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Unformatted text preview: Electromagnetic Theory, PHYS 441B Norbert L¨utkenhaus Due: Wednesday, 11. February 2009, 10:30 100 Points Assignment 4 Remark: All known results from situations in Electrostatics and Mag- netostatics can be used in without derivation in assignments and exams. Problem 1: Plane monochromatic waves 20 P In the lectures we found the solutions to vacuum Maxwell’s equations in the potential formulation. Starting with the complex-valued solution for the vector potential A = ~ A e i ( ~ k.~x- ωt ) and vanishing scalar potential. Here let ~ k = ~e z be the unit vector in z- direction, and ~ A is a vector over the complex numbers. a) Give the general form of ~ A that follows from the gauge condition ∇ . ~ A = 0 with ~ A = Re [ ~ A ]. b) Calculate the electric and magnetic fields ~ E and ~ B for this solution. c) Show that ~ E ⊥ ~ B for all ~x and t . d) Calculate the time averaged energy density of the electric and the mag- netic field separately. In which field is more energy stored?...
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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.
- Winter '09