Key Concepts: Maxwell’s Equations (Introductory)

Maxwell's Four Equations

These equations unify electricity and magnetism and predict electromagnetic waves.

• Gauss's Law (Electric): Electric flux through a closed surface ∝ enclosed charge. ∮E·dA = Q/ε₀.
• Gauss's Law (Magnetic): No magnetic monopoles exist. ∮B·dA = 0 (field lines always form closed loops).
• Faraday's Law: A changing magnetic field induces an electric field. ∮E·dl = −dΦ_B/dt.
• Ampère-Maxwell Law: Magnetic fields are produced by currents and by changing electric fields. ∮B·dl = μ₀I + μ₀ε₀(dΦ_E/dt).

Electromagnetic Waves

• Maxwell showed that changing E and B fields propagate as waves at speed c = 1/√(μ₀ε₀) ≈ 3 × 10⁸ m/s.
• This predicted that light is an electromagnetic wave — later confirmed by Hertz.