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

title: "AP Physics C: Electricity and Magnetism Last-Minute Review (Night Before)" description: "The night-before AP Physics C E&M checklist: must-know formulas, Gauss/Ampère/Faraday laws, symmetry tables, transient curves, common traps, and morning-of advice." date: "2026-01-15" examDate: "May AP Exam" topics:

• Formula Sheet
• Theorems & Laws
• Common Traps
• Score Boundaries

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

1. Gauss's law symmetry: You must state which surface (spherical, cylindrical, planar). Rubric demands it.
2. Capacitors in series: They have same charge, different voltage. Use $\frac{1}{C} = \sum \frac{1}{C_i}$. (Not like resistors!)
3. Steady state: In a DC circuit with a capacitor after $t \gg \tau$, the current through the capacitor is $0$, not the voltage across.
4. RC vs RL: $\tau = RC$ (charge decay), $\tau = L/R$ (current decay). Don't mix.
5. 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."
6. 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.
7. 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).
8. Units: Always check units at the end. Volts, Amperes, Tesla, Coulombs, Farad, Henry — if your answer has wrong units, recalculate.
9. 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.
10. 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):

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

FRQ section (45 min for 3 questions):

1. Read all 3 before starting.
2. Start with whichever you're most confident on (build momentum).
3. Always write the law or integral setup, even if you don't complete it. Partial credit is real.
4. State your symmetry choice (Gauss, Ampère).
5. Cite Lenz's law if the question asks for direction.
6. Check units on every numerical answer.
7. 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 →.