midtermreviewsol

midtermreviewsol - 110 A MIDTERM REVIEW SOLUTIONS SPRING...

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110 A MIDTERM REVIEW SOLUTIONS SPRING 2008 1 (a) Just invert the answers for a charge outside a grounded sphere. The formu- las have the same form: for a charge q a distance a from a sphere of radius R , the image charge has charge and position Q = qR a b = R 2 a . (b) Drawing the picture should be straightforward, and one Fnds there are an inFnite number of image charges. If you are having trouble, look at part (c). (c) We just repeatedly apply the formulas in (a). The results are: # Image of in sphere charge (Q) position (d) 0 - - q b 1 0 a qa b a 2 b 2 0 c qc b c 2 b 3 1 c qc a bc 2 a 2 4 2 a qa c ba 2 c 2 5 3 a qa 2 bc a 4 bc 2 6 4 c qc 2 ab c 4 a 2 b 7 5 c qc 2 a 2 ba 4 a 4 8 6 a qa 2 c 2 a 4 b c 4 There are an inFnite number of charges, so we could keep going. Note, however, that at a distance of about b , the potential from charge 7 is V Q d b Q d = qa 2 bc 2 , and from charge 8 is V Q b d q b = qa 2 bc 2 . In the approximation given, that
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midtermreviewsol - 110 A MIDTERM REVIEW SOLUTIONS SPRING...

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