PHYS 2421 Fields and Waves

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1 PHYS 242 Felds nd Wves Instucto: Joge A. López Offce: PSCI 29 A, Phone: Textook: Unvesty Physcs e, Young nd Feedmn 23. Electc potentl enegy 23.2 Electc potentl 23.3 Clcultng electc potentl 23.4 Equpotentl sufces 23.5 Potentl gdent

2 Secton 23.: Electc potentl enegy Queston: Wht s the wok done n movng chge n feld fom to? W F d qe d qe y y Notce tht the wok s done y feld Wok s the chnge n electc potentl enegy W U U U qe y y U y qey Whch s the electc potentl enegy of pont chge n n unfom electc feld Chnge n enegy s ndependent of the pth tken: W F dl F cosdl

3 Secton 23.: Electc potentl enegy Who does the wok? Does potentl enegy ncese o decese? Wll ptcle move y tself fom to? Yes Feld does the wok nd potentl enegy deceses Wll ptcle move y tself fom to? No Feld does not do the wok nd potentl enegy nceses Hwk Sect. 23.: Questons 23. nd 23.2 (oth th nd 2 th Eds.)

4 Secton 23.: Electc potentl enegy Wll ptcle q move y tself fom to? Yes Feld does the wok nd potentl enegy deceses Wok done? W F d cnnot e used s the feld deceses wth dstnce. Must use: qq W F dl, F ˆ 2 4 qq qq d qq W F dl ˆ dl Agn, snce wok s the chnge n electc potentl enegy qq qq W U U U U 4 4 Whch s electc potentl enegy of two pont chges

5 Secton 23.: Electc potentl enegy Agn, esult s ndependent of pth: qq W F dl ˆ dl 2 4 qq 4 cosdl 2 qq d qq Homewok: Pols. 23., 23.5 ( th Ed) o 23., 23.7 (2 th Ed)

6 Secton 23.: Electc potentl enegy Consde poston flyng ne fxed lph ptcle s shown, wht velocty wll t hve when t s t 2x - m wy? Consevton of enegy: EA KA U A EB KB UB 2 KB mvb K A U A UB 2 K U U A B A U U K vb m mva kg 3 m/s 4. J C.6 C 2 2 q q e Nm /C 2.3 J 4 2 m C.6 C 2 2 q q e Nm /C 4.6 J 4 m 2 B A A m e+ =9.x -3 kg q =3.2x -9 C q e+ =.6x -9 C v B m/s

7 Secton 23.: Electc potentl enegy Wht s the potentl enegy of q? qq qq2 qq3 U U U2 U In genel U q 4 q Homewok: Polem 23.2 (oth th nd 2 th eds.) Answe:.2 N

8 Secton 23.: Electc potentl enegy Wok needed to ng chge q 3 fom nfnty? Consevton of enegy (ssumng ll chges t est) U qq Wok done y feld s: W U 2 qq q q q q qq 3 q2q3 W U U2 U e e e e e e e Wok done y feld s postve Wok must e done y n extenl souce

9 Secton 23.: Electc potentl enegy Summy of Secton 23. Potentl enegy chnge y movng chge q n unfom E U y qey If ptcle moves y tself Feld does the wok nd potentl enegy deceses Potentl enegy of chge q t dstnce fom chge q Potentl enegy of chge q n the pesence of collecton of pont chges qq U U q 4 4 q Homewok fo Secton 22.: th Ed.: Questons 23. nd 23.2, Polems 23., 23.5, th Ed.: Questons 23. nd 23.2, Polems 23., 23.7, 23.2

10 Secton 23.2: Electc potentl Electc potentl enegy qq U of system t nfnty 4 qq Move q close to q U 4 Chnge n potentl enegy qq U( ) U( ) U( ) 4 Chnge of potentl enegy pe unt chge U( ) q q 4 q Ths s known smply s Potentl 4 Unts: J/C = olts Potentl of pont chge Homewok: Polem 23.3 ( th Ed.) o 23.5 (2 th Ed.) Alessndo olt, Fench physcst, Invento of electcl ple

11 Secton 23.2: Electc potentl Exmples If ()=5 olts, t mens, t took n enegy of U= q () to move q fom nfnty Fo.5 ttey, t mens tht.5 And t tkes enegy U= q x.5 move q fom to Fo collecton of chges q 4 And the enegy n movng chge q fom nfnty to pont s qo q U qo 4

12 Secton 23.2: Electc potentl Fo contnuous dstuton of chges dq 4 Wok done n movng chge q fom to? W q Ths s the dvntge of usng, t does not nvolve vectos! ut lso Whch mens W F dl q E dl q E cosdl Ths yelds the potentl dffeence n tems of the electc feld E dl

13 Secton 23.2: Electc potentl New unt of enegy U q If q s n unts of e, the electc chge of n electon, U cn e gven n e : electon-volts e.6 C.6 C J/C.6 J Homewok: Polems 23.5 nd 23.7 ( th Ed.) o 23.3 nd 23.7 (2 th Ed.)

