How did James Clerk Maxwell predict the existence of radio waves?

James Clerk Maxwell did not specifically set out to predict "radio waves" by name; rather, he predicted the existence of electromagnetic radiation through his theoretical unification of electricity, magnetism, and optics in the 1860s.1

By manipulating his equations for electric and magnetic fields, Maxwell derived wave equations showing that changing magnetic fields produce electric fields, and vice versa. This process creates self-propagating waves of coupled fields. Maxwell calculated the speed of these waves using constants from electrostatics and magnetostatics and found the result matched the known speed of light. Consequently, he concluded that light itself is an electromagnetic disturbance.23

Maxwell’s theory implied that electromagnetic waves could exist at various frequencies, not just those of visible light. It was not until 1888 that Heinrich Hertz experimentally confirmed this by generating and detecting long-wavelength electromagnetic waves, which we now identify as radio waves, proving they shared the same fundamental properties as light.143