Hi, I have the following question on my problem sheet, and I just want to check that my answer to it is correct as I need to use the result in a later problem. If someone could confirm it is correct, or point out mistakes/erros that would be great.(adsbygoogle = window.adsbygoogle || []).push({});

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Q. Derive the wave equation forEin empty space (Form the curl of Maxwell II and use a vector identity.). Find the condition that the plane wave E =eyEycos(wt - kx) is a solution (k=2pi/lamda). Use Maxwell II to find theBfield associated with this electric field.

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A. I've done the derivation fine to get:

LaplacianE= epsilon-0.mu-0. d^2E/dt^2 [these are partial derivatives]

this is the same as d^2E/dx^2 = (1/c^2).(d^2E/dt^2) which can be solved using separation of variables to get E =eyEycos(wt - kx).

To find the associatedBfield, we used Maxwell II, ie. curlE= -dB/dt.

CurlE= -keyEysin(wt - kx)

B= integral - [curlE] dt

B= k/w.eyEycos(wt - kx)

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Thanks

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# EM Waves

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