Lect05 - Physics 212 Lecture 5 Today's Concept: Electric...

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Unformatted text preview: Physics 212 Lecture 5 Today's Concept: Electric Potential Energy Defined as Minus Work Done by Electric Field Physics 212 Lecture 5, Slide 1 Physics Music Who is the Artist? BB A) B) C) D) E) Tito Puente Buena Vista Social Club Louis Prima Freddie Omar con su banda Los Hombres Calientes Cuban Jazz !! Thanks to Ry Cooder for bringing these guys Thanks to our attention !! to Why ?? Tiempo Libre at Krannert’s Opening Night Opening Party This Friday Party Should be Great Physics 212 Lecture 5, Slide 2 Physics Your Comments “Lots of clicker questions please.” “It would be nice to discuss more about the signs of the potential energy, energy, whether it is negative or positive” whether “I love Boise State” “Gauss' law still confuses me.” Discussion Sections Discussion this week should help this “Compared to the homework problems this Compared seemed easy. I would like to discuss more about Gauss's Law, flux and electric fields.” about 40 WORKED EXAMPLES There is now a link on the There homepage to the Worked Examples. Examples. 30 20 10 0 05 Confused Confident Physics 212 Lecture 5, Slide 3 Physics Recall from physics 211: r2 W = ∫ F idr WTOT = ∆K r1 F dr W>0 Object speeds up ( ∆K > 0 ) Object W<0 Object slows down ( ∆K < 0 ) Object F dr or F dr F dr 9 W=0 Constant speed ( ∆K = 0 ) Constant Physics 212 Lecture 5, Slide 4 Physics Potential Energy ∆U ≡ −Wconservative If gravity does negative work, potential energy increases! Same idea for Coulomb force… if Coulomb force does negative work, potential energy increases. + + ∆x + + F Coulomb force does negative work Potential energy increases Physics 212 Lecture 5, Slide 5 Physics Preflight 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 “Potential energy is transferred into kinetic energy” 60 “It will be like a ball rolling down a hill. potential It energy will never go up” energy 40 20 0 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 Lecture 5, Slide 6 Physics ACT You hold a positively charged ball and walk due west in a You region that contains an electric field directed due east. region FE E FH dr BB WH is the work done by the hand on the ball WE is the work done by the electric field on the ball Which of the following statements is true: A) B) C) D) 14 WH > 0 WH > 0 WH < 0 WH < 0 and WE > 0 and and WE < 0 and and WE < 0 and and WE > 0 and Physics 212 Lecture 5, Slide 7 Physics Conservative force: ∆U = - WE Conservative FE E Not a conservative force. Does not have any ∆U. Does FH dr B) WH > 0 and WE < 0 and Is ∆U positive or negative? A) Positive BB 16 B) Negative Physics 212 Lecture 5, Slide 8 Physics Example: Two Point Charges Calculate the change in potential energy for two point charges originally very far apart moved to a separation of “d” d q1q2 ∆U = − ∫ k 2 dr r12 ∞ d q1 q1q2 ∆U = k d q2 1 q1q2 ≡ 4πε 0 d Charged particles w/ same sign have an increase in potential energy when brought closer together. For point charges often choose r=infinity as “zero” potential energy. 19 Physics 212 Lecture 5, Slide 9 Physics ACT Case A Case B d 2d BB In case A two negative charges which are equal in magnitude are In case two separated by a distance d. In case B the same charges are separated In case the by a distance 2d. Which configuration has the highest potential 2d Which energy? energy? A) Case A B) Case B 22 Physics 212 Lecture 5, Slide 10 Physics ACT Discussion • As usual, choose U = 0 to be at infinity: As q1q2 1 U (r ) = 4πε 0 r q2 1 UA = 4πε 0 d Case A d Case B 2d q2 1 UB = 4πε 0 2d U(r) UA > UB U(d) U(2d) r r 0 0 23 Physics 212 Lecture 5, Slide 11 Physics Preflight 2 60 BB 50 40 30 20 10 0 A B C D E U1 = “kQq/r is the potential at a point so the difference in these two potentials will be found by doing kQq((1/r2)-(1/r1))” “Since the