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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 z-dependence. 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 ) + s-k ( 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