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EAD 234A: E&M Homework #7 Due Thursday, March 4, 2010 1. A capacitor consists of two circular conducting plates of radius a and separation da ± .Leads connected to the centers of the plates insert and remove a current 0 cos I It ω = . (a) What are the directions of the electric and magnetic fields? (b) Calculate the electric and magnetic fields between the plate to leading order in . (Neglect edge effects.) (c) Calculate the electric and magnetic fields between the plates including terms up to second order in powers of . (d) Show that the stored electric and magnetic energies to leading order in are 22 00 , 8 em I dI d WW a == (e) Show that to leading order in the equivalent circuit element has capacitance and inductance: 2 ,2 4 a CL d d and that the resonant (X = 0) frequency of the system is 22/ res ca = . Compute the next order correction. See if you can show that the factor 22 is more accurately given as the first zero of J 0 (x); x 01 = 2:40483. 2. A wire loop, of negligible thickness, has a radius R and carries a counter-clockwise current I. The loop is centered at the origin of the x y plane, so that the z axis passes through the center of the loop.

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