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ECE107-Midterm3-Solution - #3(10 points A cylinder is made...

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ECE107 - Electromagnetism Spring 2010 Midterm Exam#3 #1 (10 points) A perfectly conducting V-shaped wire isoriented in the x-y plane asshown. There isa "- uniform magnetic field zBo' A rod with resistance per unit length of R' starts at the apex of the Vat t=O, A and moves with velocity xu . a) Find the magnitude of the EMFvoltage IV(t) I along the bar b) Find the current I asshown in the diagram (include both magnitude and sign). #2 (10 points) Awave ispropagating inthe +zdirection, and it i (z,t)=(O,O),the electric field is xEo' Find the electric field at a) (z,t)=(O, 2:) 19 Eo 7 S;Y7Oe. '2!':: ,-T; -? CJne -'1i~ jk7?eq' 41Iix,../ kCi,'2a, b) (Z,t)=(~ ,0) E!=J
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Unformatted text preview: #3 (10 points) A cylinder is made of resistive material, and has perfectly conducting caps at both ends. The cylinder has length .e, radius a, and total resistance R. Its axis is oriented along z . A voltage V is applied across the two caps, as shown. a) Find the electric field E and magnetic field H at the surface of the cylinder, r=a. b) Find the Poynting vector S at the surface of the cylinder, r=a. c) Find 4 8 . iA over the surface of the cylinder. f--", ;t VI· (!5 :-Z7. tz 2 n/. I .-v' '~l '1 7 ~ 'if I il~-4> 2';0{ IT 1 . ~ 1~ i-tt~& ~ _ -=-=-:!,"_u _ + v...
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