Lect05 - Physi cs 212 L ectur e 5 Today's Concept: El ectr...

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Unformatted text preview: Physi cs 212 L ectur e 5 Today's Concept: El ectr i c Potenti al Ener gy Defi ned as M i nus Wor k Done by El ectr i c Fi el d 40 30 20 10 0 Confused Confident Avg = 3.3 Physi cs 212 L ectur e 5, Sl i de 1 M usi c Taj Mahal Keb Mo Ry Cooder Corey Harris Derek Trucks BB Who is the Artist? ) A) ) B) C) D) ) E) Why? H e's pl ayi ng at Kr anner t Fr i day ni ght !!! Al so.. Der ek Tr ucks Band i s al so pl ayi ng Thur sday openi ng ni ght... p.s. M adel i ne Peyr oux was excel l ent l ast Fr i day ni ght... she changed her phr asi ng on al l of her ol d songs... Physi cs 212 L ectur e 5, Sl i de 2 Physi cs 212 L ectur e 5 Today's Concept: El ectr i c Potenti al Ener gy Defi ned as M i nus Wor k Done by El ectr i c Fi el d 40 30 20 10 0 Confused Confident Avg = 3.3 Physi cs 212 L ectur e 5, Sl i de 3 Recall fr om physics 211: r r W = Fg dr WTOT = K r r1 Object speeds up ( K > 0 ) r r2 F dr F dr F dr F dr 9 W>0 or W<0 Object slows down ( K < 0 ) W=0 Const ant speed ( K = 0 ) Physi cs 212 L ectur e 5, Sl i de 4 Potenti al Ener gy U + -W conservative + If gravity does negative work, potential energy increases! Same idea for Coulomb force... if Coulomb force does negative work, potential energy increases. F x + + Coulomb force does negative work Potential energy increases Physi cs 212 L ectur e 5, Sl i de 5 Pr efl i ght 8 A charge is released from rest in a region of electric field. The charge will start to move A) in a direction that makes its potential energy increase B) in a direction that makes its potential energy decrease C) along a path of constant potential energy 100 80 60 40 20 0 The charge will move according to the force of the electric field, making the work done by the field increasingly positive. Since work done by the field equals the opposite of the potential energy, the potential energy will be decreasing as the charge moves. The charge will always want to lower its potential energy. Think of it as a ball rolling down a hill. F x It will move in the same direction as F Work done by force is positive U = -Work is negative Nature wants things to move in such a way that PE decreases 34 Physi cs 212 L ectur e 5, Sl i de 6 ACT You hold a posit ively char ged ball and walk due west in a r egion t hat cont ains an elect r ic field dir ect ed due east . E F E F BB dr W i s the wor k done by the hand on the bal l H E W i s the wor k done by the el ectr i c fi el d on the bal l Whi ch of the fol l owi ng statements i s tr ue: E 14 Physi cs 212 L ectur e 5, Sl i de 7 Conser vat ive for ce: U = - W Not a conser vat ive for ce. Does not have any U. E F E F E dr B) W > 0 and W < 0 I s U posit ive or negat ive? H A) Posit ive BB B) Negat ive 16 Physi cs 212 L ectur e 5, Sl i de 8 Exampl e: Two Poi nt Char ges Calculat e t he change in pot ent ial ener gy for t wo point char ges or iginally ver y far apar t moved t o a separ at ion of "d" q1q2 U = - k 2 dr r12 d d q1 q2 q1q2 U = k d 1 q1q2 4 0 d Char ged par t icles w/ same sign have an incr ease in pot ent ial ener gy when br ought closer t oget her . For point char ges oft en choose r =infinit y as "zer o" pot ent ial ener gy. 19 Physi cs 212 L ectur e 5, Sl i de 9 ACT Case A d Case B 2d BB I n case A t wo negat ive char ges which ar e equal in magnit ude ar e separ at ed by a dist ance d. I n case B t he same char ges ar e separ at ed by a dist ance 2d. Which configur at ion has t he highest pot ent ial ener gy? A) Case A B) Case B 22 Physi cs 212 L ectur e 5, Sl i de 10 ACT Di scussi on As usual, choose U = 0 t o be at infinit y: q2 1 UA = 4 0 d 2d q1q2 1 U (r ) = 4 0 r Case A d Case B U(r ) q2 1 UB = 4 0 2d UA > UB U(d) U(2d) r r Physi cs 212 L ectur e 5, Sl i de 11 23 0 0 Pr efl i ght 2 60 50 40 30 20 10 0 