• Tags: Maxwell, four-equations, symmetry
• Difficulty: Moderate

Maxwell unified electricity and magnetism into four equations: (1) Gauss's law for E: electric flux through a closed surface = $\frac{Q_enclosed}{epsilon_0}$. Electric field lines originate from positive charges and terminate on negative charges. (2) Gauss's law for B: magnetic flux through any closed surface = 0. There are no magnetic monopoles; magnetic field lines are always closed loops. (3) Faraday's law: a changing magnetic flux induces an electric field (EMF). This is the basis of electromagnetic induction. (4) Ampere-Maxwell law: a current or changing electric flux produces a magnetic field. The symmetry between (3) and (4) is striking: a changing B produces E, and a changing E produces B. This mutual generation is the basis of electromagnetic wave propagation. Maxwell predicted EM waves purely from these equations, before Hertz confirmed them experimentally in 1887.