Assignment 08

Assignment 08 - F F . How does it transform? 3. Starting...

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Electromagnetic Theory, PHYS 441B Due: Wednesday, 25.March 2009, 10:30 100 Points Assignment 8 Remark: All known results from situations in Electrostatics and Mag- netostatics can be used in without derivation in assignments and exams. Problem 1: Griffiths, Problem 10.18, page 441. 30 P Suppose a point charge q is constrained to move along the x axis. Show that the fields at points on the axis to the right of the charge are given by ~ E = q 4 π± 0 1 r 2 ( c + v c - v ) ~e x , ~ B = 0 . What are the fields on the axis to the left of the charge? Problem 2: 30 P 1. Write down the explicit transformation rules for the following(otherwise unspecified) tensors F αα and F α α . 2. Let F μν from now on denote the electromagnetic field tensor. What is
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Unformatted text preview: F F . How does it transform? 3. Starting from the inhomogeneous Maxwell equation, which is given by F = J derive the continuity equation. Note: the last two items will make sense to you only after the Friday lecture. Problem 3: Assume that at some point of space-time we have ~ E and 40 P ~ B to be not perpendicular. Show that we can choose an inertial frame so that both vectors become parallel at that point. Show that a Lorentz transform to a frame with ~v = 1 + v 2 c 2 ~ E ~ B k ~ B k 2 + k ~ E k 2 c (1) achieves this. Does there also exist a frame in which the two are perpendic-ular? 1...
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This note was uploaded on 07/28/2009 for the course PHYS 441B taught by Professor Norbertlutkenhaus during the Winter '09 term at Waterloo.

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