emhw13 - Electromagnetic Theory I Problem Set 13 Due 28...

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Unformatted text preview: Electromagnetic Theory I Problem Set 13 Due: 28 November 2011 49. Consider the ideal circular parallel plate capacitor of radius a and plate separation d a , hooked up to a straight current-carrying wire on the axis as pictured in the figure to J, Problem 6.14. The current in the wire varies harmonically, I ( t ) = I cos ωt = Re I e- iωt . In this problem we neglect the effect of fringing fields, which means that the fields within the capacitor are assumed to be those between infinite parallel plates, which discontinuously drop to zero at the edge of the capacitor. This exercise will give you experience with the use of complex fields in solving physical problems. a) In the approximation described above we may make the ansatz that the (complex) fields within the capacitor have the form E = ˆ zf ( ρ ) e- iωt , B = ρ × ˆ zg ( ρ ) e- iωt From the (complex) Maxwell equations determine g in terms of f and show that f ( ρ ) satisfies the n = 0 Bessel equation, whose solution is f (...
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