AP Physics C: E&M · Reference

AP Physics C Electricity and Magnetism equation sheet every formula, grouped by topic.

Here is the full AP Physics C Electricity and Magnetism equation sheet, also called the formula sheet, organized by topic from electrostatics through induction. The College Board provides this calculus-based reference on exam day, so the goal is knowing which relationship a problem needs — and which integral to set up — not memorizing the list.

Updated June 2026Part of AP Physics C: E&M Review

Is the equation sheet provided on the AP Physics C E&M exam?

Yes. The official equation sheet is provided for both the multiple-choice and free-response sections, and a calculator is allowed throughout. Because this is the calculus-based course, the sheet gives you the relationships but assumes you can evaluate the derivatives and integrals yourself — it will not tell you how to exploit symmetry in a Gauss’s law problem or how to set up a Biot–Savart integral.

That is where the points actually live. The version below is grouped the way the course is taught, so each equation connects to the unit it belongs to.

The AP Physics C E&M equation sheet, by topic

Every relationship you are handed on test day, with a plain-language note on when to use it.

Electrostatics: force, field & Gauss’s law

F = (1/4πε₀) · (q₁q₂ / r²)

Coulomb’s law — the force between two point charges.

E = F / q

The electric field as force per unit charge.

Φ_E = ∫ E · dA

Electric flux through a surface.

∮ E · dA = Q_enc / ε₀

Gauss’s law — pick a symmetric surface and the integral collapses.

E = − dV/dr

The field is the negative gradient of the potential.

Electric potential & energy

V = (1/4πε₀) · Σ (q_i / r_i)

Potential from a set of point charges — a scalar sum, so no vectors.

U_E = qV = (1/4πε₀) · (q₁q₂ / r)

Electric potential energy of a pair of charges.

ΔV = − ∫ E · dr

Potential difference from the field along a path.

Conductors & capacitors

C = Q / V

The definition of capacitance.

C = κε₀A / d

Parallel-plate capacitor, with dielectric constant κ.

U_C = ½QV = ½CV²

Energy stored in a capacitor.

Series: 1/C_s = Σ 1/C_i · Parallel: C_p = Σ C_i

Note this is the reverse of the resistor rules.

Electric circuits

I = dQ / dt

Current as the rate of charge flow.

R = ρℓ / A

Resistance from resistivity and geometry.

V = IR · P = IV

Ohm’s law and electrical power.

Series: R_s = Σ R_i · Parallel: 1/R_p = Σ 1/R_i

Combining resistors.

RC circuits: τ = RC

The charging and discharging time constant.

Magnetic fields

F = qv × B

Magnetic force on a moving charge — use the right-hand rule.

F = ∫ I dℓ × B

Force on a current-carrying wire.

B = μ₀I / (2πr)

Field around a long straight wire.

dB = (μ₀/4π) · (I dℓ × r̂) / r²

The Biot–Savart law, for fields from arbitrary current shapes.

∮ B · dℓ = μ₀I_enc

Ampère’s law — the magnetic counterpart of Gauss’s law.

Electromagnetic induction

Φ_B = ∫ B · dA

Magnetic flux through a loop.

ε = − dΦ_B / dt

Faraday’s law — the minus sign is Lenz’s law.

ε = − L (dI/dt)

The induced emf across an inductor.

U_L = ½LI²

Energy stored in an inductor.

RL circuits: τ = L / R

The time constant for current growth and decay.

Constants provided on the sheet

ε₀ = 8.85 × 10⁻¹² C²/(N·m²)

The permittivity of free space.

1/4πε₀ = 9.0 × 10⁹ N·m²/C²

Coulomb’s constant, k.

μ₀ = 4π × 10⁻⁷ (T·m)/A

The permeability of free space.

e = 1.60 × 10⁻¹⁹ C

The elementary charge.

How the E&M and Mechanics sheets differ

They share a format and both are calculus-based, but they cover different physics: the Mechanics sheet is built on forces, energy, momentum, and rotation, while this one is built on fields, potential, circuits, and induction. The E&M sheet also leans harder on line and surface integrals, since Gauss’s law, Ampère’s law, and Faraday’s law are all integral statements. If you are sitting both exams, our Mechanics formula sheet covers the companion reference.

How to use the equation sheet

Treat the sheet as a map, not a crutch. In your studying, practice naming which relationship and which calculus operation a problem calls for, because that judgment is exactly what the exam tests. With Gauss’s and Ampère’s laws in particular, the skill is choosing a surface or loop where the symmetry makes the integral simple — the sheet cannot do that for you.

Knowing the layout also saves time under pressure. For the full picture of the format, units, and a study plan, use our AP Physics C: E&M review guide, and the score calculator turns a practice raw score into a 1–5.

Frequently asked questions

Quick answers — written by humans, not a chatbot.

Is the AP Physics C E&M equation sheet provided on the exam?

Yes — the official equation sheet is available for both sections, along with a calculator, so you do not need to memorize the formulas.

Is the AP Physics C E&M equation sheet calculus-based?

Yes. It includes integral relationships like Gauss’s law, Ampère’s law, and Faraday’s law, and it assumes you can evaluate the derivatives and integrals yourself.

What is the difference between the AP Physics C E&M and Mechanics equation sheets?

Both are calculus-based, but E&M covers fields, potential, capacitors, circuits, and induction, while Mechanics covers forces, energy, momentum, rotation, and oscillations.

Do I need to memorize formulas for AP Physics C E&M?

No — they are provided. You do need to know which relationship applies and how to set up the right integral, especially for Gauss’s and Ampère’s laws.

Can I use the equation sheet on the free-response section?

Yes. The same equation sheet and a calculator are available for both the multiple-choice and free-response sections.

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Mechanics Formula Sheet

The other Physics C equation sheet.