![]() To obtain the electromagnetic wave equation in a vacuum using the modern method, we begin with the modern ' Heaviside' form of Maxwell's equations. Maxwell's derivation of the electromagnetic wave equation has been replaced in modern physics education by a much less cumbersome method involving combining the corrected version of Ampère's circuital law with Faraday's law of induction. The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws. ![]() In Part VI of his 1864 paper titled Electromagnetic Theory of Light, Maxwell combined displacement current with some of the other equations of electromagnetism and he obtained a wave equation with a speed equal to the speed of light. In his 1865 paper titled A Dynamical Theory of the Electromagnetic Field, James Clerk Maxwell utilized the correction to Ampère's circuital law that he had made in part III of his 1861 paper On Physical Lines of Force.
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