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MIT OpenCourseWare 6.641 Electromagnetic Fields, Forces, and Motion Spring 2009 For information about citing these materials or our Terms of Use, visit: .
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Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.641 Electromagnetic Fields, Forces, and Motion Final Exam 5/15/2008 NOTE: 6.641 Formula Sheet at the end of exam. You are also allowed both sides of two 8½“x11” pages for 6.641 course material that you have prepared yourself. 1. 25 points V = 0 a a ε 0 V V 0 cos x = k 0 b ε 0 - b V = 0 Depth d A sheet with electric potential distribution ( = 0) = V 0 cos kx V y is placed at y = 0 , parallel and between two parallel grounded perfect conductors at zero potential at y b = . The = − and y a regions above and below the potential sheet have dielectric permittivity of free space ε 0 . Neglect fringing field effects. a) What are the electric potential solutions in the regions 0 and ? y a b y 0 b) What are the electric field distributions in the regions 0 < < and < < ? y a b y 0 c) What are the free surface charge distrbutions at y b , = , and y a = y 0 = ?
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