14 Secton 23.2: Electc potentl Foce on poton? F qe.6 C.5 N/C 2.4 N Wok done y feld? W 2 2 Fd 2.4 N.5 m.2 J Potentl dffeence -? E=.52x 7 N/C q p =.6x -9 C d=.5 m 2 W.2 J q.6 C 6

15 Secton 23.2: Electc potentl Potentl t pont? q q m.4 m C.2 C 9 Nm /C Potentl t pont? Nm /C.4 m.4 m 93 Potentl t pont c? C C Nm /C.3 m.3 m C C

16 Secton 23.2: Electc potentl Potentl enegy of q=4 nc t pont? U 9 6 q 4 C J Potentl enegy of q=4 nc t pont? U 9 6 q 4 C J Potentl enegy of q=4 nc t pont c? U 9 q 4 C J Hwk: Polem 23.9 (oth th nd 2 th Eds.)

17 Secton 23.2: Electc potentl Potentl t dstnce fom q? ( ) ( ) ( ) E dl q d 4 4 q 4 2 q Hwk: Polem 23.2 (oth th nd 2 th Eds.)

18 Secton 23.2: Electc potentl Speed of q t pont? E K U E K U 2 2 K mv K U U q q The potentls e: C 3 C 9 Nm /C 35. m.2 m v 2q m q =2 nc M=5x 9 kg C 3 C 9 Nm /C 35.2 m. m 22 9 C q v 9 m 5 kg 46 m/s Hwk: Polem 23.3 (oth th nd 2 th Eds.)

19 Secton 23.2: Electc potentl Summy of Secton 23.2 Potentl t dstnce fom pont chge q Potentl due to collecton of chges Fo contnuous dstuton of chges U( ) q q dq q Relton etween Wok nd potentl W q Relton etween potentl nd E feld E dl

20 Secton 23.2: Electc potentl Homewok fo Secton 23.2: Polems 23.3, 23.5, 23.7, 23.9, 23.2 nd 23.3 oth th nd 2 th eds.

21 Thee e two usul outes to clculte : Route : 4 q o 4 dq Route 2: E dl Choose one dependng on wht s known out the polem

22 Dffcult: Bette use: 4 dq E dl E cosdl Tke,, q Guss lw: ER, E 2 R 4 Fo R Fo < R q q d q ˆ () dl ( ) ( R) E R R dl ( ) ( R) q 4 R

23 Fo R Fo < R q () 4 q () 4 R Constnt! Potentl nsde conductng oject s constnt Hwk: Polem ( th Ed.) o (2 th Ed.)

24 Notce: A postve chge would move y tself fom to potentl enegy deceses fom to U() > U() () > () etween pltes? Defne = t dstnce x: Check t x= nd x=d: x E dl Ed Ex Ed Ex E d x E d Ed : xd x : Ed x x E dl Ex x x xd E d d

25 Wht s the dffeence n ths cse? Ogn s t not t Integl fom to s gnst dy Smltes? Potentl enegy deceses fom to U() > U() () > () etween pltes? Defne = t heght y: y y : : yd d E dl Edy E d Ed Ed Ed y y y E dl Edy Ey Ey Hwk: Polem ( th Ed.) o 23.4 (2 th Ed.)

26 Dffcult: 4 dq Bette use: E dl Guss lw: E 2 d Tke two ponts: ˆ dl ln ln 2 Is t convenent to set ln,? 2 No! Smply defne t ny = ln 2

27 Snce on xs: E kxq 2 2 x 3/ 2 ˆ Integl would e dffcult: E dl Ths tme s ese to use: dq 4 dq Q dq Homewok: Polem (oth th o 2 th Eds.)

28 Snce on xs: E x x kq 2 2 Integl would e dffcult: E dl ˆ Ths tme s ese to use: 4 dq y 2 2 dq dy Q/2 x ln 4 4 x y 4 x y

29 Summy of Secton 23.3 Thee outes to q o clculte : 4 4 Chged conductng sphee: Fo R Fo < R Chged ng dq And q () 4 q () 4 R Lne of chge x E dl Pllel pltes E d x Infnte lne chge Q /2 Q x ln x 2 ln Hwk Secton 23.3: Pols 23.33, nd ( th Ed.) o 23.33, 23.4 nd (2 th Ed.)

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