Electromagnetism
Cheat Sheet

Maxwell's equations and applications. From electrostatics to electromagnetic waves.

Maxwell's Equations

Gauss's Law (Electric)

∮ E · dA = Q/ε₀

Electric flux through closed surface equals charge enclosed divided by permittivity.

Gauss's Law (Magnetic)

∮ B · dA = 0

No magnetic monopoles exist.

Faraday's Law

∮ E · dl = -dΦ_B/dt

Changing magnetic field induces electric field.

Ampere-Maxwell Law

∮ B · dl = μ₀I + μ₀ε₀ dΦ_E/dt

Magnetic field from current and changing electric field.

Electric Fields

Coulomb's Law

F = kQq/r²
k = 1/(4πε₀) = 8.99 × 10⁹

Electric Field

E = F/q = kQ/r²
V = Ed (uniform field)
C = Q/V = ε₀A/d

Magnetic Fields

Force on Current

F = BIL sin θ
F = Bqv sin θ

Electromagnetic Induction

EMF = -N dΦ/dt (Faraday)
Φ = BA cos θ (flux)

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