MIT6_641s09_quiz2006_2

MIT6_641s09_quiz2006_2 - MIT OpenCourseWare...

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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 .
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Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.641 Electromagnetic Fields, Forces, and Motion Quiz 2 May 3, 2006 6.641 Formula Sheet appears at the end of this quiz. You are also allowed to bring two 8 ½” x 11” sheet of notes (both sides) that you prepare. Problem 1 (50 points) z θ 2 2 , ε σ 1 1 , R E = E i 0 z A constant electric field is applied at r = ∞ lim E = E i 0 z r →∞ which is incident upon a sphere of radius R whose center is located at z = 0 . The sphere, with dielectric permittivity 1 and ohmic conductivity 1 , is placed within a medium with dielectric permittivity 2 and ohmic conductivity 2 . The system is in the time independent steady state. a) What are the necessary boundary conditions to solve for the electrostatic scalar potential Φ (, ) θ and electric field E )
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