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Unformatted text preview: PHY6938 Proficiency Exam Fall 2002 September 13, 2002 E & M 1. A positive charge is uniformly distributed throughout a very long cylin drical volume of radius R . The charge per unit volume is . (a) Find the electric field ~ E everywhere as a function of the distance r from the axis of the cylinder. Lets start by finding the electric field outside of the cylinder. Build a Gaussian surface out of a cylinder of length L and radius r > R . Then by symmetry the field must point radially outward on the curved part of the Gaussian surface and must be parallel to the surface on the end caps. This means that the flux of the electric field through this surface is I E d A = E (2 rL ) . (1) Now Gausss law tells us that this is also Q encl / , where Q encl is the enclosed charge. The volume of the charged cylinder cut out by our surface is V = R 2 L , so the enclosed charge is Q encl = R 2 L (2) and Gausss law gives E (2 rL ) = 1 R 2 L, E = R 2 2 r . (3) Since the electric field points radially outward, we have E = R 2 2 r r .....
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This note was uploaded on 03/11/2012 for the course PHY 3900 taught by Professor Staff during the Fall '1 term at FSU.
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