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# Lect05 - Physics 212 Le cture5 Today's C pt once Ele ctric...

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Unformatted text preview: Physics 212 Le cture5 Today's C pt: once Ele ctric Pote ntial Ene rgy De d as Minus Work Doneby Ele fine ctric Fie ld 40 30 20 10 0 Confused Confident Avg = 3.3 Physics 212 Le cture5, S 1 lide Music ho is the Artist? ) ) ) ) ) Taj Mahal Keb Mo Ry Cooder Corey Harris Derek Trucks BB Why? Why? He’s playing at Krannert Friday night !!! He’s Also.. Derek Trucks Band is also playing Thursday opening night… p.s. Madeline Peyroux was excellent last Friday night… p.s. she changed her phrasing on all of her old songs… she Physics 212 Lecture 5, Slide 2 Physics 212 Le cture5 Today's C pt: once Ele ctric Pote ntial Ene rgy De d as Minus Work Doneby Ele fine ctric Fie ld 40 30 20 10 0 Confused Confident Avg = 3.3 Physics 212 Le cture5, S 3 lide Re fromphysics 211: call rr W = ∫Fg dr WTOT = ∆K r r1 r r2 F dr F dr F dr F dr 9 W>0 Obje spe ds up ( ∆ K > 0 ) ct e Obje or W<0 Obje slows down ( ∆ K < 0 ) ct Obje W=0 C onstant spe d ( ∆ K = 0 ) e Physics 212 Le cture5, S 4 lide Pote ntial Ene rgy ∆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 Physics 212 Le cture5, S 5 lide Pre flight 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. energy. 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 Physics 212 Le cture5, S 6 lide AC T You hold a positive charge ball and walk duewe in a re ly d st gion that You contains an e ctric fie dire d duee ld cte ast. contains le E F EF BB dr W is thework doneby thehand on theball H E W is thework doneby thee ctric fie on theball le ld Which of thefollowing state e is true m nts : E 14 Physics 212 Le cture5, S 7 lide Conse rvativeforce ∆ U = - W : Conse Not a conse rvativeforce . Doe not haveany ∆ U. s Doe E F EF E dr B) W > 0 and W < 0 I s ∆ U positiveor ne gative ? positive H A) Positive BB B) Ne gative 16 Physics 212 Le cture5, S 8 lide Exam : Two Point Charge ple s C alculatethechangein pote ntial e rgy for two point charge originally ve far ne s ry apart m d to a se ove paration of “d” q1q2 ∆U = − ∫ k 2 dr r12 ∞ d d q1 q2 q1q2 ∆U = k d 1 q1q2 ≡ 4πε 0 d C harge particle w/ sam sign havean incre in pote d s e ase ntial e rgy whe brought ne n close toge r. r the For point charge ofte chooser=infinity as “ze pote sn ro” ntial e rgy. ne 19 Physics 212 Le cture5, S 9 lide ACT CaseA d CaseB 2d BB I n caseA t wo ne gativecharge which aree s qual in m agnitudearese parate by a distanced. d case I n caseB t hesam charge arese e s parate by a distance2d. Which configuration has the d case 2d Which highe pote st ntial e rgy? ne highe A) C A ase B) C B ase 22 Physics 212 Le cture5, S 10 lide 10 ACT Discussion • As usual, chooseU = 0 t o beat infinity: As q2 1 UA = 4πε 0 d 2d q1q2 1 U (r ) = 4πε 0 r CaseA d CaseB U(r) q2 1 UB = 4πε 0 2d UA > UB U(d) U(2d) r r Physics 212 Le cture5, S 11 lide 11 23 0 0 Pre flight 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 4πε0 r1 U2 = 1 Qq 4πε0 r2 ∆U ≡ U 2 − U 1 = Qq 1 1 − 4πε0 r2 r1 Physics 212 Le cture5, S 12 lide 12 Pote ntial Ene of Many Charge rgy s Two charge arese s parate by a distanced. What is thechangein pote d ntial e rgy whe a ne n t hird chargeq is brought fromfar away to a distanced f romtheoriginal two charge s? Q2 qQ1 1 qQ2 1 ∆U = + 4πε 0 d 4πε 0 d (supe rposition) Q1 d d q d 25 Physics 212 Le cture5, S 13 lide 13 Pote ntial Ene of Many Charge rgy s What is thetotal e rgy re ne quire to bring in thre ide d e ntical charge frominfinite far s, ly away to thepoints on an e quilate triangleshown. ral A) 0 B) Q1 4πε 0 d C) Q2 1 ∆U = 2 4πε 0 d D) Q2 1 ∆U = 3 4πε 0 d E) Q2 1 ∆U = 6 4πε 0 d ∆U = Work to bring in first charge : Work Work to bring in se cond charge: Work to bring in third charge: 2 Q BB d d 3 Q2 W = ∑ Wi = − 4πε0 d 3 Q2 ∆U = + 4πε0 d Q W1 = 0 d 1 Q2 W2 = − 4πε0 d Q 1 Q2 1 Q2 2 Q2 W3 = − − =− 4πε0 d 4πε0 d 4πε0 d Physics 212 Le cture5, S 14 lide 14 27 Pote ntial Ene of Many Charge rgy s S upposeoneof thecharge is ne s gative Now what is thetotal e rgy re . ne quire to bring the d t hre charge in infinite far away? e s ly A) 0 Q2 1 B) ∆U = +1 4πε 0 d Q2 1 C) ∆U = −1 4πε d 0 2 Q1 ∆ D) U = +2 4πε d 0 Q2 1 E) ∆U = −2 4πε d 0 Work to bring in first charge : Work Work to bring in se cond charge: Work to bring in third charge: 29 Q BB d d 1 Q2 W = ∑ Wi = + 4πε0 d 1 Q2 ∆U = − 4πε0 d Q d Q W1 = 0 1 Q2 W2 = + 4πε0 d 1 Q2 1 Q2 W3 = + − =0 4πε0 d 4πε0 d Physics 212 Le cture5, S 15 lide 15 Pre flight 4 40 30 20 10 BB 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 equation. The potential energy would decrease if the charge were positive, yet increase if negative. 31 Physics 212 Le cture5, S 16 lide 16 Pre flight 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 Physics 212 Le cture5, S 17 lide 17 Exam ple BB A positivechargeq is place at x=0 and a ne d gativecharge-2q is place at x=d. At how m d any diffe nt place along thex axis could anothe positivechargebeplace without changing the re s r d t otal pote ntial e rgy of thesyste ? ne m q X=0 -2q X=d x A) B) C) D) 0 1 2 3 37 Physics 212 Le cture5, S 18 lide 18 Exam ple BB At which two place can a positivechargebeplace without changing thetotal pote s d ntial e rgy ne of thesyste ? m 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 Le calculatethepositions of A and B t’s 40 Physics 212 Le cture5, S 19 lide 19 Le work out whe A is ts re r d q X=0 -2q X=d x A ∆U = + 1 Qq 1 2Qq − 4πε0 r 4πε0 r + d Set ∆ U = 0 Set 1 2 = r r+d r=d 43 Physics 212 Le cture5, S 20 lide 20 Le work out whe B is ts re r q X=0 d-r B -2q X=d x Setting ∆ U = 0 Setting 1 2 = r d −r 2r = d − r d r= 3 Physics 212 Le cture5, S 21 lide 21 46 Sm um ary 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 Physics 212 Le cture5, S 22 lide 22 ...
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