19.1 Electrical Potential Energy. Special Case 1. v B

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1 9. lectcl Potentl neg Specl Ce We elee tet chge between the plte o cpcto. Dung ome tme t moe om to B How e the ntl nd nl peed nd B elted? pp Sole th poblem b ung the concept o electcl potentl eneg B

2 9. lectcl Potentl neg P: lectcl Potentl neg o the tet chge nde the cpcto: wok done b ou gnt the electcl oce to moe the tet chge om the zeo P eeence pont to ptcul locton.e. P uncton o the locton o oce ou need to ppl to moe ound (lowl): pp pp pp Chooe the negte plte (hee ) to be the zeo P eeence pont

3 3 9. lectcl Potentl neg P: lectcl Potentl neg o the tet chge nde the cpcto: wok done b ou gnt the electcl oce to moe the tet chge om the zeo P eeence pont to ptcul locton.e. P uncton o the locton o pp oce ou need to ppl to moe ound (lowl): pp Reew : WORK done b contnt oce ( coθ ) W C, θ ngle between dplcement C nd P (W pp ) pp coθ But ( coθ ) etcl component o nd mgntude o pp : pp P C Chooe the negte plte (hee ) to be the zeo P eeence pont θ Th n mgn moement pp

4 4 9. lectcl Potentl neg P: lectcl Potentl neg o the tet chge nde the cpcto: wok done b ou gnt the electcl oce to moe the tet chge om the zeo P eeence pont to ptcul locton.e. P uncton o the locton o oce ou need to ppl to moe ound (lowl): ( coθ ) W C, θ ngle between dplcement pp nd P B (W pp ) B pp B coθ B Reew : WORK done b contnt oce But ( coθ B ) etcl component o B B nd mgntude o pp : pp P B B C C Chooe the negte plte (hee ) to be the zeo P eeence pont θ B Th n mgn moement pp pp B

5 9. lectcl Potentl neg P: lectcl Potentl neg o the tet chge nde the cpcto: wok done b ou gnt the electcl oce to moe the tet chge om the zeo P eeence pont to ptcul locton.e. P uncton o the locton o oce ou need to ppl to moe ound (lowl): pp pp pp pp Reew : WORK done b contnt oce ( coθ ) W C, θ ngle between dplcement C nd C Chooe the negte plte (hee ) to be the zeo P eeence pont B P (W pp ) pp coθ P B (W pp ) B pp B coθ B B P ( ) 5

9. lectcl Potentl neg We now nclude electc potentl eneg P pt o the

knetc eneg k Reew: Wok-neg Theoem: wok done on n object chnge n t

oce, Knetc eneg potentl eneg contnt O: K P.

6 9. lectcl Potentl neg We now nclude electc potentl eneg P pt o the totl eneg tht n object cn he: m Iω mgh P Tnlton knetc eneg Rottonl knetc eneg k Reew: Wok-neg Theoem: wok done on n object chnge n t knetc eneg W K, whee K½ m Lw o Coneton o neg: In the bence o dpte oce, Knetc eneg potentl eneg contnt O: K P... Gttonl potentl eneg ltc potentl eneg lectcl potentl eneg nd combnng thee two: W (P) P -P 6

7 9. lectcl Potentl neg Wok-neg Theoem Chnge n knetc eneg o the tet chge t moe unde the nluence o the cpcto electc eld om to B eul to the wok done b the electc eld K m W B B B m coθ ( B Th epeon n ld onl o contnt oce ) θ pp Coneton o neg In the bence o dpte oce (e.g. YOU, but ou e not ntectng wth the tem hee), the totl eneg KP coneed untt: K m B Note: B B W B ( P) B m ( m P Wok done BY the electc eld chnge n P om to B (P B ) B B P ) Chooe the negte plte (hee ) to be the zeo P eeence pont B 7

