQs at 15 pts each):

Score	Range	Comment
5	~75–108	You can get ~70% and still earn a 5.
4	~60–74	Solid understanding of 3–4 units.
3	~45–59	Concepts clear; execution inconsistent.
2	~30–44	Some unit mastery; major gaps elsewhere.
1	<30	Minimal understanding.

Key insight: You do not need a perfect score. If you can reliably solve 1 full Gauss's law FRQ, 1 circuit FRQ, and 1 Faraday FRQ (that's ~45 pts), plus 20–25 MCQs, you're at a 3 or 4 already.

Morning-of checklist

☐ 8 hours of sleep (not optional; REM sleep consolidates the right-hand-rule).
☐ Breakfast with protein + slow carbs (eggs & oatmeal, not just sugar).
☐ 2 sharpened #2 pencils + blue/black pens.
☐ Approved calculator + spare batteries (seriously, test them).
☐ Photo ID + AP ID label sheet.
☐ Water bottle, light snack for the break.
☐ Watch (if the exam room doesn't have a visible clock).
☐ Arrive 20–30 minutes early to settle nerves.

During the exam

MCQ section (55 min for 35 questions):

Read each question fully. Underline numbers and what you're solving for.
If it takes >90 sec, mark and skip. You have time to come back.
Cross out obviously wrong answers. Process of elimination is your friend.
For calculator section: use nDeriv() for derivatives, fnInt() for integrals, and graph + intersect for complex equations.

FRQ section (45 min for 3 questions):

Read all 3 before starting.
Start with whichever you're most confident on (build momentum).
Always write the law or integral setup, even if you don't complete it. Partial credit is real.
State your symmetry choice (Gauss, Ampère).
Cite Lenz's law if the question asks for direction.
Check units on every numerical answer.
If you finish a part, move on. Don't redo algebra. The rubric will see your work.

One final thought

You've prepared. You know Gauss's law. You know Lenz's law. You can set up an integral. The exam is just the same stuff, repeated three times (MCQ + 3 FRQs).

Show up rested, breathe between sections, and trust your preparation.

You've got this. 🎯

Need one more drill? Browse the 7-day study plan → or revisit the FRQ practice guide →.