.. Multiple choice questions: Question Exam A ExamB MCI VI VI MC2 viii 11 MC3 a a MC4 g g1. (20 marks) Two 1.0-cm-diameter non-conducting spheres have a total charge of 75.0 J..lC (shared between them) and are placed 1.05 m apart. The spheres are not connected to each other /0 a) If the force each exerts on the other is 11.0 N and is attractive, what is the charge on each? l(j b) If the force each exerts on the other is 11.0 N and is repulsive, what is the charge on each? I/J+tlz. :'7S.o)(/~-(,C IF/: u!rr 18' (7S.0XIO-'--j')/C: II.oN IT () 7/fC.D (I.OS)2.})t1. a.) J( I~a ~ a1h~ / !bt !' and jz. ~...u t( #H.di:.~n , ~ S! (7S".OX/o-/;'-jJ ~ _//.() . . . 'frrc~ . (i. 05)" /( f' z. -75.0)( /0·(,%, ..... 11.l>.x. (l.bS)2'~lT"'" B.ISJc/O-/~ ~ 6 '! / - 7 S'. 0 ~ 10-'" g I - / • .3 5' )( 10-tj : 0 . . _ 7S.0)(10·('" ~) S.'2SxIO·r I-S.¥Jl.IO·' g,z Z ; 90)/ /0 -I-tYZ.. IS x It) -, ..• tJnt ~ ..a190,~.:'i(~~ d ~,;f/uz. to -/S:~CI b) JjiC11ce..d~) ~ !'ah1d~ ~~ -lilAPJm.L.A.tr . ~ 'SI (7S:f»)(/o~'-il) + /1 . . 'flTco (t, OS")~ ~ ... . , 7s,oXlo·":! JS,62~-v/(:rlJ -1i.'1¥/t:J-f . .31 -2 r -¥S X /0-' d'2. 30x I() -&. X tX.J'Ul(1'tl: a.) --L- $, (/()C)x/()-"-~) ~ -7,73 b) .J--Z'{I«;)(/O-~-J'), .,. 7.7.3 .flr~ (/.25)' Jfff'co (t,z~y· .'. ~ ~~"u 1-I:~s.etUC I iJGI O~..u "'.3o,~p C I t/ -/00 x /()-b~1 -I. 3tflf :J{ /D-9 ~O 'Ii ; 100)(/0-1..,.) /D·' -$.3'1 ~/O·Y q ~ 100 1( If) -/" ~ .110 -g ~ S-J 'i)( 10'_' :z /) I ~ 2 : 8'If X /0-'-til /6 ~ 10 ~, 112;<./D-" M 12. -<10-1. .'. ~~s ~I+ 8J.f.t:flC ~ "'//'.1 C tUtd -/2,0 C2. (20 marks) Find the total electric field E (as a vector) at the origin 0 in the figure as a result ofthe charges QJ and Q2, under the following conditions: JO a) The distances e are 25cm, and the charges are QI = +5.0 f!C and Q2 = + 1 0.0 f!C; j(J b) The values ore and QJ are the same as in part (a) but Q2 = -10.0 ~lC. y °1 e x :/-/. 2'1 x 10" Nk. t ~ /. Lflf )(10" IV Ie J lEI;: /·9())(IOI.N/C ¢: -/.31° . h)~ 1fL~ 'IQ2. . . if ~ -9.ox /D9NmYc:r. [-IO,OX /c:rt.C,J( {J.El.' t + (5.t>x /6'"'t. -IO.DIoItr'-e .. .'~ &. . . (0. 2S'm) 2... :/1. 2.5"x /O~ ille t I, .... 3. (20 marks) A thin cylindrical shell of radius R, = 3,0 cm is surrounded by a second concentric cylindrical shell of radius R2 = 7,0 cm. Both cylinders are 7,0 m long and the inner one carries a total charge Q, = -4,8 ).lC and the outer one Q2 = +5,6 ).lC, The charges are uniformly distributed over the respective cylinders. For points far from the ends of the cylinders, determine the electric field at a radial distance r from the central axis for the following cases: , (a) 2,8 cm; 7 (b) 5,0 cm; -r (c) 9,0 cm. a.) E (z.~ C/it'l) • Ii = .'.[£;ol -Lf.iyltr'C 1-b) E (s.OC/JK) . 27T (o.os-m) -'- = 7,OM CO E -if. fxIO-' C : 27f (6.Dbm) X 7.Drtl )( c;, 8~x){);Jl c.'h.J" I :-2.5 x IDS" N Ie (f&JUJtJAeM 1!Urt!iJt) I c) E(9.oC¥!)' 27f (o.o9m) :1.:; -r 6.g )(/D-~t:. 1.. 7.0'7"1'1 eo E _ f tJ. lS" xllr'C - 277 (o.CYI"'fYt): 'J( 7·om x E.~S.xID-lzCYN;nZ. I '1-2.3 x /D1 AI Ie (p~.o.w':) I X~: a-) £(f.~Q,01)· 27T{o.DvS"mJ-...e... :: -(j.tj)( IO-"C.l 7.0)116 E - - (!).f/x /tTl, C - 2JI{o.Og5'"?1'I) ' oX 7.0?1. x g.~sx/trJZC~rtlz. i -2.1f-)lIO"/V / c. (p~Mtr un) I ..J h) £ (t.o (htI). 271' (O. 06 ')til) J. ; iI. tj x/crt.C e 7.0."., Co E ~.Vx/()-tc. = vr(o.UO"M) J< 7-(:')11 Xf/.fS".x/O-I2.CYNM· : /+ 2./ x /osN/c re9Vn~J ~I c) no cAtVlcY..d "Mtc;burl. [£=D/, ... 4. (20 marks) A thin rod of length 2L is centered on the x axis as shown in the figure. The rod carries a uniformly distributed charge Q. Determine the potential Vas a function of y for points along the y axis. Let V = 0 at infinity. y f ...... --21:;--'1--' x L V • ~.Ifl = ~Efi0' -L = :-c. ~(x + jX'~lf'L: ~ ~ !k(L +Ji~"9z) -k(-Lf~ 7'/TcQ : 2-.M 1JFfi1+L) .tffE() . :. (fL/""Jl. ~ L - Q ," -