8 8 mple: (hozontl) pllel plte cpcto he the ollowng ttbute: e o plte: 4.5m Plte epton:.cm Q chge o Q.5µC plced on the top plte, nd Q on the bottom plte. poton (m.67-7 kg) h ntl eloct o.5 6 m/ n the hozontl decton when njected nto the gp. The njecton pont ectl hl the dtnce between the two plte. You m neglect gt. / () nd t nl peed t che nto the bottom plte. (b) nd the ngle φ between the nl eloct nd the noml to the bottom plte -Q φ

9 9 Q.5µC, 4.5m,.m, m.67-7 kg,.5 6 m/,.6-9 C nd (), nd (b)φ Q / -Q φ

10 Q.5µC, 4.5m,.m, m.67-7 kg,.5 6 m/,.6-9 C nd (), nd (b)φ Q / -Q φ φ

11 Q.5µC, 4.5m,.m, m.67-7 kg,.5 6 m/,.6-9 C nd (), nd (b)φ Q Conde wok done on the poton b the electc eld: W P σ ε 5.65 W 9.4 Q ε 5 6 (.6 W ( K) N/C 9 J (4.5 m C)(5.65 m (.5 )[8.85 m ( / ) 5 m( -6 C) C N/C)(.m) /(N m ) )... (wok - eneg theoem) / -Q φ W / m (W / m) (W / m) 6 6 (9.4 kg m () (.5 m/) 7.67 kg (b) n the ecto decompoton dgm o / ).83 6 m/ φ nφ φ n 6.5 m/ m/ φ 55.3 o

12 W STOPPD HR ON JN 3 TH NXT THR SLIDS R OR YOUR INORMTION ONLY

13 Q.5µC, 4.5m,.m, m.67-7 kg,.5 6 m/,.6-9 C nd (), nd (b)φ Method (): contnt downwd oce: me pojectle moton (Secton 3.3) umng the poton tt t (,) Hozontl njecton, The electceld puel n the decton,, whee / m / m t, Q ε t, t t (4.5 m It conenent hee to ole o the downwd cceleton : σ ε (.6 9 t t (.5 )[8.85 C)( N/C) /(N m 7 3 / m (9.4 N) /(.67 kg) 5.43 m/ Thee wee ectl the me lue we hd n the emple nolng njectng poton long on eb. Hee the njecton pependcul to C) C 9.4 N Q / - Q 5.65 ) 4 5 N/C φ 3

14 Q.5µC, 4.5m,.m, m.67-7 kg,.5 6 m/,.6-9 C nd (), nd (b)φ The poblem h mpled to : whee 5.43 Net : ole o tme t bottom plte :, 3 om pojectle moton : t t t, t, t ( m/ t whch the poton che nto the t t Q / - Q. m m/ 8 6 m/ )(.9 ).45 t m/ φ.5 6 m/, nd 6 6 () (.5 m/) (.45 m/) (b) n the ecto decompoton dgm o.83 6 m/ φ tnφ φ tn 6.5 m/ 6.45 m/ 55.3 o 4

15 Q.5µC, 4.5m,.m, m.67-7 kg,.5 6 m/,.6-9 C nd (), nd (b)φ Q The poblem h mpled to : whee, t, Net : ole o tme t bottom plte : 5.43 t, 3 m/ t whch the poton che nto the t / om pojectle moton : t t t ( t m/. m m/ )(.9 8 t.9 8 -Q ).45 6 m/ φ.5 6 m/, nd 6 6 () (.5 m/) (.45 m/) (b) n the ecto decompoton dgm o.83 6 m/ φ tnφ φ tn 6.5 m/ 6.45 m/ 55.3 o 5

16 9. lectcl Potentl neg Specl Ce P o tet chge n the electc eld o ouce chge : () men uncton o dtnce P( ) k ***Deton o () om () eue ntegl clculu lectc eld ceted b pont chge : (dgm dwn umng >) () Decton: pontng dectl w om t n pont. () Mgntude gen b Coulomb Lw ( ) k *** () () Th omul wok een one o both chge e negte 6

