EMWaves - Electromagnetic Waves The main reason Maxwell’s...

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Unformatted text preview: Electromagnetic Waves The main reason Maxwell’s equations are named after him is that he incorporated them into a theory that predicted the existence of electromagnetic waves . Suppose that somewhere out in space an electric field exists that is oriented purely in one direction—the y-direction, for argument’s sake—and that intersects the x-axis. In this case, the integral term making up the first half of Faraday’s law, ᷈ E ѐ ·d l ѐ , can be simplified greatly using a mathematical relation called Stokes’s theorem . The result is an area integral - ∫ d A (dE/dx) that is oriented in the z-direction and which can be approximated, assuming the area we integrate over is very narrow, as - A (dE/dx) . Assuming this area A is constant, it can be extracted from the magnetic flux term on the right side of Faraday’s law and cancelled out, reducing the whole equation to dE/dx = dB/dt ....
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