AP Physics C E&M Formula Sheet 2027
A reference-first Electricity & Magnetism equation system covering electrostatics through LC circuits, with exam-reference relationships separated from derived models and special cases.
What is actually given—and what you still have to know?
The exam supplies reference information, so this resource is organized around a more useful distinction than “memorize everything.” Exam reference marks relationships present in the current course reference information. Derived / course marks relationships, special cases, or model extensions that are useful for the course but are not being treated here as printed equation entries.
Before substitution, identify the system or source, representation/geometry, governing law, assumptions, sign convention, and limiting behavior. On Physics C problems, the missing step is often deciding what to differentiate or integrate—not recalling the final algebraic form.
E&M equation-selection map
Source → field
Identify charge/current geometry. Use superposition generally; use Gauss or Ampère as calculation tools only when symmetry is strong enough.
Field → potential
Potential is scalar, field is vector, and ΔV=−∫E⃗·dℓ⃗ controls the sign relationship.
Boundary → capacitance
For conductors/capacitors, establish electrostatic boundary conditions and geometry before choosing a capacitance result.
Circuits need topology
Series/parallel reduction, Kirchhoff rules, and RC/LR/LC differential models solve different structures and time regimes.
Flux needs orientation
Electric/magnetic flux depend on an area vector; induction also requires the sign logic of Lenz’s law.
Magnetic force is directional
Cross products determine direction. Magnetic force on a point charge is perpendicular to velocity and therefore does no work.
More than an equation list: know the reference information around the equations
The current Physics C reference information supplied for exam use includes equations plus supporting constants, unit symbols, prefixes, standard modeling conventions, vector/calculus identities, and geometry/trigonometry. This page reorganizes those tools for learning rather than copying the official booklet layout.
Core E&M constants
k = 1/(4πε₀) ≈ 9.0×10⁹ N·m²/C², ε₀ ≈ 8.85×10⁻¹² C²/(N·m²), μ₀ = 4π×10⁻⁷ T·m/A, e = 1.60×10⁻¹⁹ C, c = 3.00×10⁸ m/s, plus particle masses, eV/u conversions, G, and g.
Default E&M conventions
Use an inertial frame; neglect friction/drag unless stated; treat strings, springs, pulleys, batteries, wires, and meters as ideal; take conventional current as positive-charge drift; treat resistors/lightbulbs as ohmic and capacitors as air-filled unless stated; isolated-point-charge potential is zero at infinity.
Vector identities
Resolve components first. Dot products control work/flux-type projections; cross products control torque and magnetic-force directions. Magnitude and unit-vector notation are part of the supplied mathematical toolkit.
Calculus identities
The reference information supports standard derivative/integral identities, but it does not choose limits, signs, paths, surfaces, or the physical integrand for you. Those decisions remain part of the physics.
Geometry + trigonometry
Area/volume relations, right-triangle relations, arc-length geometry, and common-angle trig values are reference aids. They are most useful after you draw and label the geometry correctly.
Formula-family coverage on this sheet
| Formula family | Exam-reference | Derived / course | Role |
|---|---|---|---|
| Potential | 6 | 5 | Searchable formula family |
| Circuits | 4 | 9 | Searchable formula family |
| Capacitors | 5 | 4 | Searchable formula family |
| Electrostatics | 4 | 5 | Searchable formula family |
| Current | 3 | 2 | Searchable formula family |
| RC Circuits | 1 | 5 | Searchable formula family |
| Dielectrics | 1 | 4 | Searchable formula family |
| Biot–Savart | 1 | 3 | Searchable formula family |
| Magnetism | 1 | 2 | Searchable formula family |
| Magnetic Force on Wires | 1 | 1 | Searchable formula family |
| Faraday’s Law | 1 | 0 | Searchable formula family |
| Charged Particle Motion | 0 | 2 | Searchable formula family |
| Lorentz Force | 0 | 1 | Searchable formula family |
| Crossed Fields | 0 | 1 | Searchable formula family |
The table shows the largest formula families first. Use the category filter below to reach every smaller family without scrolling through the full library.
High-value derivation routes
Source → electric field
Use Coulomb superposition generally. Replace the direct integral with Gauss’s law only when symmetry lets E be treated simply on the Gaussian surface.
Electric field ↔ potential
Use ΔV=−∫E⃗·dℓ⃗; recover a field component from a spatial derivative of V. Decide whether vector field or scalar energy is the more efficient language.
Potential → capacitance/energy
Apply conductor boundary conditions and geometry first, then C=Q/|ΔV|. Build stored-energy forms from charging work rather than treating them as unrelated equations.
Charge flow → circuits
Start from I=dQ/dt and material/circuit constraints. Kirchhoff equations depend on topology and sign choices; RC behavior follows from a first-order differential equation.
Current → magnetic field/force
Use Biot–Savart generally; use Ampère only with suitable symmetry. Magnetic-force direction comes from a cross product and provides an immediate no-work check for point charges.
Flux change → induction
Define Φ_B with an area-vector orientation, then apply Faraday–Lenz. Add circuit laws for induced currents, or inductance for LR/LC differential models.
Symbol collisions that cause avoidable errors
| Symbol | Meaning here | How to disambiguate |
|---|---|---|
| I | electric current | Do not confuse with rotational inertia when crossing to Mechanics. |
| R / r | resistance vs radius/distance | Use capitalization and context; both may occur in one circuit/geometry problem. |
| ε / ε₀ | emf vs permittivity | EMF is a voltage-like source/induced quantity; ε₀ is a material constant of vacuum. |
| ρ | resistivity or charge density | Units and the integral/constitutive relation identify which meaning is intended. |
| Φ | electric or magnetic flux | Always attach the field label and define the area-vector orientation. |
| k / κ | Coulomb constant vs dielectric constant | κ is dimensionless relative permittivity; Coulomb k carries N·m²/C². |
Interactive equation library
Search by quantity, equation, unit, model, or purpose. Switch between exam-reference and derived/course relationships, isolate a formula family, or hide equations for active-recall practice.
Five-step equation check before you calculate
Represent
Draw or label the graph, free-body diagram, field/circuit geometry, axis, path, surface, or state variables.
Choose the model
Name the governing law or definition before choosing a special-case result.
State conditions
Check symmetry, constancy, idealizations, system isolation, no-slip constraints, or transient endpoint assumptions.
Set signs/orientation
Fix axes, loop directions, area vectors, torque signs, current directions, and potential references before substitution.
Verify
Check units, direction, t=0/∞ endpoints, zero-angle/zero-field limits, and whether the result matches the original qualitative prediction.
Explanations, examples, interactive tools and study organization are original Salar Cafe content. AP® is a registered trademark of College Board, which is not affiliated with or endorsing this site.