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An essential calculus-based resource for one of the College Board’s most challenging tests is the AP Physics C: Electricity & Magnetism equation sheet. In contrast to AP Physics 2, Physics C E&M uses Maxwell’s equations, vector calculus, and line and surface integrals to solve problems involving electrostatics, circuits, magnetism, and induction.
Only 30% of American students receive a 4 or 5, so mastering the equation sheet and knowing when to apply Gauss’s Law, Ampère’s Law, and Faraday’s Law is what sets top scorers apart. This helps students stand out at prestigious STEM programs and earn engineering credit.
| Resource Type | Description | Access |
| Official College Board E&M Equation Sheet (2026) | The precise equation sheet that was given on test day is crucial for preparation. | View Online |
| Annotated E&M Equation Sheet | An official sheet that includes additional calculus applications and the appropriate times to use each formula | Download Guide |
| Maxwell’s Equations Explained | Detailed explanation of each of the four Maxwell equations using calculus derivations | Download Guide |
| Vector Calculus Reference for E&M | Physics’s line integrals, surface integrals, divergence, and curl | Download Guide |
| Gauss’s Law Applications Guide | When and how to apply Gauss’s Law to electric fields | Download Guide |
| Ampère’s Law & Faraday’s Law Guide | Calculating magnetic fields and electromagnetic induction | Download Guide |
| Color-Coded E&M Equation Sheet | Topic-specific visual arrangement (electrostatics, circuits, magnetism, induction) | Download Sheet |
| Equation Navigation Practice | Timed exercises to help you find formulas fast during an exam. | Practice Now |
The College Board equation sheet for E&M is extensive and requires deep understanding of vector calculus:
Complete Equation Sheet Breakdown
| Category | What’s Included | Calculus Elements |
| Electrostatics | Electric potential, capacitance, Gauss’s Law, Coulomb’s Law, and electric field | Surface integrals: Φ = ∮E·dA, line integrals: V = -∫E·dl |
| Conductors & Capacitors | Dielectrics, energy storage, and capacitance formulas | C = Q/V, U = ½CV², energy density |
| Electric Circuits | Kirchhoff’s rules, Ohm’s Law, RC circuits, and power | Exponential functions for RC: Q(t) = Q₀(1-e^(-t/RC)) |
| Magnetic Fields | Magnetic force, Ampère’s Law, and Biot-Savart Law | Line integrals: ∮B·dl = μ₀I_enc, cross products |
| Electromagnetic Induction | RL circuits, inductance, Lenz’s Law, and Faraday’s Law | Time derivatives: ε = -dΦ_B/dt, Φ_B = ∫B·dA |
| Maxwell’s Equations | Each of the four integral and differential equations | Divergence and curl operators |
| Physical Constants | Electron/proton mass, elementary charge (e), k, ε₀, and μ₀ | Exact values provided |
In addition to the cheat sheet, students have access to:
| Formula Sheet PDF | Practice FRQs and MCQs. |
| Worksheets according to topics | Comprehensive practice exams |
Electrostatics: Electric Fields and Gauss’s Law
| Concept | Equation | Calculus Required | When to Use |
| Coulomb’s Law | F = kq₁q₂/r² | No (algebra) | The force that exists between point charges |
| Electric field (point charge) | E = kq/r² | No (algebra) | field caused by a single point charge |
| Electric field (general) | E = kq/r² (discrete), E = ∫kdq/r² (continuous) | Yes – integral over charge distribution | Constant charge distributions |
| Gauss’s Law | Φ = ∮E·dA = Q_enc/ε₀ | Yes – surface integral | High symmetry (planar, cylindrical, and spherical) |
| Electric potential | V = kq/r (point charge), V = -∫E·dl | Yes – line integral | Identifying potential in the field |
| Potential from charge | V = ∫kdq/r | Yes – integral over distribution | Constant charge distributions |
| Electric field from potential | E = -∇V = -dV/dx (1D) | Yes – gradient (derivative) | Using the potential function to find the field |
Critical Understanding: Gauss’s Law
Selecting a Gaussian surface and calculating the surface integral are necessary for Gauss’s Law ∮E·dA = Q_enc/ε². Only when symmetry permits E to remain constant across the surface is it useful.
Capacitance and Electric Energy
| Concept | Equation | Calculus Application |
| Capacitance | C = Q/V | Algebra (definition) |
| Parallel plate capacitor | C = ε₀A/d | Algebra |
| Energy stored | U = ½QV = ½CV² = Q²/(2C) | Algebra |
| Energy density | u = ½ε₀E² | Algebra |
| Dielectric constant | C = κC₀ | Algebra |
Electric Circuits with Calculus
| Circuit Element | Key Equations | Calculus Form |
| Ohm’s Law | V = IR | Algebra |
| Power | P = IV = I²R = V²/R | Algebra |
| Kirchhoff’s Loop Rule | ΣV = 0 | Algebra |
| Kirchhoff’s Junction Rule | ΣI_in = ΣI_out | Algebra |
| RC circuits (charging) | Q(t) = Q₀(1 – e^(-t/RC)) | Solving differential equation |
| RC circuits (discharging) | Q(t) = Q₀e^(-t/RC) | Exponential decay |
| Time constant | τ = RC | Algebra |
Critical RC Circuit Understanding:
You get Q(t) = Q₀(1 – e^(-t/RC)) from dQ/dt = I and V = Q/C – IR. FRQs may require you to set up the differential equation, but the equation sheet offers the solution.
