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sp09test1s - Question 1[8 points I The figure shows a...

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Unformatted text preview: Question 1 [8 points] . _ I . The figure shows a central particle of charge —2q, stirrounded by two circular rings of charged particles. The radii of the rings are r and R, as shown. (i) (4 pts) What is the magnitude of the net electrostatic force on the central particle doe to the other particles? Circle the right answer. Attract-4W.-. fete . ALL chm ,3 (a) 4kq/Rz (b) 4kq2/R2 ((LctceL ewe/st— _* LI? 617;” EH“? ECHDW‘ ‘ (c) 8kq/R2 63mm i ( ' ' P 7 L“ 7f“ {2. 2 (d) 8kq2/R2 R (6) zero (ii) (4 pts) What is the direction of the net electrostatic force on the central particle due to the other particles? (circle the right answer): (a) rightward (b) upward 7 ‘Iliuq d) downWard (3) rec is zero, no direction ....1...-—,-.-,....W...y w:warez-mnew»:xwwxf<msw,:mWmm-WWW—t“WV—qwmmw.wl.w.»fimw.mmmarrow Problem 1 [17 points] The figure shows two point charges q, = +4Q and q2 = “Q which are held at separation L 7 on an x—axis. . (i) (4 pts) Where on the x—axis can a charge q3 = —Q be placed so that it is in equilibrium? 7v”) (Circle the right answer) (a)To the left of g} (b) Between .511 and q2 (c) To the right of qz ' (ii) (3 pts) Briefly explain your answer in (i) a NLLS t" 1m: F if like?” M“ “f; film/w" lying/{gm CL’E/‘v’éfi ( a‘ :» 1” big ) U UU ‘ . t l: ‘ Hut“, [fl oLLf'glciq CLtAfdg 5 56.65991,er 3ft g m W“ £35an 3 (iii) (10 pts) Give an expression for the x—coordinate of this point, in terin‘s of L: “ €49?“ 5r L112 Fag ; fr32. (1) (may : d; 2 ‘ ‘2 (all: LMQ w gig up” : Ci‘OL PM 1 a a,» gif cit—awry) : aka; 3% —~ lLol «- L2 e0 +24- :‘ QLZ’L’ 3‘93} 5: + L is“ oi ‘ g "m a "W e L 9 “g: : 3 4—)?“ [L {s fasé‘r/v've: 3:7 Dief‘m'txmq_ M”? So fir-CoMOUI/‘alfi [A a amt — 2_L_ i M Question 2 [8 points] _ Figure (a) shows a plastic rod which has charge —Q uniformly spread along its length. In Figures (b), (c), and (d) more plastic rods are added to form sides of a square, each rod has the same negative charge —Q. The point P is at the center of the square. (i) (3 pts) Indicate the direction of the electric field at point P, for figure (c) (circle the right answer: Q / ‘— (ii) (5 pts) Rank the scenarios according to the magnitude of the electric field at point P (circle the right answer): n>m>n>nl :&=n>m>m MMe m>a=a>a apa>m>m EL :0 J E“ :— EC ICLCoL flow 0% §L°L€ Eb (wood begun: fad?“ “M mm»mml1-.-vwwflwmwwm..Ww,MW4wmfimmmwmmmy.mmmm.w.mw.m..mnw« Problem 2 [17 points] An electric dipole, with equal and oppOsite charges of magnitude 5.1 JuCthat are separated by 450 nm, is located in a uniform electric field of magnitude 10 MC. The dipole is initially held at 30° with respect to the electric field, as indicated in the figure: (a) (4 pts) Calculate the magnitude of the electric dipole moment: 2 - 3 - in"; Cwl -———_.___ -——__.___‘ IF) “Vi *— 94-«3’95 .og-D.m"iw : (b) (3 pts) If the dipole were not held in place, in which direction would it rotate? Answer with words or indicate on the figure. coda/aim (c) (10 pts) Instead, the dipole is rotated from an angle of 30° to an angle of 115°. Calculate the change in the potential energy of the dipole. LL {acreage} I ski-{e M cut fiUflEMJf’ who—L Ct' 0Jde 1'13 ()0. {ML " Hf ’ Vi: _ _‘ 13G (05 “in .