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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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