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Electric Potential Energy and Work Done by Electric Field

This lecture discusses the concept of electric potential energy and its relation to the work done by an electric field. It also addresses various scenarios and calculations related to potential energy. Additionally, student comments and questions are addressed.

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Electric Potential Energy and Work Done by Electric Field

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  1. Physics 212 Lecture 5 Today's Concept: Electric Potential Energy Defined as Minus Work Done by Electric Field

  2. Music • Who is the Artist? • Tito Puente • Buena Vista Social Club • Louis Prima • Freddie Omar con su banda • Los Hombres Calientes Cuban Jazz !! Thanks to RyCooder for bringing these guys to our attention !! Why ?? Cuban Jazz at Krannert (Ellnora) Friday night (10:30pm) Marc Ribot y CubanosPostizos Remembering Arsenio Rodriguez FREE Physics 212 Lecture 5

  3. Your Comments Right! Nothing really new “This really seems like a rehash of mechanics with electric charges instead of masses.” “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.” SIGNS! “When solving for the potential energy, does r1 get subtracted from r2? or is it the other way around?” “Homework problem style examples would be helpful, the checkpoints felt too easy.” Example today: calculation for CP 3 “Still generally confused on some questions about the potential energy, like the third checkpoint.” Discussion Sections this week should help WORKED EXAMPLES! “Had there been office hours this week I definitely would have been there. I'm still not 100% sure about Gauss' Law.” “Labor Day Weekend and Physics must definitely have the same charge because the weekend kept pushing the homework and this prelecture from getting done.” 05

  4. F W > 0 Object speeds up ( DK > 0 ) dr F dr or W < 0 Object slows down ( DK < 0 ) F dr F W = 0 Constant speed ( DK = 0 ) dr Recall from physics 211: 9

  5. Potential Energy F + + Dx + + If gravity does negative work, potential energy increases! Same idea for Coulomb force… if Coulomb force does negative work, potential energy increases. Coulomb force does negative work Potential energy increases

  6. Checkpoint 4 F Dx 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 increaseB) in a direction that makes its potential energy decreaseC) along a path of constant potential energy “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.” It will move in the same direction as F Work done by force is positive DU = -Work is negative Nature wants things to move in such a way that PE decreases 34

  7. Example: Charge in External Field FE FH You hold a positively charged ball and walk due west in a region that contains an electric field directed due east. dr E 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) WH> 0 and WE> 0 B) WH> 0 and WE< 0 C) WH< 0 and WE< 0 D) WH< 0 and WE> 0 14

  8. Not a conservative force.Does not have any DU. Conservative force: DU = - WE FE FH dr E B) WH> 0 and WE< 0 • IsDUpositive or negative? • Positive • Negative 16

  9. Example: Getting the signs right In 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? • Case A • Case B Case A d Case B 2d 22

  10. Example: Getting the signs right Case A d Case B 2d r 0 U(d) U(2d) • As usual, choose U = 0 to be at infinity: U(r) UA > UB 23

  11. 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 q1 q2 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

  12. Checkpoint 1 A charge of +Q is fixed in space. A second charge of +q was first placed at a distance r1 away 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 r2 from +Q. What is the change in the potential energy of the charge +q in the process? A. kQq/R B. kQqR/r12 C. kQqR/r22D. kQq(1/r2 - 1/r1) E. kQq(1/r1 - 1/r2) “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” Note: +q moves AWAY from +Q. Its Potential energy MUST DECREASE DU < 0 34

  13. Potential Energy of Many Charges d q d 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 (superposition) Q1 25

  14. Potential Energy of Many Charges Work to bring in first charge: W1 = 0 Work to bring in second charge : Work to bring in third charge : 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 B) C) D) E) Q d d d Q Q 27

  15. Potential Energy of Many Charges Work to bring in first charge: W1 = 0 1 Work to bring in second charge : 2 Work to bring in third charge : Suppose one of the charges is negative. Now what is the total energy required to bring the three charges in infinitely far away? A) 0 B) C) D) E) Q d d d Q Q 29

  16. Checkpoint 2 Two charges which are equal in magnitude, but opposite in sign, are place at equal distances from point A. If a third charge is added to the system and placed at point A, how does the electric potential energy of the charge collection change? A. Increases B. decreases C. doesn’t change D. The answer depends on the sign of the third charge “inserting another charge is going to increase the magnitude of the potential energy.” “No matter what the sign is the potential energy would be a positive number minus a negative number minus another negative number. ” “the change in potential is found by adding another kqq/r term. this term is dependent on the sign of the new charge.“ 31

  17. Checkpoint 3 You start with two point charges separated by some distance. The charge of the first is positive. The charge of the second is negative and its magnitude is twice as large as that of the first. • Is it possible to find a place to which you can bring a third charge in from infinity without changing the total potential energy of the system? • YES, as long as the third charge is positive B. YES as long as the third charge is negativeC. YES, no matter what the third charge is D. NO “The positive third charge will cancel out the negative charge.“ “It doesn't matter what the sign is. Place the new charge twice the distance from the - as the + charge. It doesn't matter what the sign is because the U added to the system will now be zero.” “Adding a third charge that is opposite to at least one other charge will cause a change in potential energy” LET’S DO THE CALCULATION !! 34

  18. Example: Potential Energy Changes 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? -2q q x X=0 X=d • 0 • 1 • 2 • 3 37

  19. Example: Potential Energy Changes At which two places can a positive charge be placed without changing the total potential energy of the system? -2q q A x B C D X=0 X=d • A & B • A & C • B & C • B & D • A & D Let’s calculate the positions of A and B 40

  20. Lets work out where A is d r -2q q A x X=0 X=d Set DU = 0 Makes Sense! Q is twice as far from -2q as it is from +q 43

  21. Lets work out where B is d - r r -2q q x B X=0 X=d Setting DU = 0 Makes Sense! Q is twice as far from -2q as it is from +q 46

  22. Summary For a pair of charges: r Just evaluate q1 q2 (We usually choose U = 0 to be where the charges are far apart) For a collection of charges: Sum up for all pairs

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