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A calculus-based resource for one of the College Board’s most difficult tests is the AP Physics C: Electricity & Magnetism formula sheet. It includes induction formulas, vector calculus, line and surface integrals, and Maxwell’s equations, all of which call for an understanding of when and how to use them correctly.
Only about 30% of American students receive a 4 or 5, so mastering the formula sheet – particularly Gauss’s Law, Ampère’s Law, and Faraday’s Law – is what sets top scorers apart and enables students to receive engineering credit at prestigious STEM programs.
| Resource Type | Description | Access |
| Official College Board E&M Formula Sheet (2026) | The precise formula sheet that was given on test day is crucial for preparation. | View Online |
| Annotated E&M Formula Sheet | Additional calculus applications and variable definitions on the official sheet | Download Guide |
| Maxwell’s Equations Reference | An explanation of the integral and differential forms of all four Maxwell equations | Download Guide |
| Vector Calculus Formula Guide | For physics, line integrals, surface integrals, gradient, divergence, and curl | Download Guide |
| Gauss’s Law Applications Chart | When and how to apply symmetry conditions to Gauss’s Law | Download Chart |
| Electromagnetic Induction Formulas | Applications of inductance formulas, Lenz’s Law, and Faraday’s Law | Download Guide |
| Formula Navigation Practice | Timed exercises to find formulas fast during the test | Practice Now |
The College Board formula sheet for E&M is extensive and requires deep understanding of vector calculus and electromagnetic theory:
Complete Formula Sheet Organization
| Section | What’s Included | Calculus Elements | Critical Formulas |
| Electrostatics | Potential, capacitance, Gauss’s Law, electric field, and Coulomb’s Law | ∮E·dA, ∫kdq/r², V = -∫E·dl | ∮E·dA = Q_enc/ε₀, E = -∇V |
| Conductors & Capacitors | Dielectrics, capacitance, and energy storage | Energy density formulas | C = Q/V, U = ½CV² |
| DC Circuits | Kirchhoff’s rules, Ohm’s Law, and RC circuits | Exponential functions: Q(t) = Q₀e^(-t/RC) | V = IR, τ = RC |
| Magnetic Fields | Ampère’s Law, Biot-Savart Law, and force | ∮B·dl, vector cross products | ∮B·dl = μ₀I_enc, F = qv × B |
| Electromagnetic Induction | RL circuits, inductance, Lenz’s Law, and Faraday’s Law | Time derivatives: ε = -dΦ_B/dt | Φ_B = ∫B·dA, ε = -L(dI/dt) |
| Maxwell’s Equations | Each of the four in differential and integral forms | ∇·E, ∇·B, ∇×E, ∇×B | Complete set of electromagnetic laws |
| Physical Constants | k, e, c, electron/proton mass, ε₀, and μ¹ | Numerical values | Exact values for calculations |
In addition to the cheat sheet, students have access to:
| Formula Sheet for AP Physics 2 PDF | Practice FRQs and MCQs. |
| Worksheets according to topics | Comprehensive practice exams |
| Concept | Formula | Calculus Form | When to Use |
| Coulomb’s Law | F = kq₁q₂/r² | Algebra | The force that exists between point charges |
| Electric field (point) | E = kq/r² | Algebra | field caused by a single point charge |
| Electric field (continuous) | E = ∫kdq/r² | Integral over charge distribution | Any distribution of charges |
| Gauss’s Law | ∮E·dA = Q_enc/ε₀ | Surface integral | Only with symmetry that is spherical, cylindrical, or planar |
| Electric potential | V = kq/r (point), V = -∫E·dl | Line integral | Possibilities in the field |
| Field from potential | E = -∇V = -dV/dx (1D) | Gradient (derivative) | Potential function field |
| Potential energy | U = kq₁q₂/r | Algebra | Configuration of energy of charge |
Critical Understanding:
Gauss’s Law (∮E·dA = Q_enc/ε₀) is only applicable when symmetry permits E to remain constant across a Gaussian surface. For all other cases, use direct integration (E = Ψkdq/r²).
| Concept | Formula | Application |
| Capacitance (definition) | C = Q / V | Any kind of capacitor |
| Parallel plate capacitor | C = ε₀A / d | uniform electric field and flat plates |
| Capacitor with dielectric | C = κC₀ | The presence of the dielectric constant κ |
| Energy stored in capacitor | U = ½QV = ½CV² = Q² / (2C) | The electric field’s stored energy |
| Energy density | u = ½ε₀E² | In an electric field, energy per unit volume |
| Capacitors in series | 1 / C_eq = 1 / C₁ + 1 / C₂ + … | Comparable to parallel resistors |
| Capacitors in parallel | C_eq = C₁ + C₂ + … | Comparable to resistors connected in series |
| Circuit Element | Formula | Calculus Application |
| Ohm’s Law | V = IR | Fundamental relationship |
| Power | P = IV = I²R = V²/R | Energy dissipation rate |
| Kirchhoff’s Loop Rule | ΣV = 0 (around loop) | Conservation of energy |
| Kirchhoff’s Junction Rule | ΣI_in = ΣI_out | Conservation of charge |
| Resistors in series | R_eq = R₁ + R₂ + … | Additive |
| Resistors in parallel | 1/R_eq = 1/R₁ + 1/R₂ + … | Reciprocals add |
| RC charging | Q(t) = Q_max(1 – e^(-t/RC)) | Exponential growth to Q_max |
| RC discharging | Q(t) = Q₀e^(-t/RC) | Exponential decay |
| Time constant | τ = RC | Time to reach 63% (charging) or 37% (discharging) |
Critical RC Circuit Understanding:
Kirchhoff’s Loop Rule and Q = CV are used to derive the differential equation dQ/dt = (ε – Q/C)/R, which has exponential solutions.
