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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 ψ ( x, t ) = f ( x − ct ) solves the wave equation parenleftbigg −∇ 2 + 1 c 2 ∂ 2 ∂t 2 parenrightbigg ψ = 0 (1) in the unprimed frame. a) Find the function ψ ′ ( 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
- Special Relativity, Lorentz, different frames