17 9. lectcl Potentl neg Totl Potentl eneg o tem o pont chge We tt wth thee pont chge:,, 3 k U P o, j U j k j j U U U3 U 3 k U U 3 3 k 3 3 The oell potentl eneg the mount o wok eued o n etenl gent to emble th et o chge th cn be done n deent w, o emple: () Bng n om (no cot), W (b) Bng n om : W U (c) Bng n 3 om : W 3 U 3 U 3 Totl W W W UU U 3 U 3 Cn do th n n ode nd obtn the SM eult tendng to N pont chge k N j U j j j k j j Thee e N(N-)/ dtnct p 7

18 9. The lectc Potentl Deence DINITION O LCTRIC POTNTIL The electc potentl t gen pont the electc potentl eneg o mll tet chge dded b the chge tel: V P o SI Unt o lectc Potentl: joule/coulomb olt (V) ( V ) B P o B V B V P o B W o B lectcl Potenetl Deence om to B deence, pe unt chge, o the P o tet chge WOULD HV om locton to locton B P k, V k k V ( ) B B P B k B, V B k B 8

19 9.3 The lectc Potentl Deence Ceted b Pont Chge 9 mple The Potentl o Pont Chge Ung zeo eeence potentl t nnt***, detemne the mount b whch pont chge o C lte the electc potentl t pot.m w when the chge () pote nd (b) negte.

20 9.3 The lectc Potentl Deence Ceted b Pont Chge mple The Potentl o Pont Chge Ung zeo eeence potentl t nnt***, detemne the mount b whch pont chge o C lte the electc potentl t pot.m w when the chge () pote nd (b) negte. () (b) V k 9 8 ( 8.99 N m C )( 4. C) 3 V V k. m 9 8 ( 8.99 N m C )( 4. C) 3 V. m *** In Ch. 6 ou lened tht the choce o the eeence zeo o gttonl potentl eneg bt. Th lo tue o P nd hence o the electc potentl V. The choce o zeo t nnt onl ld o collecton o pont chge, nd not o pllel plte cpcto o nnte we

21 9.3 The lectc Potentl Deence Ceted b Pont Chge W V W V W V... Σ(... coθ ) Σ( coθ )... mple The Totl lectc Potentl t locton nd B, nd the totl electc potentl.

22 9.3 The lectc Potentl Deence Ceted b Pont Chge You lened n chpte 6 tht the wok done b deent oce (o emple, hee, b the electc eld o deent pont chge) dd cl. dect coneuence, the totl electcl potentl lo the cl um o nddul potentl (o emple, thoe om deent pont chge: W V W V W V... Σ(... coθ ) Σ( coθ )... mple The Totl lectc Potentl t locton nd B, nd the totl electc potentl. k V V V k Sml (but DIRNT) eult o V B V V B ( 8.99 N m C )( 8. C) ( 8.99 N m C )( 8. C) 4 V. m.6 m ( 8.99 N m C )( 8. C) ( 8.99 N m C )( 8. C).4 m.4 m V

23 9.3 The lectc Potentl Deence Ceted b Pont Chge 3 mple Whee the Potentl eul to Zeo? Two pont chge e ed n plce. The pote chge nd the negte chge. On the lne tht pe though the chge, how mn plce e thee t whch the totl potentl zeo? Whee e the?

24 9.3 The lectc Potentl Deence Ceted b Pont Chge mple Whee the Potentl eul to Zeo? Two pont chge e ed n plce. The pote chge nd the negte chge. On the lne tht pe though the chge, how mn plce e thee t whch the totl potentl zeo? Whee e the? 4 ) (, 3 3 ) (, ) (, : 3ce k k V > < < < > < < < tneou oot: < md e not comptble

9.5 Cpcto nd Delectc pllel plte cpcto cont o two metl plte, one cng chge nd the othe cng chge. It common to ll the egon between the plte wth n electcll nultng ubtnce clled delectc.

