PHYS 211 Exam 1 with Solution, Spring 2013

PHYSICS 211 Quiz I TIME: 60 minutes February 27,2013 NAME IDNumber FORE YOU ARE TOLD TO BEGIN E Check if solution is continued on the back' Score: 1- (35) Consider a sheet of a conducting metal charged negatively with a charge density -o. The thickness of the sheet is d and its area is 4 with A>> d in a way that the sheet can be considered as infinitely wide' a) (5) The figure above illustrates a cut through this object. Illustrate and explain briefly how the charges are distributed in this sheet. ?-,r,- tlc ,rL"rl ; Jn oL J', N'rc ;; nb^f l't, *& r'w t% aVbct b) (15) Show that the electric field magnitude at a distance x>d ftomthe object il:-'";i^ G on*'s /*,r, Qr' LV Ja, % Jo-s, 2o '( d.diz o rwrzct 0e 50- ervV' b- ;d.dft z e A ^t,Lt E'{ro rh n . YD 1*,"1;{*r,4,- EH B8 i- Q,n=cA '+ ERzAn/+ s> fl Check if solution is continued on the back. 2 c) (5) What is the elechic field direction and amptitude at a distance O<c<d? | /t ^ t aft_ atlzc .r,haudc /L O(ff< d tM/tM" (*A un/Lrrlv, url'*< 7zO d) Another identical conductor charged positively with +o is placed at a distance D as shownbelow' -+ ? ? 4aDg E: ;r"";):itr:;;i-/ " '"n")ii)*" /" /' &. fr cn<o /: ;h^'/ t 4 ane'I b - c b "11-"'*lz tb lk'L ";*J fu +C J, Er= Er-o,.>- Ekc\ =Q Fm lr!/ 4; )etermme tne electnc nelo at a<-x<u . / / ol< a (D t i; i;o a'Vhrea /" a-' 4'zh't l/, pffiz€ il-tz"z/og)L + fr = (zFd+ E (.4 = zV+ (4) What is the potential different between the two plates? . (3) Determine the electric field at dq<D hn w Lt. ei'"A'u| 'l-U{./ :\ t\ =- IY-;T i,,te J € = "Jt {" c [lu k+--> , € % ? )c =+ € -4 <F ; " AV*e - lt . , t r 2 l\e.vqsl ' l' I I Check if solution is continued on the back. Score: 2- (15) For an object charged with a totalcharge Qwith.an arbitrary shape we have seen that the electric field is gtrvenby E = k" t 41. Demonstrate how this equation was obtained. , oii"rt f- tn/e oliv,bt, 11, "TiAt "9 ti.,l' "{,'"lY P'r'/16/-l ul4 ,n":J 7vtuf?th ' n'il,u ei, /",J/ P i'rol* oorl,tLc( Ab rbtwnl/ bd ho"twts fu, , i. 4-s. a o $o*' co"'ltn'/ Qx JrY ' e 1 ' ',i h rii -J', ,-/, tu'/'h' n' +> E ((^6-0,) = ?L:dl r> f, = l" + '/*n' l" = h 4 Mnu, *NXt+}"n6"*' ^!-l t/' 'yJ pfihtt^eus)8" Al\q "L) v' 3- (15) What is the total electric flux across a sphere with radius r that is gteater than an arbitrary charged obj ect? 4D ,/,rt* k /:,yL, rIL ,Urtt tr /i anb,hszl ,b/y aa?tb a ol&*' q)*;J ,M/ ui'/*""^^ tt r ' .- -LJ\.'--J 'ttfl'* 6oryt &. !1. ,/ry '; 'Lfu'"'/'/"t'Y Qe, % l,*, Q;*= A a) 4-(15) Consider the configuration shown below, with a positive charge Qs at position -rs: 0 and another positive charge Qq at position xr along the x-axis- At which positionx2 could a third clg8e positipbe added, such that the Oo does not m o v e ? t h l > F Z h>o Qo>o xo: 0 QPO x : x l q=o{t E Check if solution is continued on the back. Score: h ,/"^ fr q, */ f" '{772tvc, q, 4"o/ ' /- */ri .rn- r/ ), tr*/ dz /L "4- ZVru =)Hnd "a -) 0/b, .7ryu/'^nd Fz =o -) fi= Fz W- d: flL- P -W,, 5- (20) The x axis is the symmetry axis of a stationary uniformly charged ring of radius R and charge Q. A point charge Q'of mass M is located initially at the center of the ring. 4,n/ oice ,/ oi/, e7 n+ = Lo3 E"' b) When the charge Q' is displaced slightly, the point charge u".GG along the x axis to infrnity. Deterrnine the ultimate speed of the point charge. TL, illlre U4 yee,l 4;'*h'hJ ,{-tqh fu;,,*'L,,w,/tu% / U4,= KE;r?E; cU+ =KE7r,r/ -: O + ltrrc' = !,rnVz + ; .x-e o -)V+D E Check if solution is continued on the back. Score: