phys133 Electromagnetism Exam1 Saunders Spring04 - .A A...

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Unformatted text preview: ,\ .A A ’ Name & Section- Saunders Physics 133 -- Electromagnetism --Exam 1 ° You must do and show/explain your own work. Partial credit will be awarded. However, a correct answer without explanatory material will not receive full credit. 0 Clearly indicate your final result with a box or circle. 0 If you need more space go onto the back and indicate "OVER". Possibly helpful information: NOTE: These formulae just give the magnitudes. You need to determine the direction. F =qE point: E Kq , F — Kq‘qz =_2 point points - r2 - - . _ Q . . _ g lmear charge dens1ty. A - I surface charge den31ty. n — A “infinite” line: Eline = gK—A “infinite” plane: Eplane = '—n-— r 280 ideal capacitor: E = fl— £0 4): = :EAcos(0) Gauss’s Law: 4): = Q‘" 80 surface area of a sphere: 4J'L’r2 , K = 1 4Jt80 £0 = 8.85x10'12C2/(Nm2) e=1.6x 10-‘9c, K=9x109Nm2/C2 V Page 1 of’7 kaS 4/17/05 133505x1.doc Q1. (20 pts) Point charges are at three corners of a square of _ 1 side a. q1= - q, q2= +4q, q3= - q. A 1g pith ball with charge q4=-lnC is placed at point P at the other comer. 1 (a) (Spts) On the diagram indicate, using arrows, the direction and relative magnitude of the force acting on the pith ball at point P due to each charge. (You should show 3 vectors at P.) t\§° 3 “ ” "‘9 LI 1 .. 1 (b) (10pts) Determine the net force (in component form, i.e. i and j) experienced by the pith ball, if q=1nC and a=5cm. ‘7. t we” F : Milli.“ _ (Elam) .: 3.5VID"" Ng‘ / r m 9 “rah-z ‘ o.os ~ 6,»? 3 : (“’“lP‘W’Dqll‘ww : mwfl K mm“ (0‘ 0§ 52.31 . '._ l f; w % 2 mm a: my mm mm _ ..t / — 2 {Wm - _ év 10 N I) a ' (o .6331 4 g. -‘7 ‘\ a = - - .w )t + {emf : “7.2xronws “6°? -— 7-25Jn45 3‘ FM? (1pm 5 ‘0 *9-5‘0'3wopys _ m g 3M Io - ’- e‘io‘lxr («Snow/Io J .3 A. 6 a 45m : ammo N2 + goamo‘ M? (c) (Spts) Determine the magnitude and direction of the initial acceleration experienced by the K pith ball. You can specify the direction by drawing a diagram and calculating the appropriate angle (as I did in class). m Mu.- » mafier b a.» xwwm'l Wm» munwu m; ‘ , 1X GM ‘9 (empowd‘g A/«L, g A m a ' ’— 4 P ql 59 ” .(S‘Oqsxmday‘a- (3,OQIWO“>~Z I (o. (DO/£55“ / L4" 3 7WD“6 A! 3. (mom 9%,) a kfcs 4/17/05 133505xl.doc Page 2 of 7 /T\ y Q2. (20 pts) A thin rod (length L) with total charge Q (>0) is situated E between y=a and y=b on the +y-axis. We are interested in the electric b I field on the x—axis at some point P=(xo,0). m" (a) (8 pts) Write an expression for the x and y components of the electric field at P due to a generic chunk of charge dq located at a , Ag ‘ at position (0,y) on the rod? $0M V f :W" g, f a? ' A x .____.._._._ E : ’4 A ,_r (b) (12 pts) Now write an expression for the total electric field at P. These should be 2 integrals involving fie variable and constants in a form that could be looked up. Do not evaluate the integrals. is an ’3: Variables, _memmmmn u s W“ M b kfcs 4/17/05 133505xl.doc a K Page 3 of 7 Q3. (20 pts) We have a "large" sheet of plastic with a surface charge density n: +2710 on it. Nearby there is a “long” line charge with constant charge density 4.0. (a) (5 pts) On the “Side View” diagram indicate the approximate direction of the net electric field at “X”. ’1 mama “(3 25 gamma A «HA L Wang 4:; (fiance? bi N50434:“ 3d view Side View (b) (10 pts) What are the components of the electric field at “X”? (in terms of m, M, b, and constants) F‘ 3' ’Ef/IO‘M I“ (".2337 ” ” (watt) ‘ "2643‘ Elm Ea ’U‘l‘wz 7: Ex .. Y no / i 'é-o ‘ (c) (5 pts) A point charge (~q) is placed at “X” at rest. What is the force experienced by the point charge? kfcs 4/17/05 133505x1.doc Page 4 of 7 Q4. (20 pts) A 0. lg pith ball hangs by a thread in the center of an ideal parallel-plate capacitor. The capacitor plates are + 5.00m by 5.00m and are spaced 1cm apart. When the ball has + charge q = +10nC and the capacitor plates have charge :Q, + r q the ball hangs at a 30 angle. +Q + . + + + + + + <-—> lcm (a) (15 pts) What is the strength of the electric field in the capacitor? ‘5 v n”) :fo.°ooIE5‘)(fi.Df§_} E r 3 [lr?*)0‘\'/\/ ng‘N g” f L! )1 )O ' M£;Wm «w / é?) =0 T(*‘9.‘BWD“’N>+ 7.94870 1' agar/a '1 C 2.3%“ N -‘ 75.; a 76‘7" a RV mwmw Tramsm A! mu, WC / Q 15,: «:5; = wmwv “has 8’79-4- 1‘ paw”... r; s: w ~ )o’“5'A/ / (b) (Spts) What is the charge Q? _ a; A G _ MS?“ fl ’ T ‘ loos)? p.002é n N / G? I. 3 F :- Q 50 5"”! :0-0025m1>($’8§4/0./2 / O . P, .i r 1 a : @MY’ 0002551 new > Shiv”? Q r / l3 7* w” "’ C log , - 5 }%fl kaS 4/17/05 133505xl.doc ' Page 5 of7 Q5. (20 pts) A point charge (- 4Q) is at the center of a hollow, conducting, thick spherical shell (inner radius a, outer radius b) that \I/ has its own net charge (+2Q). I (a) (15 pts) Using Gauss’s Law determine the electric field ' K everywhere, r<a, a<r<b, b<r, put your answers in the table. Be ‘ecp sure to give magnitude/direction: e. g.“ 1 %, outward” or similar. 8fl80 r FOIL Ail. CALCLM A"?! 0N5 : ' a» ~ 941' »- F E 5 9L ( « é” " .JA so éo <1 (La 04 : ,qa Egon: "uG‘QQ f”: M M 2' ~ 2 Q Am :2..- arr—o Wm M ‘ CE 5: rifle I 4‘ (A :0 9869 i. LEM N417?“ ea 0 ekd'V'4~ '6‘ ‘ ----’1’" w awn/:66 / "SIM a (anch-a‘r 'z‘m’ é" / ‘/ (b) (5 pts) What is the charge on the outer surface of the spherical shell? Explain your reasoning. (1:)? ANN (S a clan): a? “VG pm 444.9“, Pavel (Mam-.32.) 4M was/[£3 Suffifinum (i Jive gl‘efl HAL/[5+ have a thaw», 016 +qQ 56 5" "l is ”‘ 54H" W“””’""‘""“ Wag/acme, +24. awlv Surthu {VT-‘Ol’wyl- lam/e ‘1 CL away-k a“? 0% AM SM” m5 4+ ‘4‘. ,— kfcs4/17/05133505x1.doc 2‘52 (W3 “m "' 2Q) SEE WCfl/ggtnm “2G 41: firearm a. m-l- chargx ’ l ...
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