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106-20002-MT1 - mom(1{25 points 3 3 m paint charges are...

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Unformatted text preview: mom (1} {25 points} 3 3 m paint charges are initially located as mi :11 the fights. {flfiadthnworkraquiredmamvefifrmnktm detu w.0)..usms) 1‘” H L. —2q mun. 1‘ $.33; Ed 3-4- . 3d _ I ‘- _-?kfla_ l Ug—kfl.-k3_i ““1 ltd 54 _ 3 a3" ”‘3‘“? - 3 $1.. 1 HI Ug-LLA-i-E-kT—(-~é-k%-) = w 4‘ ifik'fi" {In} Find the alectmmatic fare: on +q “its new locafian B. (Us: unitflttor notation) (ID p13.) 3:5..‘13‘: m4. 1+4 T (HA? 4 - A F; = h. :31 {Ia-.533“ {-1} .1. Bird?!- 1} [541‘ _ “I" a .. *- ...k.——-'1541 (—1-; +J5-J) “h-lfi 4 II .9 Pk}: IWFirnflhdmm Pmifl'fi mum: PROBLEM {2) (25 points} '- 3 4 A nonconducfing sphere of radius ZR has a uniform volume charge density p. A spherical cavity of radius R is hollewed out ofthe sphere. as shown in the figure. 1‘ {b} W. find me magnitude and direction of me electric field at point PHR, B) on the Gaussian surface ofpan {a}. {15 pm.) ' ' -! -r E E '4 E? '.' _f 3 - k. f-g-rrizn.)1.t + k. P a'fifl' if“ 51:...“ tad-- nonmali- {HF-3'1 in)" ifhflt helium“ hill-I- rr- pn'mi- charge. Phwmsfiunm mew mamas: . ' 35 PROBLEM {3) {25 pomts) Two nonconducting rings of radii R and 2!? lie in the .1): plane. as shown in the figure. The linear charge densities of the inner and outer rings are +1] and +14. respectively. (a) With V: [I at infini .what is the electric potential at point P“? {1 pts.) Cnmidu Maui-er rima M, e h. fir. = t; age-.93.. r (11+H1‘Y” HT 1 R. an: =9 VD "-' Iii-U; -.' ._"._- 2_‘-._—- d9 E ITE- te1+ue‘i’-“-5, E19. _ _._.—--- Simi‘inrij, V» = LIB" =7 VP: Vie-Va : in?“ -+ m——-—--'L"R‘ if a. 1. ”I. zfotit+t1}1 Eu {'1 4‘“:- J a {h} WW find the-magnitude and direction of the electric field at point F. {it} me.) .- {-2) Suppose an electron of mass m and charge «—e is released from rest at point an). t}, 4R). What is the acceleration of the electron just when it was released? {5 pts.) a -e- F = -9. E A. .._. .. E LIE "I'K 4. AIR ‘1'“- ! L “AWN-+1111”; e. (Iae‘ana‘ih Phys I06 First Mitfl'erm Page 555 More}: 3! . 2001 3 6 PROBLEM {4) (25 points) Censi der an infinitelyr long neneonducting I Axis cylindrical shell of inner radius R and outer | radius 2R, as shown in the figure. The volume - charge dfil'ISitji of the cylindrical shell is p = Kr, where K is a positive eenstant and r is the distance from the axis of the cylinder. {a} find the eieetric field {magninsde and direction] in the region rs» 2.12. (15 pm.) éE-d-‘z : QEIIM'. {-e :a :1 E {/y/ryfiz .L: E: u 5!. Kr (2111-er1- '5 E. a. ll. _ mm. fi\ «es 3 a. = flag (aa‘ #13) E4 3 3 I... A "h 3 VE‘Vl 1- E {is ._.i—-—p-- —-"I~ 'l 43" 3 = _ 3 Eds a '1". =" 5 Ed:- 3!. = .. S“; '4‘": it. .3 En. r' ll. 3 fl .=_ '4"- 5 EL“. in! F MarcfiiiJfl'I-‘I ...
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