329sum11hw7sol - ECE 329 Homework 7 Solution Due: July 8,...

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Unformatted text preview: ECE 329 Homework 7 Solution Due: July 8, 2011, 5PM 1. Verifying vector identity H E- E H = E H for E = 2 e- z x and H = 4 e- z y. Solving the left-hand side of the identity gives H E- E H = (4 e- z y ) x y z z 2 e- z- (2 e- z x ) x y z z 4 e- z = (4 e- z y ) (- 2 e- z y )- (2 e- z x ) (4 e- z x ) =- 8 e- 2 z- 8 e- 2 z =- 16 e- 2 z and the right-hand side gives E H = ( 2 e- z x 4 e- z y ) = ( 8 e- 2 z z ) = z ( 8 e- 2 z ) =- 16 e- 2 z , hence, the identity is verified. 2. Continuity equation. a) Taking the divergence of J = ( 4 z 2 x + 3 x 3 y y + 2 z ( y- y o ) 2 z ) A / m 2 we get J = x ( 4 z 2 ) + y ( 3 x 3 y ) + z ( 2 z ( y- y o ) 2 ) = 3 x 3 + 2( y- y o ) 2 ....
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329sum11hw7sol - ECE 329 Homework 7 Solution Due: July 8,...

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