Fundamentals of Physics II: Electromagnetism, Optics, and Quantum Mechanics: 2 (The Open Yale Courses Series) by R. Shankar
Author:R. Shankar [Shankar, R.]
Language: eng
Format: azw3
Publisher: Yale University Press
Published: 2016-07-18T16:00:00+00:00
This simple pair is enough to deduce the existence of electromagnetic waves.
Take the partial y-derivative of the first equation and add it to the partial t-derivative of the second equation to obtain
We recognize Eqn. 14.45 as the wave equation for Ez.
By adding μ0ε0 times the t-partial derivative of the first to the y-partial derivative of the second equation we obtain the wave equation for Bx:
This is the first dramatic moment: to discover that Maxwell’s equations (including the term Maxwell added) imply electromagnetic waves. What is oscillating now is not some string or medium. It is just the electric and magnetic fields varying in vacuum.
The second dramatic moment follows if we compute the velocity v. Since 1/v2 multiplies the second time derivative in the wave equation, we infer that
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