Physics 212 Lecture 5, Slide 1Physics 212Lecture 5Today's Concept:Electric Potential EnergyDefined as Minus Work Done by Electric FieldMusicWho is the Artist?A) Tito PuenteB) Buena Vista Social ClubC) Louis PrimaD) Freddie Omar con su bandaE) Los Hombres CalientesCuban Jazz !!Thanks to Ry Cooder for bringing these guys to our attention !!Why ??Cuban Jazz at Krannert (Ellnora) Friday night (10:30pm)Marc Ribot y Cubanos PostizosRemembering Arsenio RodriguezFREEPhysics 212 Lecture 5Physics 212 Lecture 5, Slide 3Your Comments05“This really seems like a rehash of mechanics with electric charges instead of masses.” “Labor Day Weekend and Physics must definitely have the same charge because the weekend kept pushing the homework and this prelecture from getting done.” “Had there been office hours this week I definitely would have been there. I'm still not 100% sure about Gauss' Law.”“When solving for the potential energy, does r1 get subtracted from r2? or is it the other way around?” “Please discuss in lecture about how the point charges will affect the electric field in different situations where it has both same charge or where it has opposite charges. I am confused about this. Also, please go over the potential energy equation to refresh my memory.”“Homework problem style examples would be helpful, the checkpoints felt too easy.”“Still generally confused on some questions about the potential energy, like the third checkpoint.”Discussion Sections this week should helpWORKED EXAMPLES!Right! Nothing really newSIGNS!Example today: calculation for CP 3Physics 212 Lecture 5, Slide 4=∫i21rrW F drRecall from physics 211:= ∆TOTW KFdrW = 0Constant speed ( ∆K = 0 )FdrW > 0Object speeds up ( ∆K > 0 )W < 0Object slows down ( ∆K < 0 )FdrFdror9Physics 212 Lecture 5, Slide 5Potential EnergyconservativeU W∆ ≡ −If gravity does negative work, potential energy increases!Same idea for Coulomb force… if Coulomb force does negative work, potential energy increases.+ +F+ +∆xCoulomb force does negative workPotential energy increasesPhysics 212 Lecture 5, Slide 6Checkpoint 4A charge is released from rest in a region of electric field. The charge will start to moveA) in a direction that makes its potential energy increaseB) in a direction that makes its potential energy decreaseC) along a path of constant potential energy34“Since potential energy is negative, the charge will try to increase its potential energy, bringing it to zero..” “It wants to go to a spot with less PE.” “constant potential energy would require no work to preform.”F∆xIt will move in the same direction as FWork done by force is positive∆U = -Work is negativeNature wants things to move in such a way that PE decreasesPhysics 212 Lecture 5, Slide 7FEFHEdrWHis the work done by the hand on the ballWEis the work done by the electric field on the ballWhich of the following statements is true:A) WH> 0 and WE> 0B) WH> 0 and WE< 0C) WH< 0 and WE< 0D) WH< 0 and WE> 014You hold a positively charged ball and walk due west in a region that contains an electric field directed due east.Example: Charge in External FieldPhysics 212 Lecture 5, Slide 8FEFHEdrB) WH> 0 and WE< 0Conservative force: ∆U = - WENot a conservative force.Does not have any ∆U.Is ∆U positive or negative?A) PositiveB) Negative16Physics 212 Lecture 5, Slide 9Example: Getting the signs rightIn case A two negative charges which are equal in magnitude are separated by a distance d. In case B the same charges are separated by a distance 2d. Which configuration has the highest potential energy?A) Case AB) Case Bd2dCase ACase B22Physics 212 Lecture 5, Slide 10Example: Getting the signs right• As usual, choose U = 0 to be at infinity:1 201( )4q qU rrπε=U(r)0rdCase A2014AqUdπε=U(d)2014 2BqUdπε=2dCase BU(2d)UA> UB23Physics 212 Lecture 5, Slide 11Example: Two Point Chargesq1q2dCalculate the change in potential energy for two point charges originally very far apart moved to a separation of “d”∞∆ = −∫1 2212dq qU k drr∆ =1 2q qU kdCharged 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.19πε≡1 2014q qdPhysics 212 Lecture 5, Slide 12Checkpoint 1“It is inversely proportional to the first radius.”“Simple conservation of energy problem: final potential minus initial potential should equal change. ”“1/r1 will be larger then 1/r2 and this must be positive”340 114initialQqUrπε=0 214finalQqUrπε=0 2 11 14f iQqU U Ur rπε ∆ ≡ − = −  Note: +q moves AWAY from +Q. Its Potential energy MUST DECREASE∆U < 0A charge of +Q is fixed in space. A second charge of +q was first placed at a distance r1away from +Q. Then it is moved to a new position at a distance R away from its starting point on a straight path. The final location of +q is at a distance r2from +Q.What is the change in the potential energy of the charge +q in the process?A. kQq/R B. kQqR/r12C. kQqR/r22D. kQq(1/r2 - 1/r1) E. kQq(1/r1 - 1/r2)Physics 212 Lecture 5, Slide 13Potential Energy of Many ChargesTwo 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? Q1Q225πε πε∆ = +1 20 01 14 4qQ qQUd d(superposition)dqddPhysics 212 Lecture 5, Slide 14Potential Energy of Many ChargesWhat is the total energy required to bring in three identical charges, from infinitely far away to the points on an equilateral triangle shown.A) 0B) C) D) E) Q QdQ27πε∆ =2014QUdπε∆ =20124QUdπε∆ =20134QUdπε∆ =20164QUdddWork to bring in second charge :dQW20241πε−=dQWWi2043πε−==∑Work to bring in first charge: W1= 0dQdQdQW2020203424141πεπεπε−=−−=Work to bring in third charge :dQU2043πε+=∆Physics 212 Lecture 5, Slide 15Potential Energy of Many ChargesSuppose one of the charges is negative. Now what is the total energy required to bring the three charges in infinitely far away?A) 0B) C) D) E) Q QdQ29πε∆ = +20114QUdπε∆ = −20114QUdπε∆ = +20124QUdπε∆ = −20124QUddd0414120203=−+=dQdQWπεπεWork to bring in third charge :dQWWi2041πε+==∑dQU2041πε−=∆Work to bring in first charge: W1= 01Work to bring in second charge :dQW20241πε+=2Physics 212 Lecture 5, Slide 16Checkpoint 231“inserting another