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Unformatted text preview: R and uniform line charge densityλ . For a given point on zaxis, the distance between it and the element of charge on each wire r = p R 2 + ( zd ) 2 r = p R 2 + ( z + d ) 2 . Potential at the given point V ( z ) = 1 4 πε λ 2 πR ± 1 r1 r ² = λR 2 ε " 1 p R 2 + ( zd ) 21 p R 2 + ( z + d ) 2 # . b) E z =∂ ∂z V ( z ) =λR 2 ε µ z + d [ R 2 + ( z + d ) 2 ] 3 / 2zd [ R 2 + ( zd ) 2 ] 3 / 2 ¶ ˆ z . σ  z =0 = ε E z  z =0 =λRd ( R 2 + d 2 ) 3 / 2 . c) Total induced charge is the same as the image charge(Why?): Q ind =λ 2 πR. (Hint: take a hemispherical Gaussian surface with the great circle just above the xyplane and the south pole inside the conducting plane, then let the radius of the hemisphere tend to inﬁnity.) 1...
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 Fall '11
 D.Romeo
 Electromagnet, Electric charge, Euclidean geometry, line charge density, uniform line charge, total induced charge

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