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How do electric and magnetic fields form an electromagnetic wave?

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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.

Electromagnetic waves are formed through the mutual interaction of time-varying electric and magnetic fields. When an electric charge accelerates, it creates a changing electric field, which in turn induces a magnetic field. Conversely, a changing magnetic field induces an electric field, as described by Faraday’s law of induction.1234

In free space, these fields propagate together as an electromagnetic wave where each time-varying field continuously regenerates the other. These waves travel in a transverse mode, meaning the electric field, the magnetic field, and the direction of wave propagation are all mutually perpendicular to one another. This relationship is mathematically defined by Maxwell’s equations, which provide a complete description of how these fields are produced and interrelated. In an ideal vacuum, these waves propagate at the speed of light.524