AP Physics C Electricity and Magnetism equation sheet: every formula, grouped by topic.
College Board hands you this reference on exam day — it now calls it the Exam Reference Information — so the exam is not testing whether you memorised it. It is testing whether you know which relationship a problem needs, and which integral to set up. Every formula below is grouped the way the course is taught.
Is the equation sheet provided on the AP Physics C E&M exam?
Yes. The official sheet is provided for both the multiple-choice and free-response sections, and a calculator is allowed throughout. It appears in Bluebook, the digital exam app, and you can open it during the test preview before exam day — so there is no reason to meet it for the first time under time pressure.
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 AP Physics C Electricity and Magnetism equation sheet, by topic
Every relationship you are handed on test day, with a plain-language note on when to use it. The six groups follow the Course and Exam Description unit order.
Electrostatics: force, field & Gauss’s law
| Equation | When you use it |
|---|---|
| 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. |
| ΦE = ∫ E · dA | Electric flux through a surface. |
| ∮ E · dA = Qenc / 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
| Equation | When you use it |
|---|---|
| V = (1/4πε0) · Σ (qi / ri) | Potential from a set of point charges — a scalar sum, so no vectors. |
| UE = 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
| Equation | When you use it |
|---|---|
| C = Q / V | The definition of capacitance. |
| C = κε0A / d | Parallel-plate capacitor, with dielectric constant κ. |
| UC = ½QV = ½CV2 | Energy stored in a capacitor. |
| Series: 1/Cs = Σ 1/Ci · Parallel: Cp = Σ Ci | Note this is the reverse of the resistor rules. |
Electric circuits
| Equation | When you use it |
|---|---|
| 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: Rs = Σ Ri · Parallel: 1/Rp = Σ 1/Ri | Combining resistors. |
| RC circuits: τ = RC | The charging and discharging time constant. |
Magnetic fields
| Equation | When you use it |
|---|---|
| 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 = μ0Ienc | Ampère’s law — the magnetic counterpart of Gauss’s law. |
Electromagnetic induction
| Equation | When you use it |
|---|---|
| ΦB = ∫ B · dA | Magnetic flux through a loop. |
| ε = − dΦB / dt | Faraday’s law — the minus sign is Lenz’s law. |
| ε = − L (dI/dt) | The induced emf across an inductor. |
| UL = ½LI2 | Energy stored in an inductor. |
| RL circuits: τ = L / R | The time constant for current growth and decay. |
Constants provided on the sheet
| Constant | What it is |
|---|---|
| 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
These used to be one document. College Board now publishes a separate Exam Reference Information sheet for each Physics C exam, so revise from the E&M one — guides that tell you the two sheets are identical are out of date.
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. E&M also leans harder on integration: Gauss’s law is a surface integral, Ampère’s law is a line integral, and Faraday’s law is a derivative of one. If you are sitting both exams, our Mechanics formula sheet is the companion to this one.
How to use the equation sheet
Treat the sheet as a map, not a crutch. When you practise, name the relationship and the calculus operation each 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. A handful are worth knowing cold so you are not hunting for them: Gauss’s law, Faraday’s law, and the two time constants, τ = RC and τ = L/R. That is about speed, not memorisation — they are all still printed for you.
The full AP Physics C: E&M exam guide covers format, timing and a study plan. When a timed practice attempt gives you a raw score, the E&M score calculator turns it into a 1–5.
Frequently asked questions
Quick answers to the questions students actually ask.
Is the AP Physics C E&M equation sheet provided on the exam?
Yes — the official sheet is available for both sections in Bluebook, along with a calculator, so you do not need to memorize the formulas. You can also open it in the test preview before exam day.
Is the AP Physics C E&M equation sheet calculus-based?
Yes. It includes integral relationships like Gauss’s law and Ampère’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?
They are now two separate documents. 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.