WB_Solution_Ch30

WB_Solution_Ch30 - Potential and Field 30.1 Connecting...

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Unformatted text preview: Potential and Field 30.1 Connecting Potential and Field 1. The top graph shows the x-component of E as a function of x. Ex (Wm) On the axes below the graph, draw the graph of V versus x in this same region of Space. Let V: O V at x = O m. Include an 100 appropriate vertical scale. (Hint: Integration is the area under the curve.) 3. w AV: flg‘ExflkX o x(m) O M 0 l 2 V(V) The, aware fialJ is are. macaw o'P fie 510,02 610 H26. x011} V V6. X 1 % ~— 9.00 / ‘ shire z -—[oo % 2. 21. Suppose that L7? = 5 Vim throughout some region of space. Can you conclude that V: 0 V in this region? Explain. N0. Bot-f yam can cma/ua/e #4} 4V :0 V—— +haf “Hit: looren'fia/ [5 “0% diary/L7 I}: 711147! Ara/9;, 075' 9/24“. b. Suppose that V: 0 V throughout some region of space. Can you conclude that E = 5 Wm in this region? Explain. yes. 49 {0:43 as V: caes+m71 in Me. r7152: of Space 441% 5:0 EzaAV __-—u- 5 30—1 30-2 c H A PT E R 30 - Potential and Field 30.2 Finding the Electric Field from the Potential 3. The top graph on the right shows the electric potential as a WV) function of x. On the axes below the graph, draw the graph of Ex versus x in this same region of Space. f; [/11 consign)" in 6t. Pei/01¢ ‘Hleu [kl/=0 aha! chr‘effire ELO it/So 00 1 mm) 100 [\J Ex (Wm) M Mai rfjlbu- 4. For each contour map: i. Estimate the electric fields E; and Eb at points a and b. Don’t forget that E is a vector. Show how you made your estimate. ii. Draw electric field vectors on top of the contour map. a_ DIV 101V zirv solv 401V fig: ugly-L10!- s a e a a As "m “‘ 1 a 1 : e: b 1 a v l A l I l A l _. _ a at i a 55:, 5 EV '0 "" l i I l l x 0m 1m 2m 3m 4m b _ 01V 10:"; 7(}:V 301V 40:" V... o V = 5 y— ; : : : : E: aim—0'“ h“ t a I I b | a I I I Ovfla‘ov... V ,4: . s M4 _ —g\0._ : E : :Eb: : Eb: Hm 3m W I o_ l I I I I I l l l x 0m 1m 2m 3m 4m Th6 Ml'nus Sle’I In 7’41?» EBMQZI'IIOV} means 7";1‘14' ‘HIe elect-rte fie;le V€o+0r [jolt-1+5 “Jaw” h“//” on “HIE, Cflnrour Mot/o- Potential and Field - CHAPTER 30 30-3 5. The top graph shows EJc versus x for an electric field that is parallel to the x—axis. a. Draw the graph of V versus x in this region of space. Let V: O V at x = 0 In. Add an appropriate scale on the vertical axis. (Hint: Integration is the area under the curve.) b. Draw a contour map above the x—axis on the right. Space your equipotential lines every 20 volts and label each equipotential line. c. Draw electric field vectors on top of the contour map. Exw/m) V: o V V: 30 v 1/:er V vséov V230 l/ 40 : l 20 ‘ I I l Hp 4:——.=—5 o x (m) l J- 51'- l “’1 I 0m 1m 2m 3m 6. Draw the electric field vectors at the dots on this contour map. The length of each vector should be preportional to the field strength at that point. 7. Draw the electric field vectors at the dots on this contour map. The length of each vector should be proportional to the field strength at that point. x x ,0“ “I” ,-—_fi x —1ov I I ’ ‘ z ‘ r a" ’ \ —20V " I I \ ’1 \ I .r I —. ‘..__- ,- -30V \ \ +9 I, M 0 I, _4¢r_ov ‘5 ‘ e." l I \ | \ \ I I r v' r. z ’— s g \ x ‘ ‘ l\,’ ‘N " / ,’ ’ \ \ ‘ \ I , / \ - _,_ _. , z \ ._ 30—4 CHAPTER 30 - Potential and Field 8. Rank in order, from largest to smallest, the electric field 0v strengths E1, E2, E3, and E4 at the four labeled points. 