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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 âˆ‡Ã— ( âˆ‡Ã— A ) = âˆ‡ ( âˆ‡Â· A )âˆ‡ 2 A , where âˆ‡ 2 A â‰¡ ( âˆ‚ 2 âˆ‚x 2 + âˆ‚ 2 âˆ‚y 2 + âˆ‚ 2 âˆ‚z 2 ) A is Laplacian of A and âˆ‡ ( âˆ‡Â· A ) is the gradient of divergence of A . Verify the identity for A = ( x y ) Ë† x + ( x + y ) Ë† y by calculating each side of the identity and showing them to be the same. 2. Is E = 2Ë† x + z Ë† y a possible electrostatic field? Discuss. 3. Given that E = 2 Ë† x + 2 y Ë† y + 3 Ë† z V/m, determine the potential V (1 , 2 , 3) if V (0 , , 0) = 0 . 4. Given the fields E = Ë† xy Â± Ë† yx V/m, determine the circulation C E Â· 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 = (Ë† x + Ë† y ) dx and E = Ë† xx Â± Ë† yx on the slant edge of C ....
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 Summer '08
 Kim
 Electrostatics, Electric charge, Fundamental physics concepts, Surface charge, surface charge densities

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