midterm2_117_Sp_10 - UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Scences EECS117 Midterm 2

midterm2_117_Sp_10 - UNIVERSITY OF CALIFORNIA College of...

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Unformatted text preview: UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Scences EECS117 Midterm 2 Examination Spring 2010 T.K. Gustafson ; Kedar Patel April 19 2010 PRINT YOUR NAME: SID. : SIGNATURE: Do your work on the exam. If you do need to use extra sheets attach these to the exam so that these are considered as well. Make your methods clear so that partial credits is possible. There are two problems THE PROBLEMS ARE EACH WORTH THE SAME 2 Problem Number One) Consider a point charge Q located a distance h from the origin along the z—axis. Z Point r Char e at zg=% a) What is the electric potential at point P in terms of 71 ? Vm = Q. “mew—k b) Express the electric potential of part a) in terms of r and 6 using the cosine law ( r and 6 are the spherical coordinates ) ,‘ /"b wt: Lr‘l—W‘ — 1H4 Lege\ \ILP\= Q lI ‘mec (WW: wk c036) 1’ A second charge —Q is now placed at Z : —h. c) What is the total potential at P due to the two charges in terms of 71 and 7‘2, the distance from the second charge to the point P “a 3 Now the Charges are made to oscillate by having a sinusoidal current flow between the two Charges. ( I : [elm/2 + 0.0.) ~ d) If the Charge is represented in phasor forni ( q : (jam/2 + 0.0 ) how is (1 related to I? Com—Hm v C’E‘fl EcLUanovx CW <7 » I «— 645 : o Q N i 3 t Qfi J E “kc-'9 \A “4": 2,15de OVQV‘ CW.“ $PLLQ.V‘{- t cw: 4V Xq -: aw =g1-Ag a; Q, dc-QJ. a t ‘K‘ C - G .7, a \ 1, Ua.’ —— Q 3 K‘s“ Lméaiiaflut L; W ‘ —v .2 "' g {— C - - c 3’: 'x l : ~ e) Obtain the first non—zero term in the potential (the dipole approximation) (new for the oscillating Charge pair. gout—kn. unobkmj \lC\°\-‘ 3 tie, _Le, ‘Efiée / \'.VV\e. e. au W” Va; e'dfiue. dALLL e. ‘lco OQUJTP t mm _L Qicti—hwgeQ 3 a: - LCV— lease) (-1, V— v- 'b- r ' _ e — \r . g‘bkv“; 3:)‘ka $w§\fl&LKC\+J~L\\/\COSG7 - \u SKMfKOLV I kw _ QTLKW"; 2, Q’)“ L ( —— Co$6\ ' t ._ 'kv‘ . \lLC’lg g L bk” 9),” K gr. hLfiSewC\'\-LK<\’\ (1396‘ «en V W x» cm“? — U —E toga“ “1-” “‘36” Vz/A—f/ — 9.. v L {1330}: 2:);kv L °‘\’_\. («9%93 + (30%) \ ~ ‘E’Cxe \C \C M— 4 Problem Number Two) 7 Consider an infinite line current [1 : Iéeiwt’kz Take to : 0 and k: : 0 for parts a), b), P M Mw/z I1 “’X I2 <——— d —-> Currents are in z- direction 0), and d). a) Using Amperes law, What is the magnetic field as a function of 71, the radial distance from the line current, [1 7 Ecgu:y§_\& l. 1L,er ix b) A second parallel line current f2 : —Ié’eiwt+kz is located a distance d from the first. What is the total magnetic field as a function of X in the plane of the two Wires for w : 0 and ‘= fie .1. — Ix " T5 5} (sleigh n: d/ +50 3) wk: 3—39 5 c) Calculate the magnetic flux between the Wires for a differential distance A2 and —L < at<+_L_3WhereL<d. Z ’1. gangs-Q“ Ly L4) — w (‘14—‘13) ; 5&1 m {our r. A; Tl L (3: L4,) @563- "/Q 1T cl d) Using c), obtain an expression for the inductance per unit length F\Ux: L 4‘1 I ._I .. L: \V\ OLE: tr M e) Does the result in d) change When w 71$ 0. State a reaon for your answer. D663 W01? WWI-ta; . Two wKVeQ‘C\*eMA gvvfuvhk TE M Nome Se AcV-CLVLaVeN‘Ke, Quick tbquhw {3% a. JroJrCc. $0 \u'l-i'cwrg Tku$ L Vemem—s Hue. gamma. f) Is there an electric field When w 71$ 0 7 If so give its value ( and direction ) along X for y=0and —L<a:<+L. Cowk-{wui'tfi q t T. f @573 :0 Gian/munch * A: m _ Do \Me dmavcse $3 = E E :— 1/“?Qlia—usgygl Tke. ‘6 v CTOLAR-QS Law, W \ m A 95th ~Jikz. E II <16? b I, I I, ‘r’ [0 Problem Number Three A thin Wire carrying a current I is located parallel to a conducting plane and a distance d from it. Determine the direction and force per meter on the Wire. [Hintz use the method of images] \\’\C)‘kJC€—‘l v QJV Q {ck ‘auV 2:19 Lomdek‘l‘A-g QUUUCW " /' $mr$<1££ Qumrde 16* e—fi :H A We .c H E vaoJ-eud“ 4w V‘e.$u\."ck‘.vx Q-U‘OM q_vx “Mg, 2, QUthwk- TI wbxcdn w\ keg Us»: 3 I gow+\\A\/ou& 1" 4 x ggq- R—mce Quwexffi Q,quva QM," Force, \$ 'HMJS KL, 1 won‘tko V‘L‘QUKSK‘UL (aft-r 164 ‘M ...
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