10V ,\ E }, ‘IOV Order: E3 > El I a "2035‘ \\ i I; "—go_v_‘\ . {I} \\\ x l ,1. 2/ \\\ Explanatlon: , .—-~ \w r ,.-—, \ 77m clear-rte field” 51935974! ’5 74 4g?) ‘2 'I r' 7:46» l4 ‘- {atjasi' in H6 Fair-on where 7%; x ,1 x I, I P0+6I77LIQU /II:LC~5 an: G/OjeS‘lL “‘~~—" flaw-er“. / § 9. For each of the figures below, is this a physically possible potential map if there are no free charges in this region of space? If so, draw an electric field line diagram on t0p of the potential map. If not, why not? ' a. . . I /’:/"0V b' ::\ MO. I:’; 10V ~ \ ” \xx‘ ”// ‘CQK ~ 10V rag” ‘:\\\”‘~_ 0" xx“? \ \ ———' I’ I \ \ "-—--"' I’ I \.‘ \ Kl»; \\ \\‘ I, I, \ I \ \ ’ .l l ‘\ I ’ I \\ I, l l \ x I | x ’ ' —10v: [>1 t—IOV 0v: [>1 rev 1 ,’ \x 1I f ” \‘\ ‘ I} ail Xx f! r” x \‘ I \ \ n‘ l \ \ r _ —__ \ I .""""-~- \\ 41:3’ 10v “(i-3:} Iii/2”” 0" “£53 I}, XS: 0v 7’7 \S“ 10v 5, '5 N34. pogstljtlmit ts. "dunnleer loom We W V ,ewoimm. “Mu CnnWadid-s N 4nd: W Jtlne. Gem dime—km We be bum); SPetiieoL- Cd: end/x a swat. 10. The figure shows an elec 'c held diagram. Dotted lines 1 and 2 are two Surfaces in space, not physical objects. a. Is the electric potential at point a higher than, lower than, or equal to the electric potential at point b? Explain. The elec'l'rt'c field“ vac/"ar- pal-n+5 +0Way‘d Acct/Basin fo7lw+flafi flareFore. Vat > b. b. Rankin order, from largest to smallest, the potential differences AVa , AVcd, and AVef. Order: 41/41; > A Vcd > 4 V8! Explanation: AV: *EAS TAe minus 591') reverses 4335 4 4 Scot 4 4 Se; +53 ,nézm¢/,3Ly alfremho'n. c. Is surface 1 an cquipotential surface? What about surface 2? Explain why or why not. >435 Sum-Face / 1‘5 an egwkm‘emL/ci/ jar-face because {7" {‘5 perpendtch/ar +0 #1,: alco+rfc 795/} tree/firs, Surface 0? f5 not per/oewdrcw/ar‘ 30 ff 13 170+ cm 6%W‘porcmL/ér/ surface. Potential and Field - {7 H A pr E R 30 30-5 30.3 A Conductor in Electrostatic Equilibrium 11. The figure shows a negatively charged electroscope. The gold leaf stands away from the rigid metal post. Is the electric potential of the leaf higher than, lower than, or equal to the potential of the post? Explain. E aim} When 61 canalbte‘hr [.5 H": 6/30'?£1’05+¢7l(él eguili'br-ittml Ha: “ha confide/For 1's 6L7L Has 5QM£ [notary-hit /. 12. Two metal spheres are connected by a metal wire that has a switch Sphere 1 in the middle. Initially the switch is open. Sphere 1, with the larger radius, is given a positive charge. Sphere 2, with the smaller radius, is neutral. Then the switch is closed. Afterward, sphere 1 has charge Q1, is at potential V1, and the electric field strength at its surface is E1. The values for Sphere 2 are Q2, V2, and E2. a. Is V1 larger than, smaller than, or equal to V2? Explain. Switch V, = Va Eo-Hl Sphere 5 anal Hie wma become one can duoflr at(/ m" Jae. 54M£ po7Len+12L/- b. Is Q1 larger than, smaller than, or equal to Q2? Explain. (P; > (D; VIZV‘?~ Lemmas; 94:9; we raqaxPz. LHTEe YKt LIT-Ea Y5 Y] V2 (3. 