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Physics 212 Lecture 5

Physics 212 Lecture 5. Electric Potential Energy. F. W > 0. Object speeds up ( D K > 0 ). dr. F. dr. or. W < 0. Object slows down ( D K < 0 ). F. dr. F. W = 0. Constant speed ( D K = 0 ). dr. Recall from physics 211:. 9. Potential Energy. F. +. +. D x. +. +.

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Physics 212 Lecture 5

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  1. Physics 212 Lecture 5 Electric Potential Energy

  2. 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

  3. 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

  4. m Fext h m Fg Change in Potential energy Work by me - (Work by gravity) Analogy to gravity Exert force Fext = - Fg over distance h. Work by me = Fext h = - Fgh = mgh = U

  5. 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 It will move in the same direction as F Work done by E field is positive DU = -Work is negative 34

  6. 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

  7. 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

  8. Move charge q2 from r1 r2. Find the change in potential energy. q2 q2 q1 q1 From the diagram, so,

  9. d q1 q2 Calculate the change in potential energy for two point charges originally very far apart, moved to a separation of d. Charged particles w/ same sign have an increase in potential energy when brought closer together. For point charges we often choose r =  as “zero” potential energy. So the potential energy of this configuration is, 19

  10. 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

  11. 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

  12. Checkpoint 1 A B C D E 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 (by me) to bring in second charge : Work (by me) 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 ? Q d d d Q Q Work (by me) to bring in first charge: W1 = 0 27

  15. Potential Energy of Many Charges Work to bring in first charge: W1 = 0 1 2 Work to bring in second charge : 3 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 A B C D 31

  17. Checkpoint 3 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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