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Unformatted text preview: ECE 329 Homework 3 Due: June 24, 2011, 5PM 1. An important vector identity which is true for any vector field A ( x,y,z ) is ( A ) = ( A )- 2 A , where 2 A ( 2 x 2 + 2 y 2 + 2 z 2 ) A is Laplacian of A and ( A ) is the gradient of divergence of A . Verify the identity for A = ( x- y ) x + ( x + y ) y by calculating each side of the identity and showing them to be the same. 2. Is E = 2 x + z y a possible electrostatic field? Discuss. 3. Given that E = 2 x + 2 y y + 3 z V/m, determine the potential V (1 , 2 , 3) if V (0 , , 0) = 0 . 4. Given the fields E = xy yx V/m, determine the circulation C E d l for a triangular path C traversing in order its vertices at ( x,y,z ) = (- 1 ,- 1 , 0) , (1 ,- 1 , 0) , and (1 , 1 , 0) m. Hint: d l = ( x + y ) dx and E = xx yx on the slant edge of C ....
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