| Concept | Equation | Calculus Required | Application |
| Magnetic force on charge | F = qv × B | Vector cross product | Charges moving in B-field |
| Magnetic force on current | F = IL × B | Vector cross product | Wires that carry current |
| Biot-Savart Law | dB = (μ₀/4π)(I dl × r̂)/r² | Line integral: B = ∫dB | Current-induced magnetic field |
| Ampère’s Law | ∮B·dl = μ₀I_enc | Line integral | High symmetry (toroid, solenoid, long wire) |
| Magnetic flux | Φ_B = ∫B·dA | Surface integral | via a surface |
| Gauss’s Law (magnetism) | ∮B·dA = 0 | Surface integral | Absence of magnetic monopoles |
Critical Understanding: Ampère’s Law
Selecting an Amperian loop and calculating the line integral are necessary to apply Ampère’s Law ∮B·dl = μ•I_enc. Useful only if B can be tangent to the loop due to symmetry
| Concept | Equation | Calculus Required | Application |
| Faraday’s Law | ε = -dΦ_B/dt = -d/dt(∫B·dA) | Time derivative, surface integral | EMF produced by fluctuating magnetic flux |
| Motional EMF | ε = Blv | Algebra (special case) | A conducting rod traveling in a magnetic field |
| Lenz’s Law | Direction opposes flux change | Conceptual | Identifying the induced current’s direction |
| Inductance | ε = -L(dI/dt) | Time derivative | RL circuits and self-induction |
| RL Circuits | I(t) = (ε/R)(1 – e^(-Rt/L)) | Differential equation solution | An inductor’s current growth |
| Energy in Inductor | U = ½LI² | Algebra | Storage of magnetic energy |
Most Frequently Tested:
Nearly all E&M exams include Faraday’s Law ε = -dΦ_B/dt. You need to know how to take the time derivative and compute Φ_B = ΨB·dA.
| Constant | Symbol | Value | Units | Primary Use |
| Permittivity of free space | ε₀ | 8.85 × 10⁻¹² | C²/(N·m²) | Gauss’s Law, capacitance, and electric field |
| Permeability of free space | μ₀ | 4π × 10⁻⁷ | T·m/A | Inductance, Ampère’s Law, and magnetic field |
| Coulomb’s constant | k = 1/(4πε₀) | 9.0 × 10⁹ | N·m²/C² | Electric potential and Coulomb’s Law |
| Speed of light | c = 1/√(μ₀ε₀) | 3.0 × 10⁸ | m/s | Waves of electricity |
| Elementary charge | e | 1.60 × 10⁻¹⁹ | C | Electron/proton charge |
| Electron mass | mₑ | 9.11 × 10⁻³¹ | kg | Motion of particles in electric and magnetic fields |
| Proton mass | mₚ | 1.67 × 10⁻²⁷ | kg | Motion of particles in electric and magnetic fields |
Master Physics C Formula Sheet
| Mistake | Why It Costs Points | How to Fix It |
| Not knowing when to apply Gauss’s Law | Applying Gauss’s Law to low-symmetry issues | Use only for symmetry that is spherical, cylindrical, or planar. |
| Inappropriate surface for Gauss’s Law | Making a poor Gaussian surface selection | E must be constant and perpendicular to the surface. |
| Faraday’s Law’s missing negative sign | Instead of ε = -dΦ_B/dt, use ε = dΦ_B/dt. | Lenz’s Law demands a negative sign; direction is important. |
| Mixed up electric and magnetic The Laws of Gauss | Using the incorrect formula | ∮B·dA = 0 always; ∮E·dA uses ε₀ |
| Not being able to determine when Ampère’s Law applies | Aiming for intricate current distributions | only functions with high symmetry (toroid, solenoid, infinite wire). |
| Ignoring μ₀ versus ε₀ | Using the incorrect constant | Magnetic uses μ₀, while electric uses ε₀ or k. |
| Incorrect cross-product orientation | Incorrect force direction | Practice the right-hand rule a lot. |
| Inaccurately calculating flux | Errors in B·dA | Recall that flux = B × Area, or correctly integr |
| Confusion between I and dI/dt | Using the incorrect formula for inductance | Instead of ε = -LI, ε = -L(dI/dt). |
1. Do I get an equation 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 equation sheet. The full 90-minute exam is available to you.
2. Is the E&M equation sheet different from the Mechanics equation sheet?
Yes,entirely distinct tests with distinct equation sheets. Maxwell’s equations, Gauss’s Law, Ampère’s Law, and Faraday’s Law are all part of E&M and are not mentioned on the Mechanics sheet.
3. Are Maxwell’s equations provided on the equation sheet?
Yes.There are integral and differential versions of each of the four Maxwell equations. But you need to understand when and how to use them.
4. What vector calculus is NOT on the equation sheet?
How to calculate surface integrals (F·dA), line integrals (F·dl), cross products (A × B), divergence (F), and curl (F). These methods need to be acquired on one’s own.
5. When should I use Gauss’s Law vs. direct integration?
Use Gauss’s Law (∮E·dA = Q_enc/ε₀) only in spherical, cylindrical, or planar structures with high symmetry. If not, apply direct integration: E = Ψkdq/r.”
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