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Unformatted text preview: R and uniform line charge density-λ . For a given point on z-axis, the distance between it and the element of charge on each wire r = p R 2 + ( z-d ) 2 r = p R 2 + ( z + d ) 2 . Potential at the given point V ( z ) = 1 4 πε λ 2 πR ± 1 r-1 r ² = λR 2 ε " 1 p R 2 + ( z-d ) 2-1 p R 2 + ( z + d ) 2 # . b) E z =-∂ ∂z V ( z ) =-λR 2 ε µ z + d [ R 2 + ( z + d ) 2 ] 3 / 2-z-d [ R 2 + ( z-d ) 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 xy-plane and the south pole inside the conducting plane, then let the radius of the hemisphere tend to inﬁnity.) 1...
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This note was uploaded on 02/02/2012 for the course ELECTRICAL ENEE380 taught by Professor D.romeo during the Fall '11 term at Maryland.
- Fall '11