13 E1 larger than, smaller than, or equal to E2? Explain. E! 4 E; g, I $— Ea—L‘ (DR was we a la. 13. The figure shows a hollow metal shell. A negatively charged rod touches the top of the sphere, transferring charge to the shell. Then the rod is removed. a. Show on the figure the equilibrium distribution of charge. b. Draw the electric field diagram. NOTE? C/mrjes Shoulol have been Shawn a5 Marja-Him! 30—6 CHAPTER 30 - Potential and Field 14. The figure shows two flat metal electrodes that are held at potentials of 100 V and 0 V. a. Sketch a reasonable approximation of the 20 V, 40 V, 60 V, and 80 V equipotential lines. b. Draw enough electric field lines to indicate the shape of the electric field. Potential and Field - CHAPTER 30 30-7 30.4 Sources of Potential 30.5 Connecting Potential and Current 15. The figure shows two 3 V batteries with metal wires attached to each end. Points a and c are inside the wire. Point b is inside the battery. For each figure: - What are the potential differences Alt/12, AV23, All/34, and AVM? _ fl - Does the electric field at a, b, and c point left, right, up, or down? Or is E = 0? a. b. AVH=_MAV23=LL Alfig=flmfzg=fl AV34=_0_IL M34: 3 V At/34mflL zit/14: 3 V Eamabmacm amama ism 16. A continuous metal wire connects the two ends of a 3 V battery with a a? V a rectangular loop. The negative terminal of the battery has been 3 V- chosen as the point where V: 0 V. ‘ 1 a. Looate and label the approximate points along the wire where 3 v V=3V,V=2V,andV=lV. b. Points a and c are inside the wire. Point b is insidethe battery. Does the electric field at a, b, and c point left, right, up, or down? Or is E = 0? Ea WIL— Eb M E _Le_£i"_ c. Estimate the value of AV14. Explain how you did so. A 3?, ". 41/14 {‘5’ Q5 V fieWw Ema :2 RAT/“1L3 and I—I'thre [5 a emsmnr‘, Me (Wm/M71! ILL par—eafia/ is bawdy r‘elm’eaf 7‘0 ‘Hve, pas/flit»: a/mjflrc WIr‘c. d. In moving through the wire from point 2 to point 3, does the potential increase, decrease, or not change? If the potential changes, by how much does it change? flé pov‘env‘ra/ decreasej and Me Jae/“eases IS Linear m}; 3/4“: rig/Eyémce flare/3% 41'101'4146/ Me LUI-f‘en : —3 V 30-8 CH A PT ER 30 - Potential and Field e. In moving through the battery from point 2 to point 3, does the potential increase, decrease, or not change? If the potential changes, by how much does it change? Th6 Foffin‘r‘rh/ decreases 6/ 5 f. In moving all the way around the loop in a clockwise direction, starting from point 2 and ending at point 2, is the net change in the potential positive, negative, or zero? Zero. 4V3 = *3 l/ and 4%; = +3 V 17. a. Which direction—clockwise or counterclockwise—does an electron travel through the wire? Explain. CDMHTL'Cfa/é’d (Ia/tie. 7712 6/60er0» M'// M rape/[ea] by 41:6 nejaf'a'rc &/w%rad£ affie. barbflry and Wavr’w’ 74’ He posh‘nfe decfi’vfl/f- b. Does an electron’s electric potential energy increase, decrease, or stay the . . v . same as it moves through the Wire. Explain. D e 0 False 5‘ I4 C/nge always More; /}’I “Hie al/réamn o/decrcaS/Lj fozleafia/ 611eij as if fat/'45 Krhefid C. If you answered “decreaSe” in part b, where does the energy go? If you answered “increase” in part b, where does the energy come from? 778, an my); 3,065 ink “#Afl /’i0r€¢56 ’1‘? 7%9 k’fl-efic'fiharjy H5 7% e elemérm am/ Hereng /f]7(‘a an 1}, 3,34% M‘ ,‘fj— fpe ed - d. Which way—up or down—does an electron move through the battery? Explain. Down. 7716 ahcméa/ males; liq He. alarm/y 71w Fgeqrafe 7%: arm/36; by May/Ly flas‘n‘w'c céarjes L70 and hfiafl’h: Marge: do MM - e. Does an electron’s electric potential energy increase, decrease, or stay the same as it moves through the battery? Explain I)? wear Se . fie. oé <5!" 