AP Physics C E&M Equations to Memorize

Charge is quantized

Q = ne

Elementary charge

e = 1.60 × 10^-19 C

Law of Charges

Opposite signs attract, same signs repel

Electric field around a point charge

E = kQ / r²

Relationship between Coloumb constant and vacuum permittivity

k = 1 / (4πε₀)

Electric field around a continuous charge distribution

k ∫(dq / r²) ȓ

Linear charge density (and units)

λ = dq/dL

(units C/m)

Surface charge density (and units)

σ = dq/dA

(units C/m²)

Volumetric charge density (and units)

ρ = dq/dV

(units C/m³)

Gauss’s Law

Φ_E = ∮ E • dA = Q_enc/ε₀

Electric flux for a flat surface in a uniform electrical field

EAcos(θ)

Electric potential difference across a uniform electric field

∆V_{uniform E} = -Ed

Energy stored in electric field of a capacitor

½ Q ∆V

— or —

½ C ∆V²

— or —

Q² / (2C)

Electrical power

I ∆V

— or —

I² R

— or —
∆V² / R

Resistor in series

R_eq = Σ R_n

Resistor in parallel

1 / R_eq = Σ [1 / R_n]

Capacitors in series

1 / C_eq = Σ [1 / C_n]

Capacitors in parallel

C_eq = Σ C_n

Time constant τ

Time for 63.2% charge

Charge in an RC circuit

Carrying capacity growth

Current in an RC circuit

Exponential decay

Current in an LR circuit

Carrying capacity growth

Rate of change of current in an LR circuit

Exponential decay

Ampère’s Law

∮B • dℓ = μ₀I_in

Motional emf

ε = BLv

L is conductor length, NOT inductance
Assumes velocity and B field ⊥ to each other

Inductance of an ideal solenoid

L = μ₀N²A / ℓ

N = number of turns

A = cross-sectional area

ℓ = solenoid length

μ₀ = magnetic permeability

Relationship between electrical potential energy and magnetic potential energy in LC circuit

Simple harmonic motion

Period of an LC circuit

T_LC = 2π√(LC)