MIT6_641s09_sol_quiz2009

MIT6_641s09_sol_quiz2009 - MIT OpenCourseWare...

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 6.641 Electromagnetic Fields, Forces, and Motion Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . 6.641 Electromagnetic Fields, Forces, and Motion Spring 2009 Quiz 1- Solutions- Spring 2009 Prof. Markus Zahn MIT OpenCourseWare Problem 1 Figure 1: A diagram of a perfectly conducting hollow sphere filled with a perfectly insulating dielectric with a uniform distribution of volume charge (Image by MIT OpenCourseWare). A perfectly conducting hollow sphere of radius R is filled with a perfectly insulating dielectric ( = 0) with a uniform distribution of volume charge: = < r < R within a medium with permittivity . The sphere is grounded at r = R so that the scalar electric potential at r = R is zero, ( r = R ) = 0. There is no point charge at r = so that E r ( r = 0) must be finite. A Question: What is the EQS electric field E ( r ) for < r < R? Solution: 1 o d o r 2 E = r 2 r ( r 2 E r ) = dr ( r 2 E r ) = r 2 E r = r 3 + C 1 E r = o r + C 1 3 3 r 2 E r ( r = 0) is finite C 1 = 0 o r E r ( r ) = < r < R 3 1 C Quiz 1: 2009- Solutions 6.641, Spring 2009 B Question: What is the scalar electric potential ( r ) where E ( r ) = ( r ) ? Solution: d o r o r 2 E r = dr = 3 = 6 + C 2 o R 2 o R 2 ( r = R ) = 0 = + C 2 C 2 = 6 6 ( r ) = o ( r 2 R 2 ) 6 Question: What is the free surface charge density s ( r = R ) on the inside surface of the sphere at r = R ? Solution: o R R s ( r = R ) = E r ( r = R ) = 6 = 3 Problem 2 Figure 2: A diagram of a uniform line charge of height L standing perpendicular to the ground plane (Image by MIT OpenCourseWare)....
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This note was uploaded on 12/02/2010 for the course ECE 6.641 taught by Professor Zahn during the Spring '09 term at MIT.

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MIT6_641s09_sol_quiz2009 - MIT OpenCourseWare...

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