25 9.5 Cpcto nd Delectc pllel plte cpcto cont o two metl plte, one cng chge nd the othe cng chge. It common to ll the egon between the plte wth n electcll nultng ubtnce clled delectc. cpcto dece degned to toe eneg nd chge..g. debllto cont o lge cpcto tht dchge cuent (low o chge) when the pddle e ppled to ptent In electcl ccut the oten e ued to tblze electc potentl 5

9.5 Cpcto nd Delectc TH RLTION BTWN CHRG ND POTNTIL DIRNC OR CPCITOR The mgntude o the chge n ech plce o the cpcto dectl popotonl to the mgntude o the

26 9.5 Cpcto nd Delectc TH RLTION BTWN CHRG ND POTNTIL DIRNC OR CPCITOR The mgntude o the chge n ech plce o the cpcto dectl popotonl to the mgntude o the potentl deence between the plte. CV The cpctnce C the popotonlt contnt. SI Unt o Cpctnce: coulomb/olt d () C/V C /J Memo d C V coulomb d olt nce Btn : Itl 6

27 9.5 Cpcto nd Delectc TH CPCITNC O PRLLL PLT CPCITOR Smplet ce: /cuum gp (no delectc ) V potentl deence om the to the plte (b th denton, V o cpcto lw pote) chge on the plte ( on the plte) e o the plte d plte epton/gp Note the deent notton ued b the tetbook o th ecton V d lectceld n cuum/ (downwd) : ( P) V ( V ) C C V W ε [ ( coθ ) ] Potentl deence between plte (ddng out σ ε, Hee the ubcpt ndcte the pecl ce o Chnge n potentl eneg o tet chge ( ) ε d d d ε, - V θ 8 cuum/ gp om - to : o ) : - Pllel plte cpcto lled wth cuum/ ε C C d 7

28 9.5 Cpcto nd Delectc mple: pllel plte cpcto he the ollowng ttbute: e o plte: 4.5m Plte epton: d.cm The gp lled wth nd t cpctnce C V d - 8

29 9.5 Cpcto nd Delectc mple: pllel plte cpcto he the ollowng ttbute: e o plte: 4.5m Plte epton: d.cm The gp lled wth nd t cpctnce C V d Pllel plte cpcto lled wth cuum/ ε d C C - C C [ C /(N m (. m).99 n )](4.5 m ) Note tht d () e lge cpctnce Th 4.5 m plte t. cm epton ge onl ~ n 9

30 3 Cpcto n eneg toge dece: It tke wok (.e. eneg) to chge up cpcto om zeo chge to (zeo potentl to V). V V W ( )V V/C The gue how cpcto t chge, potentl deence V (between the plte nd the plte). To ncee nd V, we moe mll mount o chge om the plte to the plte. Th eue wok done BY n etenl gent, GINST the electc eld: P WXT W (done b the electc eld) ( ) d ( ) V e o the hded tpe nv. gph

31 Cpcto n eneg toge dece: (contnued) V V neg U e o tngle W ( )V ½ V ½ /C V/C To chge cpcto to (, V) om (,), the totl mount o wok e encloed b the blue tngle, whch the eneg toed n the cpcto. neg U C but CV neg U CV 3

32 3 mple: Pllel plte cpcto e o plte: 4.5m Plte epton: d.cm Plte chge:.5µc The gp lled wth () nd the oltge (potentl deence) o the cpcto. (b) nd the eneg toed n th cpcto d -

5 () V C.99 (b) neg U CV / C 9 9 (.5 C 9 6.5 C 4.3 V 9.99 C / J 9 4 (.99 C / J)(.3 V) C) /(.99 9 ).

33 mple: Pllel plte cpcto e o plte: 4.5m Plte epton: d.cm Plte chge:.5µc The gp lled wth neg U C CV () nd the oltge (potentl deence) o the cpcto. (b) nd the eneg toed n th cpcto d.5 () V C.99 (b) neg U CV / C 9 9 (.5 C C 4.3 V 9.99 C / J 9 4 (.99 C / J)(.3 V) C) /(.99 9 ).7 J - pplcton: Tpcl debllto he bnk o cpcto chged up to ~ V nd uull n eneg o up to ~ J deleed to the ptent Th men C U/V.4 m Redent l? So how do we mke cpctnce much bgge (ppo. 5 )? 33

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