Page 2 E&M - Electricity & Magnetism Equations

Symbol: A

Area

Symbol: C

Capacitance

Symbol: d

Distance

Symbol: E

Electric field

Symbol: F

Force

Symbol: I

Current

Symbol: J

Current density

Symbol: ℓ

Length

Symbol: P

Power

Symbol: q, Q

Charge

Symbol: r

Radius, distance, or position

Symbol: R

Resistance

Symbol: t

Time

Symbol: U

Potential energy

Symbol: V

Electric potential or volume

Symbol: ε

Electric permittivity

Symbol: ρ

Resistivity or charge density

Symbol: κ

Dielectric constant

Symbol: Φ

Flux

Symbol: B

Magnetic field

Symbol: L (inductance context)

Inductance

Symbol: n

Number of loops per unit length

Symbol: N

Number of loops

Symbol: v

Velocity or speed

Symbol: μ

Magnetic permeability

Symbol: τ (time constant context)

Time constant

Symbol: ω

Angular frequency

Symbol: ε (script, emf context)

EMF

Coulomb's Law (force)

F = k|q₁q₂|/r²

Electric field (definition)

E = F/q

Electric field (point charge)

E = kq/r²

Electric field (charge distribution)

E = ∫k dq/r² (r̂ direction)

Gauss's Law

∮E·dA = q_enc/ε₀

Electric potential (point charge)

V = kq/r

Electric potential (charge distribution)

V = ∫k dq/r

Potential difference from field

ΔV = -∫E·dr

Field from potential

E = -dV/dr

Potential energy (charge in field)

U = qV

Potential energy (two point charges)

U = kq₁q₂/r

Dipole moment

p = qd

Torque on a dipole

τ = p × E

Potential energy of a dipole

U = -p·E

Capacitance (definition)

C = Q/V

Parallel plate capacitor

C = ε₀A/d

Energy stored in a capacitor

U = QV/2 = CV²/2 = Q²/(2C)

Capacitor with dielectric

C = κε₀A/d

Capacitors in series

1/C_eq = Σ(1/Cᵢ)

Capacitors in parallel

C_eq = ΣCᵢ

Current (definition)

I = dQ/dt

Current density

J = I/A

Resistance from resistivity

R = ρL/A

Ohm's Law

V = IR

Electric power

P = IV = I²R = V²/R

Resistors in series

R_eq = ΣRᵢ

Resistors in parallel

1/R_eq = Σ(1/Rᵢ)

RC circuit charging current

I = C dV/dt

Kirchhoff's Junction Rule

ΣI_in = ΣI_out

Kirchhoff's Loop Rule

ΣΔV = 0 around any closed loop

Magnetic force on a moving charge

F = qv × B

Magnetic force on a current-carrying wire

F = IL × B

Biot-Savart Law

dB = (μ₀/4π) · (I dL × r̂)/r²

Magnetic field of a long straight wire

B = μ₀I/(2πr)

Ampere's Law

∮B·dL = μ₀I_enc

Magnetic flux

Φ_B = ∫B·dA

Faraday's Law of Induction

ε = -dΦ_B/dt

Induced EMF as a line integral of E

ε = ∮E·dL

Self-induced EMF

ε = -L(dI/dt)

Energy stored in an inductor

U = LI²/2

Magnetic field inside a solenoid

B = μ₀nI