Answer to Sample Tests 1

Answer to Sample Tests 1 - Dr Gangopadhyaya Sample Tests I...

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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 , 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 )) * ˆ r . The very first thing i notice is that the curl is in r hat direction, and da for the disk should be in theta direction (da = dr*r*sin(theta)*dphi*unit vector theta), right? This
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