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Unformatted text preview: Assume no other charge exists. 6. Find the potential outside a charged metal sphere having charge Q and radius R that is placed in an otherwise uniform electric field E = E o z ^ . Hint: Set V = 0 on the equatorial plane far from the sphere. Then use superposition. 7. Solve Laplace’s equation in cylindrical coordinates with no zdependence. In particular, show that the most general solution is given by V ( s , φ ) = a o + b o ln s + ∑ [ s k ( a k cos k + b k sin k ) + sk ( c k cos k + d k sin k )], where the summation is from k = 1 to ∞ . Use separation of variables for the radial equation S ( s ), and assume you may write the solution as S = s n . 8. (a) Find the potential outside an infinitely long metal pipe of radius R that is placed at right angles to an initially uniform electric field E = E o x ^ . (b) Find the surface charge density induced on the pipe. Hint: Use the results from problem 7 with V = 0 on the yz plane....
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This note was uploaded on 02/20/2012 for the course PHYS 1101 taught by Professor Lowellwood during the Fall '10 term at University of Houston.
 Fall '10
 LOWELLWOOD
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