What it is and the problem it solves
It is a second-order partial differential equation that describes how electromagnetic waves propagate through space. It solved the problem of unifying optics and electromagnetism — showing light is not a separate phenomenon but an electromagnetic disturbance.
How it works
Maxwell derived a second-order partial differential equation in 1864–1865 by combining displacement current with other electromagnetic equations. The equation governs propagation of electric (E) and magnetic (B) fields in vacuum or media. It enforces transversality via ∇ ⋅ E = ∇ ⋅ B = 0.
What works
Hertz confirmed the equation’s predictions between 1886 and 1889: he generated transverse waves using a dipole radiator (one-metre wires, spark gap, zinc spheres, ~30 kV pulses), detected them with a resonant loop and micrometer spark gap, measured wavelength (~4 m), velocity (equal to light), and demonstrated reflection, polarization, and standing waves (using a zinc reflector 12 metres away).
What does not
The equation does not describe quantum effects, particle-wave duality, or emission/absorption at atomic scales. It assumes continuous fields and breaks down at high frequencies or small scales where quantum electrodynamics applies.
What it changes
It unified light, electricity, and magnetism into a single physical framework. It shifted physics from action-at-a-distance forces to field-based causality governed by local differential laws.
Is it worth your time
Yes — if you work with wave propagation, antenna design, or foundational electromagnetism. Its predictive power is operational, not historical: it remains the governing equation for all classical EM radiation, from radio to gamma rays.