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Unformatted text preview: Electromagnetic Theory II Problem Set 8 Due: 21 March 2011 31. J, Problem 8.2. 32. J, Problem 8.5. 33. In this problem we investigate some of the normal modes for electromagnetic fields with harmonic time dependence ( i.e. ∝ e − iωt ) in a spherical cavity of radius a in a perfect conductor. Use polar coordinates with origin at the center of the cavity. When k ≡ ω/c negationslash = 0, the sourcefree Maxwell equations can be reduced in two equivalent ways to: I : B = 1 ikc ∇ × E ∇ · E = 0 ( −∇ 2 − k 2 ) E = 0 or II : E = − c ik ∇ × B ∇ · B = 0 ( −∇ 2 − k 2 ) B = 0 a) For ω negationslash = 0 the fields must be strictly zero in the bulk of the conductor. Why? Use Maxwell’s equations to prove that the fields in the cavity must then satisfy the bound ary conditions E t = B n = 0 at r = a. b) Consider the following forms for TE ( ˆ r · E = 0) and TM ( ˆ r · B = 0) modes: TE : E TE = f ( r ) ˆ r × C e − iωt ; TM : B TM = g ( r ) ˆ r × D e − iωt...
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This note was uploaded on 01/08/2012 for the course PHY 6346 taught by Professor Staff during the Spring '08 term at University of Florida.
 Spring '08
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