AP Physics C: Electricity And Magnetism Formula Sheet| Complete Guide For U.S. Students
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January 29, 2026
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AP Physics C: Electricity and Magnetism Formula Sheet| Complete Guide for U.S. Students.
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.
AP Physics C E&M Formula Sheet Resources for U.S. Students
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.
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).
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.
Magnetism: Magnetic Fields with Vector Calculus
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.
Electromagnetic Induction: Faraday’s Law and Inductance
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:
Calculate flux: Φ_B = ∫B·dA
Take time derivative: dΦ_B/dt
Include negative sign (Lenz’s Law)
Common E&M Formula Sheet Mistakes
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
Frequently Asked Questions – AP Physics C E&M Formula Sheet
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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