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Unformatted text preview: Ph1b Analytic Quiz 3 Solution Chefung Chan, Winter 2008 Problem 1 (6 points total) A spherically symmetric charge distribution is given by ( r ) = 0 ; < r < a = K r ; a < r < b = 0 ; r > b where K is a constant. At the center, r = 0, there is a point charge q . (a) (2 points) Use Gausss Law to find the electric field E ( r ) in the region a < r < b in terms of q, K, a, and r . Solution: Consider Gauss law with a spherical gaussian surface, we have E (4 r 2 ) = 4 q enclosed In this case, charge enclosed has 2 components. One is the center point charge q while another one is the charge distribution. For the distribution one : q ( r ) = Z r a 4 r 2 ( r ) dr = Z r a 4 Kr dr = 2 K ( r 2 a 2 ) E ( r ) = 1 r 2 q enclosed = 1 r 2 ( q + 2 K ( r 2 a 2 ) ) = q r 2 + 2 K 1 a 2 r 2 ( a < r < b ) (b) (1 point) Find the value of K in terms of q and a for which the electric field is a constant E (independent of r ) in the region a < r < b Solution: From (a), E...
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This note was uploaded on 04/28/2010 for the course PH 1b Anal taught by Professor Mckewn during the Winter '08 term at Caltech.
- Winter '08