| Concept | Formula | Calculus Required | Application |
| Magnetic force (charge) | F = qv × B | Cross-product of vectors | Moving charge in B-field |
| Magnetic force (current) | F = IL × B | Cross-product of vectors | Current-carrying wire |
| Biot-Savart Law | dB = (μ₀/4π)(Idl × r̂)/r² | Line integral: B = ΨdB | Magnetic field from any current |
| Ampère’s Law | ∮B·dl = μ₀I_enc | Line integral | Only with high symmetry |
| Magnetic flux | Φ_B = ∫B·dA | Surface integral | Flux through surface |
| Lorentz force | F = q(E + v × B) | Electric and magnetic combined | |
| Cyclotron frequency | f = qB/(2πm) | Circular motion of charged particles. |
Critical Understanding:
Ampère’s Law (∮B·dl = μ₀I_enc) only applies to high symmetry, such as toroids, solenoids, and infinite straight wires. Use Biot-Savart Law otherwise.
Master Physics C Formula Sheet
| Concept | Formula | Calculus Required | Critical Notes |
| Faraday’s Law | ε = -dΦ_B/dt = -d(∫B·dA)/dt | Time derivative + surface integral | Lenz’s Law is represented by a negative sign. |
| Motional EMF | ε = Blv | Algebra (special case) | A conducting rod traveling in a magnetic field |
| Lenz’s Law | Induced effects oppose change | Conceptual | Determines the induced current’s direction |
| Self-inductance | ε = -L(dI/dt) | Time derivative | Inductor resists current change |
| Inductance (definition) | L = Φ_B / I | No (definition) | Connects current and magnetic flux |
| Solenoid inductance | L = μ₀n²Aℓ | No (geometry-based) | A is the cross-sectional area and n is the number of turns per length. |
| Energy in inductor | U = ½LI² | Algebra | Inductor-stored magnetic energy |
| RL charging current | I(t) = (ε/R)(1 – e^(-Rt/L)) | Exponential solution | Current rises in the direction of the steady-state value |
| RL time constant | τ = L / R | Algebra | It takes about 63% of the maximum current to reach |
Most Frequently Tested:
Faraday’s Law (ε = -dΦ_B/dt) appears on almost every E&M exam. You must:
| Mistake | Why It Costs Points | How to Fix It |
| Using Gauss’s Law without symmetry | Can’t pull E outside ∮E·dA integral | Use only spheres, cylinders, and infinite planes. |
| Confusing ε₀ and μ₀ | Using electric constant for magnetic formula | Magnetic uses μ₀, while electric (E-field, capacitance) uses ε₀. |
| Forgetting negative sign in Faraday’s Law | ε = dΦ_B/dt instead of ε = -dΦ_B/dt | Lenz’s Law necessitates a negative—always verify |
| Wrong cross product | Using · instead of × for F = qv × B | The cross product (×) is always used for magnetic force. |
| Not recognizing when Ampère’s Law applies | Trying for complex geometries | Works only with toroid, solenoid, and infinite wire. |
| Mixing up RC and RL time constants | Using RC when should use L/R | Circuits for capacitors: τ = RC; circuits for inductors: τ = L/R |
| Wrong Maxwell equation | Using ∮E·dA when should use ∮B·dA | Magnetic Gauss: ∮B·dA = 0; Electric Gauss: ∮E·dA = Q/ε₀ |
| Searching without understanding problem | Randomly trying formulas | Determine the physics concept first, then the formula |
1. Do I get a formula sheet on the AP Physics C E&M exam?
Yes.For both Section I (MCQ) and Section II (FRQ), the College Board offers an official formula sheet. The full 90-minute exam is available to you.
2. Is the E&M formula sheet different from the Mechanics formula sheet?
Yes, quite different. Maxwell’s equations, Gauss’s Law, Ampère’s Law, Faraday’s Law, and electromagnetic constants (ε₀, μ₀) that are absent from Mechanics are all included in E&M.
3. Are Maxwell’s equations on the formula sheet?
Yes. Both integral form (∮E·dA, ∮B·dl, etc.) and differential form (∮E, ㈽B, etc.) are given for each of the four Maxwell equations.
4. What vector calculus is NOT on the formula sheet?
Calculating line integrals (∮F·dl), surface integrals (∮F·dA), cross products (A × B), gradient (∮V), divergence (∮F), and curl (∬×F). You have to be familiar with these methods on your own.
5. When should I use Gauss’s Law from the formula sheet?
Gauss’s Law (∮E·dA = Q_enc/ε₀) should only be applied in cases of high symmetry, such as spherical, cylindrical (infinite), or infinite planar charge distributions. If not, use E = Ψkdq/r.”
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