homework_2 - ELECTRODYNAMICS PROBLEM SET 2 due February 9,...

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ELECTRODYNAMICS PROBLEM SET 2 due February 9, before class Problem 1.: Field invariants a) Write the Lorentz scalars F μν F μν and ± μνλρ F μν F λρ in terms of ~ E and ~ B . b)Show that if ~ E and ~ B are seen as perpendicular in one reference frame, they are perpendicular in any other reference frame. c) Show that if | ~ E | = | ~ B | in one reference frame, | ~ E 0 | = | ~ B 0 | in any other reference frame. d) Show that if | ~ E | > | ~ B | in one reference frame, | ~ E 0 | > | ~ B 0 | in any other reference frame. Problem 2.: Relativistic invariance of Maxwell’s equations in your face An infinitely long straight wire of negligible cross sectional area is at rest ans has an uniform charge density q 0 in the in the inertial frame K 0 . The frame K 0 (and the wire) move with velocity v parallel to the direction of the wire with respect to the lab frame K . a) Write down the electric and magnetic fields in cylindrical coordinates in the rest frame of the wire. Using the Lorentz transformation properties of the fields, find the components of the electric and magnetic fields in the lab. b) What are the charges and current densities associated with the wire in its rest frame? In the lab frame?
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This note was uploaded on 12/29/2011 for the course PHYSICS 606 taught by Professor Bedaque during the Spring '11 term at Maryland.

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