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How did James Clerk Maxwell predict electromagnetic waves?

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Diagram of a tree leaf illustrating photosynthesis, with arrows showing sunlight, water, and carbon dioxide entering the leaf and sugars and oxygen being produced. A person is shown beside the tree to demonstrate the exchange of oxygen and carbon dioxide between plants and animals. — electromagnetic radiation Diagram of photosynthesis showing how water, light, and carbon dioxide are absorbed by a plant to produce oxygen, sugars, and more carbon dioxide.

In the 1860s, James Clerk Maxwell unified the fields of electricity, magnetism, and optics into a single theoretical framework. By manipulating his field equations—which were based on Michael Faraday’s observations of lines of force—Maxwell derived wave equations for electric and magnetic fields.1234

He demonstrated that a changing magnetic field produces an electric field, and a changing electric field produces a magnetic field, implying the existence of self-propagating electromagnetic waves. Crucially, Maxwell calculated that the speed of these waves was determined by constants in electrostatics and magnetostatics, resulting in a value that matched the known speed of light.34

Based on this, he concluded that light itself is an electromagnetic disturbance in the form of waves propagated through the field. This prediction was later experimentally confirmed by Heinrich Hertz in 1888, who demonstrated that electromagnetic waves possess properties identical to those of visible light.341