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ECE 2317 Exam 1 Fall 2005

ECE 2317 Exam 1 Fall 2005 - —\X 1 If symmetric about the...

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Unformatted text preview: \ . —\. \X- {/- 1' _ If symmetric about the z—axis, i.e., pV = ,0], (p) is a function of p only. 3. Using Gauss’s law, derive the following general formula for the electn'e field for such situations: K. 1 p e u r - E =—I,0 (p).0dp- e ‘ 1‘— p 6 V _ L In kin-0’0 0 . x1. F. is . i‘ -— "- If! ’1 e - a 'x i? - P J x; f .... ,. 1 0 ' L 'Dr ' PI! ? AP 2“? ‘7: f. H ‘ {\{fi _ i tf. _ ‘1 Dr 2. P\/ 9 .5 r» E'— : ‘*' We, « a“ \ 1 » “J‘- i? n" r32 £36 F U) I .5. Be sure to a) draw an appropriate sketch ofyoiiir Gaussian surface and b) Show all details of your derivation. b. Using the result of part a.) above, find expressions for the electric field if the volume charge density is as given in the (30 pts.) A certain volume distribution of charge is known to be cylindrically '- . graph shown at right. p C; U P J ‘l ‘91:: : \ ‘ ,w‘f. \V-Ix ml ' - I. 1 P L/- 1 /Acr fir a) .,.. l '3‘3' (In)? 0K. “‘ _fi______#_;,_—— 2 E 53- g; 7 a. r; (I? 4'? a 5'” EP: “ 1.. 'E'Jr : 52‘” [ ],0<p<a ‘10 (M a +--—*- in?” __s——~—-r_—"*__ I Ep' 5 x F [ ],'p>a /_ __ -' C. Derive an expression similar to that of part a) for £2]r for radially 1/ symmetric volume charge distributions, ,0}, = pV (r) . \mV 1 Dr , /,.. Agflf .1”? F“ 'v fly ‘arl (7“) Jr :Lyfiifi x“r\/"~"{ ‘- .£‘h ../ <- i ,- 1 Ip’fi ' I” “if.” p/ 2. (20 pts.) x ,4 h, a . . . . _ 3» 3 A 2 _ A The electnc flux denSIty IS given as D — pip +_.p 1|: i- g 1;, 91.5 w 3. Find the net flux leaving the of radius 21 shown above. b. Find the net charge encloseiii‘by the cylinder. flue? : SD fl ()5 j Dr” '1 :"flglfiil r; ' fifif :2 1A1 /‘ ' \ , 53>" / 1170K Dr [C] Enclosed charge = 9/” Problem 3 (20 pts) Two_ similar infinite line charges (line charge density pm) intersect at right angle. Find the electric field vector at the point specified in the figure. ' Y \‘u f A I L —\" J f‘ “ we 7 R7Wr.:a.?iyrf>{Y Y" HJ’TLA {Li : mitt ray 3X l | ' i‘ I J M A A y 1"} '/ _ ~ ail. and NI PAM H \ Ex) 1 saw—f La {—Ly'Yq-r K —/L:? flag :- [,L...\_:;Ja'_ /\ f” We we we Ea, :am. M_ . {4116042 \ )0 .\r Swifdi \F'y {'0 F Fizz- ” V K 61%“: Zigzeail _ E ; Efli: k ERG-V . @ g A A>\/ 2 Lox. /,. ., 7-: Jr « E F a new" C y Gm"- Problem 4 (30 pts) Annular ring carries a non-uniform surface charge density p5 = pcosw). The ring is in the x—y plane, its inner radius is a and the outer is b. Find the electric field vector aiong the z axis. Eon b ’" Eo—rrok l .a "kw V * PF h Q—f\r_ptl M 1 1*- “, _,_ E x ‘1. 'C-Hlfl .I k .3 O b We 3 \ i 2. ‘2" _ r?” cm¢C1€534V$ . up “w” c ‘ t .9 )0 V J c - a c. ‘ 2n 0/ , o: F 5'”? r3; (ixlk Laps"? ,_#3r———-— We; ...
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