BB A B C D E Change in potential energy equals the final potential energy minus the initial potential energy. To represent this, the expression((1/r2)-(1/r1)) is needed. This expression multiplied by kQq gives the change in potential energy. Since it is a change in potential energy, it must contain both r1 and r2, and since r1 is smaller than than r2, we subtract 1/r2 from 1/r1 34 U1 = 1 Qq 40 r1 U2 = 1 Qq 40 r2 U U 2 - U 1 = Qq 1 1 - 40 r2 r1 Physi cs 212 L ectur e 5, Sl i de 12 Potenti al Ener gy of M any Char ges Two char ges ar e separ at ed by a dist ance d. What is t he change in pot ent ial ener gy when a t hir d char ge q is br ought fr om far away t o a dist ance d fr om t he or iginal t wo char ges? Q2 qQ1 1 qQ2 1 U = + 4 0 d 4 0 d (super posit ion) Q1 d d q d 25 Physi cs 212 L ectur e 5, Sl i de 13 Potenti al Ener gy of M any Char ges What is t he t ot al ener gy r equir ed t o br ing in t hr ee ident ical char ges, fr om infinit ely far away t o t he point s on an equilat er al t r iangle shown. A) 0 Q 1 4 0 d Q2 1 C) U = 2 4 d 0 2 Q 1 U = 3 D) 4 0 d Q2 1 E) U = 6 4 d 0 B) U = 2 Q BB d d 3 Q2 W = Wi = - 40 d 3 Q2 U = + 40 d Q W1 = 0 d Q Wor k to br i ng i n fi r st char ge: 1 Q2 Wor k to br i ng i n second char ge : W2 = - 4 d 0 1 Q2 1 Q2 2 Q2 - =- Wor k to br i ng i n thi r d char ge : W3 = - 40 d 40 d 40 d 27 Physi cs 212 L ectur e 5, Sl i de 14 Potenti al Ener gy of M any Char ges Suppose one of t he char ges is negat ive. Now what is t he t ot al ener gy r equir ed t o br ing t he t hr ee char ges in infinit ely far away? A) 0 Q2 1 B) U = +1 4 0 d Q2 1 C) U = -1 4 d 0 2 Q 1 D) U = +2 4 d 0 Q2 1 E) U = -2 4 d 0 Wor k to br i ng i n fi r st char ge: Q BB d d 1 Q2 W = Wi = + 40 d 1 Q2 U = - 40 d Q d W1 = 0 Q 1 Q2 Wor k to br i ng i n second char ge : W2 = + 4 d 0 Wor k to br i ng i n thi r d char ge : 29 1 Q2 1 Q2 W3 = + - =0 40 d 40 d Physi cs 212 L ectur e 5, Sl i de 15 Pr efl i ght 4 40 30 20 10 BB 0 A B C D Adding a charge will add both a positive term and a negative term to the potential energy equation. Those terms will cancel each other out and there will be no change The potential energy would decrease if the charge were positive, yet increase if negative. 31 Physi cs 212 L ectur e 5, Sl i de 16 Pr efl i ght 6 BB Which is right, C or D ? 50 40 30 20 10 0 34 If the 2 charges are separated by a distance r then you can bring in a charge that is r/2 away from the positive charge and r away from the negative charge and those potentials will cancel leaving only the original potential of the system That is impossible if the magnitude of the two previous charges aren't equal C D Physi cs 212 L ectur e 5, Sl i de 17 Exampl e BB A posit ive char ge q is placed at x=0 and a negat ive char ge -2q is placed at x=d. At how many differ ent places along t he x axis could anot her posit ive char ge be placed wit hout changing t he t ot al pot ent ial ener gy of t he syst em? q X=0 -2q X=d x A) B) C) D) 0 1 2 3 37 Physi cs 212 L ectur e 5, Sl i de 18 Exampl e BB At which t wo places can a posit ive char ge be placed wit hout changing t he t ot al pot ent ial ener gy of t he syst em? A A) B) C) D) E) A&B A&C B&C B&D A&D q X=0 B C -2q X=d D x L et 's calculat e t he posit ions of A and B 40 Physi cs 212 L ectur e 5, Sl i de 19 L ets wor k out wher e A i s r d q X=0 -2q X=d x A U = + 1 Qq 1 2Qq - 40 r 40 r + d Set U = 0 1 2 = r r+d r=d 43 Physi cs 212 L ectur e 5, Sl i de 20 L ets wor k out wher e B i s r q X=0 d-r B -2q X=d x Setting U = 0 1 2 = r d -r 2r = d - r d r= 3 Physi cs 212 L ectur e 5, Sl i de 21 46 Summar y For a pair of charges: qq Just evaluate U = k 1 2 r r q1 q2 (We usually choose U = 0 to be where the charges are far apart) For a collection of charges: q1q2 Sum up U = k r for all pairs Physi cs 212 L ectur e 5, Sl i de 22 ...
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