1 549/ recto/7’75» doeS work +0 Safaris/1‘15 7%: wages. as +43 &/eo7£7~014 A} ,0“ng .f—oward J43 nejafln eJeUfrode/IrL: Pofchrre/meij ‘lr’lCr-ggzjes. f. If you answered “decrease” in part e, where does the energy go? If you answered “increase” in part e, where does the energy come from? We enerjy 0021466 74W” #6 WWI? Ila/re— ”: #6— almrgw 6/ fie Meméa/ rewfim ll} 7%.? e/eméeéfls. Potential and Field - CHAPTER 30 30-9 18. The wires below are all made of the same material. Rank in order, from largest to smallest, the resistances R1 to R5 of these wires. Explanation: Hot #4, ewe-M: é=flzie 74“ M“ (Mr flag/{2L}: (25’, fez/(54‘) : r6 rm?“ (“WW/OR 19. A wire is connected to the terminals of a 6 V battery. What is the potential difference AVends between the ends of the wire, and what is the current I through the wire, if the wire has the following resistances: a.R=1.Q AVmEA I: b.R=ZQ AV,,d,=—é._\/_ 1:15— c.R=3§; AVends=_é___L I=..3:...B_ d.R=6§2 AVends=_(o_L I: l 20. The two circuits use identical batteries and wires of equal diameters. Rank in order, from largest to smallest, the currents 11, I2, 13, and I4 at points 1 to 4. Order: I: :— Ia > I3 I: Z Explanati on: 'Hrcn {7’3 resi'shme i5 jmqfier (X: f?) mm/ 4’Acr67gr’c 7%6 dunner/27‘ /5 5mw//eh/_Z—___ 30—10 CHAPTER 30 - Potential and Field 21. The two circuits use identical batteries and wires of equal diameters. Rank in order, from largest to smallest, the currents 11 to I7 at points 1 to 7. Order: 14:: :. 1:21;; Explanation: ConServw/‘fim 070 curremL refumés I,;:z;:;l}, 7A6 (LOW/Nean 1}: 85:04 wring Is I-tAlf/K. 77m pair-é.) are {dark/€41 and! hare fire acme F¢5}57Lqflce.. 71¢ I’MfiQ/‘(éj 44'“- 1%6 Same po'femfié/ aflflérmca. Wervfire 1:5: Fran Coqserr/wfiaio 078 currem’j I4? 1—4315 +I6 ,JCWULS ILI. (mot Is} are. m \wgcr’c flLfl-WS. 22. Which, if any, of these statements are true? (More than one may be mie’j i. A battery supplies the energy to a circuit. ii. A battery is a source of potential difference. The potential difference between the terminals of the battery is always the same. iii. A battery is a source of current. The current leaving the battery is always the same. Explain your choice or choices. '11. True. The chemical Pear/+2071th ‘I’fie fileolerl/WLCJ Salaamfif 4’)“; pan-711% ans/nagahife ohar‘jes. flz's Gram/‘65 at Fay‘em‘xé/ 0,1.7flf81’W/I66— 7/16 éhflfjw fi/éfl/Vh I.” ‘Me Cir-cm? Adi/C, 5M;ng dte *0 441:3 pdrem‘réz/d/flermce- i5. I+ IS +mte abhou’ a bafieer}, [5 {Source (SF/aa/eh‘fli/ aiaafewhce- Eat-F Hie F0%6n%/a/ dr'fiéraace {3 WWW" fie game ONLY 5r an I'dm/ AevL—I‘ery. I“ “ "e‘l/ bawzery 'Hlere are energy /05535 50 #976 firmlg‘a/ W/7Laje LS 110+ a/woLys #1“: Same. [Li- Fa/S'C- 7716 amped /€QV{-I"7 fie, {ad/My #900106 Lt/Qoiq 441?, FBSIS'ILfihce, A}? He Clkduilf Potential andField - CHAPTER 30 30-11 30.6 Capacitance and Capacitors 30.7 The Energy Stored in a Capacitor 23. A parallel—plate capacitor with plate separation d is connected to a battery that has potential difference All/bat. Without breaking any of the connections, insulating handles are used to increase the plate separation to 261’. Mb“ a. Does the potential difference AVG change as the separation increases? If so, by what factor? If not= why not? No if doe; “ML (Jimmie because ‘7p/7C afipgffl/af—c {3 5767/ Camacho! 