Homework13 - Homework 13 Answers, 95.658 Spring 2011,...

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Homework 13 Answers, 95.658 Spring 2011, Electromagnetic Theory II Dr. Christopher S. Baird, UMass Lowell Problem 1 Show that Maxwell's equations obey Einstein's special relativity. Assume we have already proved that the electromagnetic field strength tensor is indeed covariant and transforms from one frame to another according to Lorentz transformations. Take the Maxwell equations in vacuum as written in covariant form, Lorentz transform each piece of each equation to the new frame using covariant notation, and simplify the equations to their original form. SOLUTION: Assuming we have proven that the electromagnetic field strength tensor is covariant, we know it transforms like a typical covariant tensor: F '   = F   In covariant notation, Maxwell's equations are: ' F '   = 4 c J ' and ' F '   = 0 Let us now Lorentz transform the derivative 4-vector and the current 4-vector to the K frame:  F
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Homework13 - Homework 13 Answers, 95.658 Spring 2011,...

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