- (r- FLTcos 30“) 5 FE ( ~c05llS'D + Co.) goo) ,N ' a. 360 234041 Cm- (DE - ( .«(GSHS 4(05 J a 2.011» ‘m’W —"_...._""_———'-—-'-—"' Question 3 [10 points] A11 isolated conductor of arbitrary shape has a net charge of +10 MC. Inside the conductor is a cavity within which isa point charge q = +3.0 pC. (i) (5 pts) What is the charge on the wall of the cavity? Circle the right answer. +3.0 yC “3.0 cc +10 QC —10 9C +13 uC (ii) (5 pts) What is the charge on the outer surface of the conductor? Circle the right answer: +3.0 pC —3.0 11C (i) (Aw: Gauss‘ (AMJNU'LL swine jvoi’ Jade fondch-iij mic/1&1 +10 pC +7 MC ’3 '3 ewe 2 5e§t=abr 2.0 5&(9 6 “r0 waotq mefip So ‘7MQ : firm/q- %?LLW\e_/- :0 fl fi—rofi i' 5 ,3 g‘x‘war Problem 3 [17 points] The figure shows (sections of) two very large conducting plates which have equal and opposite charge densities. A neon nucleus of charge q = +1.6 x 10'18 C and mass m = 3.4 x 10'25 kg-is at rest in between the two plates, because the "electrostatic force exactly balances the gravitational force. The electric field between the plates is uniform and is not altered by the presence of the neon nucleus. (a) (5 pts) Calculate the magnitude of the electric field between the plates: '5, ', C-n' 7 2 Eg- aeriom' Wivléz 4m -'— ’5' E z .e - m ' U” C . '—'—'_‘-—--. (b) (7 pts) Calculate the surface charge density on each of the plates: 0" . (3 r FCCoL frauds COL/Wch (3' e 50 I 00 Lure 6‘ {.5 [Wg ob ayaaat i? fem -t M .— FCAIflg Safwatecy U— : 80L: — MIL how: 40‘: Rite“. Hial— 2 all). C an}; accouud— becwe 7g“. ; KEY-[D NML I C O'Hte/ flak fwd/L5 “a CAMP ’% , lfi'lo'? A? m Lama ) (c) (5 pts) What is the magnitude of the electric field below the bottom plate: if“; dwarf. 0M Sic/h limit amine t“ - PM E" {,0 oun'k’taf CMMDF Fatal-10,241 (omothcHU We”)k Marge (‘5 . M0 CW0” cu 71h Oval-SEQ of. faks‘ Question 4 [10 points] When an electron moves from A to B along the electric field line in the figure below, the electric field does +3.20 3:1049 I of work on it. - . . ' . - , Electric (1) (4pts.) What IS the eIectnc potential dlfference VB— VA? fieid a) 0 V c) —2 V (1) None of the above are even approximately correct ,V MW) L1 McKee/t ' of L? #aLMHJ .435 __ '- Wfictd .. AV " ? a ' —mwimc "TZV (ii) (3pts.)What is the electn'c potential difference VB - VC? , ’ v c) ~2 V (1) None of the above are even approximately correct (iii) (3pts.) What is the electric potential difference VA— Vc? a) UV A“ E: b) ' n ‘ one of the above are even approximately correct Equipotentials B, C Du jam/Lg Q%m£fo&mbrq( swing \Q’W.Q V "V t *%Y942) Problem 4 [13 points] _ Consider a point charge q = 3.0 11C, point A at distance d1 = 5.0 cm from q, and point B at distance dz = 25 cm. ' l dz - (i) (4 pts.) Calculate the electric potential at point A, relative to V = 0 at infinity: i 4, NM aow’QC ' ' Vfis k l -—~ same cl'm e g'é‘iv (ii) (5 pts) If A and B are opposite to each other as shown in figure (a), what is the electric potential difference VA — VB? I 9L V/r’ve F” VA: d at; a, mm? 3.0 It)qu = ’- glficl'lo CL 2‘5.to’?'M-4 (iii) (4 pts.) What is the electric potential difference VA — VB, if A and B are located as in figure (b)? 7 game v AL'SIEMLQJ aft Sol/L the .5an ...
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