Electromagnetic Waves

When a moving charge accelerates by oscillating about a point, its electric field also oscillates. This time-varying electric field produces a displacement current, which induces a time-varying magnetic field perpendicular to the electric field. According to Faraday's law, this changing magnetic field produces another electric field, and the process continues, creating self-sustaining electromagnetic waves that propagate through space without requiring a medium.

In electromagnetic waves, electric and magnetic fields oscillate perpendicular to each other and in phase with one another, both perpendicular to the direction of propagation. This perpendicular relationship makes electromagnetic waves transverse. Maxwell's symmetry between changing electric and magnetic fields is essential to explaining how these coupled fields sustain each other and propagate through space as a unified wave phenomenon.

Electromagnetic waves are self-sustaining because changing electric fields produce magnetic fields, and changing magnetic fields produce electric fields. This mutual induction creates a continuous cycle that allows the fields to propagate through empty space. The sequential induction of both fields results in self-sustaining electric and magnetic fields in regions farther away from their origin, enabling wave propagation without a medium.

The electromagnetic waves produced have the same frequency as the oscillation frequency of the accelerated electric charge that generates them. When a charge oscillates at a particular frequency, the resulting time-varying electric and magnetic fields oscillate at that same frequency, establishing a direct correspondence between the source oscillation and the radiated wave frequency.

Maxwell combined the work of Oersted, Coulomb, Gauss, and Faraday, introducing mathematical symmetry into electromagnetism. He introduced the displacement current concept, showing that changing electric fields produce magnetic fields, just as Faraday's law shows changing magnetic fields produce electric fields. This symmetry, combined with the Lorentz force law, encompasses all laws of electricity and magnetism and explains electromagnetic wave generation.

A static electric charge creates only a stationary electric field around it. When the charge moves, it additionally produces a magnetic field orthogonal to its motion. However, only when a charge accelerates does it produce time-varying electric and magnetic fields that induce each other sequentially, creating electromagnetic waves that propagate through space.

Displacement current, introduced by Maxwell, results from a changing electric field and accounts for how a changing electric field produces a magnetic field. This concept creates the mathematical symmetry needed to explain electromagnetic waves. The displacement current source produces closed loops of field lines, enabling the mutual induction cycle that generates propagating electromagnetic waves and energy carried by electromagnetic waves.