particle is moved away from the fixed charge, the potential energy must increase. The part 1/r1-1/r2 would yield a positive answer because 1/r1>1/r2” 34 1 Qq 4πε0 r1 ∆U ≡ U 2 − U1 = U2 = 1 Qq 4πε0 r2 Qq 1 1 − 4πε0 r2 r1 Note: +q moves AWAY from +Q. +q AWAY from Its Potential energy MUST DECREASE MUST ∆U < 0 Physics 212 Lecture 5, Slide 12 Physics Potential Energy of Many Charges Two charges are separated by a distance d. What is the change in potential energy when a third charge q is brought from far away to a distance d from the original two charges? Q2 d d qQ1 1 qQ2 1 ∆U = + 4πε 0 d 4πε 0 d (superposition) q Q1 d 25 Physics 212 Lecture 5, Slide 13 Physics Potential Energy of Many Charges What is the total energy required to bring in three identical charges, from infinitely far away to the points on an equilateral triangle shown. A) 0 Q 2 Q1 B) 4πε 0 d Q2 1 C) ∆U = 2 4πε d 0 2 D) ∆U = 3 Q 1 4πε 0 d Q2 1 E) ∆U = 6 4πε 0 d ∆U = Work to bring in first charge: Work BB d d d Q 3 Q2 W = ∑ Wi = − 4πε0 d Q 3 Q2 ∆U = + 4πε0 d W1 = 0 1 Q2 Work to bring in second charge : W2 = − 4πε0 d 1 Q2 1 Q2 2 Q2 − =− Work to bring in third charge : W3 = − 4πε0 d 4πε0 d 4πε0 d 27 Physics 212 Lecture 5, Slide 14 Physics Potential Energy of Many Charges Suppose one of the charges is negative. Now what is the total energy required to bring the three charges in infinitely far away? 2 Q A) 0 Q2 1 B) ∆U = +1 4πε d 0 2 1 C) ∆U = −1 4Q d πε 0 Q2 1 D)∆U = +2 4πε 0 d Q2 1 E) ∆U = −2 4πε 0 d BB d 1 Work to bring in first charge: Work d d Q 1 Q2 W = ∑ Wi = + 4πε0 d Q 1 Q2 ∆U = − 4πε0 d W1 = 0 1 Q2 Work to bring in second charge : W2 = + 4πε0 d Work to bring in third charge : 29 1 Q2 1 Q2 W3 = + − =0 4πε0 d 4πε0 d Physics 212 Lecture 5, Slide 15 Physics Preflight 4 40 30 20 10 BB 0 A B C D “The potential energy between one of the charges and the charge pllaced at point A will always aced cancel with the potential energy of the other charge and the charge placed at point A.” cancel 31 “a positive charge would decrease the potential energy and a negative charge would increase tive the potential energy “ Physics 212 Lecture 5, Slide 16 Physics Preflight 6 BB “As long as the third charge is twice as far from the larger negative charge as it is the smaller positive charge, the total potential energy of the system will be unaffected. “ 50 40 30 “The potential energies the third charge will The contribute to the system have opposite signs but NOT equal magnitudes. So the net potential energy will not equal 0.” energy 20 10 0 34 A B C D LET’S DO THE CALCULATION !! Physics 212 Lecture 5, Slide 17 Physics Example BB A positive charge q is placed at x=0 and a negative charge -2q is placed at x=d. At how many different places along the x axis could another positive charge be placed without changing the total potential energy of the system? q X=0 A) B) C) D) 37 -2q X=d x 0 1 2 3 Physics 212 Lecture 5, Slide 18 Physics Example BB At which two places can a positive charge be placed without changing the total potential energy of the system? q A X=0 A) B) C) D) E) 40 A&B A&C B&C B&D A&D -2q B C X=d D x Let’s calculate the positions of A and B Physics 212 Lecture 5, Slide 19 Physics Lets work out where A is d r A q -2q X=0 X=d x 1 Qq 1 2Qq ∆U = + − 4πε0 r 4πε0 r + d Set ∆U = 0 Set 1 2 = r r+d r=d 43 Makes Sense! Q iis twice as far from -2q as it is from +q s Physics 212 Lecture 5, Slide 20 Physics Lets work out where B is d-r r q X=0 Setting ∆U = 0 Setting -2q B X=d x 1 2 = r d −r 2r = d − r r= 46 d 3 Makes Sense! Q iis twice as far from -2q as it is from +q s Physics 212 Lecture 5, Slide 21 Physics Summary For a pair of charges: Just evaluate q1q2 U =k r r q1 q2 (We usually choose U = 0 to be where the charges are far apart) For a collection of charges: Sum up q1q2 U =k r for all pairs Physics 212 Lecture 5, Slide 22 Physics ...
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