P25_027 - . All the charge in it is a distance r 2 + z 2...

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27. The disk is uniformly charged. This means that when the full disk is present each quadrant contributes equally to the electric potential at P ,sothepoten t ia lat P due to a single quadrant is one-fourth the potential due to the entire disk. First ±nd an expression for the potential at P due to the entire disk. We consider a ring of charge with radius r and (in±nitesimal) width dr .I t sa reai
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Unformatted text preview: . All the charge in it is a distance r 2 + z 2 from P , so the potential it produces at P is dV = 1 4 2 r dr r 2 + z 2 = r dr 2 r 2 + z 2 . The total potential at P is V = 2 Z R r dr r 2 + z 2 = 2 p r 2 + z 2 R = 2 h p R 2 + z 2 z i . The potential V sq at P due to a single quadrant is V sq = V 4 = 8 h p R 2 + z 2 z i ....
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