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Unformatted text preview: Electromagnetic Theory II Problem Set 1 Due: 19 January 2011 1. J, Problem 11.3. 2. J, Problem 11.6. 3. One way to compare length measurements in different frames is to compare how a wave packet looks in different frames. Let the function f ( x ), independent of y, z , describe a symmetric profile in the x coordinate with a definite width w . Then ( x, t ) = f ( x ct ) solves the wave equation parenleftbigg 2 + 1 c 2 2 t 2 parenrightbigg = 0 (1) in the unprimed frame. a) Find the function ( x , t ) that describes how this packet looks in the primed frame which is moving in the negative x direction at velocity v , and show that it solves the wave equation in the primed system. b) What is the width w of this profile as determined in the primed system? Notice that w /w is not the usual Lorentz contraction factor. c) To understand this difference, consider a rod of rest length L parallel to the x-axis, moving in the positive x direction with velocity...
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- Spring '08