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Homework10

# Homework10 - Homework 10 Answers 95.658 Spring 2011...

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Homework 10 Answers, 95.658 Spring 2011, Electromagnetic Theory II Dr. Christopher S. Baird, UMass Lowell Problem 1 Show whether the following laws obey Galilean Relativity: (a) The law of conservation of electromagnetic energy (b) The charge-current continuity equation SOLUTION: If we have a frame K ' moving with velocity v relative to frame K , then the coordinates transform using Galilean Relativity according to: x ' = x v t , t ' = t Expanding out partial derivatives, this means: x ' = x and t ' = v ⋅∇+ t which leads to: ' 2 =∇ 2 2 t ' 2 = v ⋅∇ v ⋅∇ 2 v ⋅∇ t 2 t 2 The law of conservation of electromagnetic energy states if energy is lost in a small volume, it must either have flowed out of the volume, or have accelerated charges: u ' t ' =∇ ' S ' + J E ' Applying a Galilean relativity transformation: v ⋅∇ u u t =∇⋅ S + J E This equation obviously does not have the same for in the K frame as it did in frame K '. The law of conservation of electromagnetic energy does not therefore obey Galilean relativity. This should be

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Homework10 - Homework 10 Answers 95.658 Spring 2011...

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