7% fie yearn/é, e/acvfrao/c 0,5 71¢“; 947%? Md He [)0 HM [4161711 a; 7%: Mare/ne/wmde. b. Does the capacitance change? If so, by what factor? If not, why not? Yefi. C: 30 tulle/p; 711’“, phi-dc Se/aara‘héw /;5 death/mi #76 OfiflaG/l/fifide decreases 57 at wram‘or 0/07. c. Does the capacitor charge Q change? If so, by what factor? If not, why not? X95. I4 also decreases by a. flag/17v a/ o?- .“ zifil/c, d. As the plates are being pulled apart, does current flow cw, ccw, or not at all? Explain. 7716 ohm-ye p/ow'j ccw. Pas/EL/V‘a CA4.ch An: added 4:9 ‘Hre mejm’vize ,a/mLe 1% decrease “He— h-C/J’ cpl/large on ache. Cafamolflr. 24. For the capacitor shown, the potential difference AVab between points a and b is b. 6-sin30° V. c. 6/sin30° V. d. 6-tan30° V. e. 6-cos30° V. f. 6fc0330° V. Explain your choice. The en-H‘ne, r'o/o ,o/cw‘c /.5 “’L VL/H’i SflMCflw‘em/‘ré/ 45 70176 pag,'-h.fe electron/fl 0f vbfle é4#er/ [5 V) ahfil “Hie 507L413”: Mark [-5 i071” “He same/gafmfié/ (/15 441e, wager/ire else/trade (0 1/). PM}; aa/Ma'far plach [s an aim/290%9n7’74/ airfares. 30-12 CH A PTE R 30 - Potential and Field 25. Rank in order, from largest to smallest, the potential differences (AVG); to (Al/(3)4 of these four capacitors. Q Q ZQ + : «viii: —Q -Q —2g 1 2 Order: (Al/5)} > Vc), :7— > (Al/Cr); Explanation: (Al/CL.— g (43%),: 5%; 544%.), (4mg: 23-19: flflll/e), (Al/ell: ESE = (AUG)! 26. Light bulbs can be used to indicate current flow in a circuit. The brightness of a bulb is proportional to the amount of current passing through it. The figure shows a battery, a switch, two light bulbs, and a capacitor that is initially uncharged. a. Immediately after the switch is closed, are either or both bulbs glowing? Explain. 50% bulbs are glow/(:1; get-WSW? Curmhf ls f/owm'j In [907% (mid as file aa/oaolror {s ée/hj M4964. b. If both bulbs are glowing, which is brighter? Or are they equally bright? Explain. They are, egcwtl/y Weigh” 5.3061045; J’Ae cur/igan 4m: 7%: 50W”- fli’i Mme amen/«7L Oily/055%.; oharfle x3 //awn'qj 0745 *Me 190%!» p/m‘e and we: 7‘68 a/Jper p/mé,’ x}; 7%? 5mm flag. c. For any bulb (A or B or both) that lights up immediately after the switch is closed, does its brightness increase with time, decrease with time, or remain unchanged? Explain. :Dfs irigév‘ness decreases w/fl 794m. A; #3, 011 Wye m flép/wr’re: mereawes/ 7%.»: [a 7Lee7L/é/ dlsflferences 451/7 -7%g wife Jeanaase 4/70/ 50 £065 ‘f’fje curraml’ If") M6 WI}? - Potential and Field - CHAPTER 30 30—13 27. Each capacitor in the circuits below has capacitance C. What is the equivalent capacitance of the group of capacitors? a. £1, Ceq=__L aHi 11 5‘1 Cm: JG 1; E d. Ceq=.___:7 Lil Cm: 3Q —EF7 aHHt 28. Rank in order, from largest to Smallest, the equivalent capacitances (Ceqh to (CECIL; of these four groups of capacitors. Z C CH fiHHt M Mr H Order; (Caz).z >(C63),f >(Ceg)3 >{C7>; Explanation: (Ceglf (“cl Wile 4-: éC (C‘eg)l:C+C+C:3C {C(53)}: 65:5 4’5) .1: (Caillrt gr: +C; 30-14 CHAPTER 30 - Potential and Field 29. Rank in order, from largest to smallest, the energies (UC)1 to (UC)4 stored in each of these T T T T order: (bide > (M6)! > (“(1)3 > ((49%; (/{l : C(Al/e)1 u;:—L(;ILC)(3AV9)£ 02”! as = 9% (016) (ewe/lg: "5“ 0/51 :. i(4c)Al/)l: g- M/ AV fic AV ...
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WB_Solution_Ch30 - Potential and Field 30.1 Connecting...

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