test2-solutions-2212p-f07 (2)

test2-solutions-2212p-f07 (2) - Problem 1 (25 pts) A thin...

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Unformatted text preview: Problem 1 (25 pts) A thin plastic rod, of length 4m, lies along the x—axis (only a portion of the rod is shown in the diagram). It has a charge of —300 nC uniformly distributed over its surface. A thin glass ring, or radius 6 cm, is centered on the y—axis, 10 cm above the rod. It has a uniform charge of +2 nC. l'lllg radius 6 cm charge +2n(_" I.lf{| (a: 23 pts) Calculate the force on a small ball with charge —5 nC placed at < 0, 0.05, 0> m. Your answer must be a vector. Clearly show all steps in your work. - ‘x, .1 “a a _ i I I I. » i r it — m -} «.2 y r E --’ a a ,r Why}. I“: {F} J ,‘ ,I K r f . .. ‘ ff“ (“fr (at l l . r11.) Ir.‘ \ r \l E; I "I .3 .v F a )r f; ". r W P l ’ \ ‘ I r r i “XI I _ illllraf'l’) _ I... I yr 5"}? r I L .- t Y [ .1 I J 1; — r f) J I} i (b: 2 pts ) Draw the force vector you calculated on the diagram. .5. All _r1,r:‘ IJ.,;‘, ,Ia {HIGH . , ' { '{r’ _: V. Problem 2 (20 pts) The arrangement of charged particles shown in the diagram is called an electric quadrupole. At locations on the x axis far from the quadrupole, the electric field due to the quadrupole has the form: E :< 1 h_ 0 0> (/1 is a constant with units C-mz, combining the magnitudes ofthe charges, and their separations). 47:50 x" ’ ' The diagram below is not drawn to scale; both locations A and B are far from the quadrupole. The origin is at the center of the quadrupole. U x <b, O, 0> l - a} a}. (" 2' a,0,0> 0, O> “- :0 (a: 5 pts) At two locations between A and B, draw arrows showing the electric field at that location. The relative magnitudes ofthe arrows should be correct (longer arrow means larger magnitude). (b: 5 pts) Is VB-VA positive, negative, or zero? Briefly but clearly explain your reasoning: “x g. .1 I. '_ l 5'! J- (c: 10 pts) What is VB—VA? Your answer should be a symbolic (algebraic) expression, which may include the constants h, a, b, and l /(47r£0) . Show all steps in your work. Problem 3 (30 pts) .F- .-;‘. "J {ESQ-'2" 1' f“ ‘4 f “5’ ._ “1,; “I; ‘IrJ,Iv:-. r' it _ (. g; \ .» . . I ’ "nlu'm ' 4 H x A , a . I A l l A charged particle starts from rest near one plate of a charged capacitor, and travels in the —x direction, passing through a tiny hole in the capacitor. At the instant shown in the diagram, the particle is at the origin. At this moment, the magnetic field at location A < -0.004, —0.003, 0> m, due to the moving particle, is <0, 0, 1.9 x 10-14> T. The angle eis 37°. W i. ,r E. a - g; ‘ ‘ I? 1' 3 (a: 5 pts) Is the particle a proton or an electron? Explain briefly how you can tell. J E- , j' rah-f” ,7le f “flit-Ff!“ J. G (or; I: t I _N Z. gr. f F ‘Iir bl :- g- 25:1 91-an '7 .l _ , __,.- .1 _. (b: 2 pts) Draw + and — charges indicating which plate of the capacitor is positive and which plate is negative. “TL. I" I... J: y! f , .1 .1 r . . C ,.. Hg," 3) J01- _ _ " -—-#— .. _H j .— ‘“ 1 (c: 15 pts) What is the speed of the particle? Show all steps in your work. , a ;; {3 ' .' ' " “r _ A \ | .‘J i"- 9 5—5:; .' ' Hr F f j\' ,2 M -y- ' , P“ .J:": ;.. - a? *- — . t .m/“r . .- - . ’— - TE. ’3: i _ - “I .‘ H , ll: _-r.| [1.9-um {1r}:ng .Qr. - . I- -- I; d; , __| I _ "' .- z‘ n " 4’ v’ pom- if} A [1/5— r. .. ,'- J- _ .. '. f-‘r . " / '0.” “If. r{,-‘f) VI- rig-lit} K. .3 ‘ I" ~'1 - _- I \I ‘. f ' I . ' .ra‘ ‘ ,f . -7 a '- . (J. fr}; v/ .r I //{,P.._5| I _ H . (In I. U __ {r}; q '_ ’2'.) {fig/(If. \ r _ __—-r‘ . '” ' - - ‘ " l a «.12; . - - ./ r _.~ - - . hwy/"‘7 ' "" “ft fl 1' I. F of ‘ 1' ' :2" J" f. I 'I - ‘ . I /IJ) _. '3‘} N i . , .. .- fi-m V ._ y f I_ I J] 5 a (ir- rt'f L.” JP: '9‘]: _- ; a! J ,n r ' . .. I,: ,v ,. {I (d: 8 pts) What is the potential difference VC-VD ? Show your work. a - ' r I" l - x r I IA ff, I I J; r _ l . H d} f I fir 1;), r; J - -' I: ---‘ i-‘r... - 9- 9., 0h - my; _.n. p r‘ a at” Fir La» C3 :7 ffifjfij, ( R. J I {by f k(-, a I 5:. LA . ' f? . -' .- :9 {an "kW-r ; g .' :u r r C :5 '1' - .- '—: 'r r ZW‘f o /L:‘H/J_ —‘,. I; I -_|") ~ I .lrl) _ ’l' I ’u" m. t J I) I . a I a. {Lfff‘l- (-1"! '-' )H I.) 5””, J) Jr Problem 4 (25 pts) A compass, which originally points North, is placed 11 cm from a coil of wire, which is composed of 8 turns of wire, of radius 2 cm, as shown in the diagram. When the coil is connected to a battery (which is not shown in the diagram), the compass deflects 18 degrees to the East. will 1r 'W (In at.- _ ,"" .-—- 5‘: f \ \. . \ _’_.‘ l i / I H (m if!" a (a: 6 pts) At each of the three locations marked 1, 2, and 3, draw an arrow representing the direction of the magnetic field due to the coil at that location. Draw the arrows to the same scale, in the sense that a longer arrow represents a larger magnitude of magnetic field. , _ I . - ' .r' I. II " u.- _.-.--".'I" .L’K?‘ (b: 19 pts) What is the magnitude of the conventional current running through the coil? If you make any approximations, state them. Show all of your work. .I r - ,- ,I l.l.l,l “I, “I? —- flu 51“” __.——.I— E— . . ,- J._ ...
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test2-solutions-2212p-f07 (2) - Problem 1 (25 pts) A thin...

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