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Unformatted text preview: Dr. Gangopadhyaya Sample Tests I Physics 351 February 19, 2006 Questions from one of you First question: On of the sample tests (TST1 351 F01.pdf), you asked to determine the divergence of the electric field in the form ( q/ 4 * Pi * epsilon ) * ( r- a ) /abs ( r- a ) 3 , where r and a are vectors and ~a = ( a, , 0). To answer the question, can we just invoke gauss’ law and say that ∇ · ~ E = ( q/epsilon ) δ ( ~ r- ~a )? I am not sure how we would derive that besides stating the answer? If it does require derivation, I am not sure how to go about doing it because the charge is not at the origin. Any advice would be greatly helpful. Thanks for your time. Second question: In sample test TST1 351 S2005.pdf, problem #4 defines the vector field = (1/r)*unit vector phi, and its asks to determine curl and integrate over a disk of radius R on the xy plane. When I use the formula for curl in cylindrical coordinates, and even when i use maple, i get curl = (1 /r 2 ) * (cos( θ ) / sin( θ ))...
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