1. Physics 212 Lecture 5, Slide 1 Physics 212 Lecture 5 Electric Potential Energy

2. Physics 212 Lecture 5, Slide 2 Recall from physics 211: Fdr W = 0 Constant speed (  K = 0 ) Fdr W > 0 Object speeds up (  K > 0 ) W < 0 Object slows down (  K < 0 ) F drFdr or 9

3. Physics 212 Lecture 5, Slide 3 Potential Energy If gravity does negative work, potential energy increases! Same idea for Coulomb force… if Coulomb force does negative work, potential energy increases. ++F ++ xxxx Coulomb force does negative work Potential energy increases

4. Analogy to gravity Work by me = F ext h = - F g h = mgh =  U Exert force F ext = - F g over distance h. Work by me - (Work by gravity) Change in Potential energy h FgFg F ext m m

5. Physics 212 Lecture 5, Slide 5 Checkpoint 4 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 34F xxxx It will move in the same direction as F Work done by E field is positive  U = -Work is negative

6. Physics 212 Lecture 5, Slide 6 FEFEFEFE FHFHFHFHE dr W H is the work done by the hand on the ball W E is the work done by the electric field on the ball Which of the following statements is true: A) W H > 0 and W E > 0 B) W H > 0 and W E 0 and W E < 0 C) W H < 0 and W E < 0 D) W H 0 14 You hold a positively charged ball and walk due west in a region that contains an electric field directed due east. Example: Charge in External Field

7. Physics 212 Lecture 5, Slide 7 FEFEFEFE FHFHFHFH E dr B) W H > 0 and W E 0 and W E < 0 Conservative force:  U = - W E Not a conservative force. Does not have any  U. Is  U positive or negative? A)Positive B)Negative 16

8. Move charge q 2 from r 1  r 2. Find the change in potential energy. From the diagram, so, q1q1q1q1 q2q2q2q2 q1q1q1q1 q2q2q2q2

9. Physics 212 Lecture 5, Slide 9 q1q1q1q1 q2q2q2q2d 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. Physics 212 Lecture 5, Slide 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? A) Case A B) Case B d 2d Case A Case B 22

11. Physics 212 Lecture 5, Slide 11 Example: Getting the signs right As usual, choose U = 0 to be at infinity:As usual, choose U = 0 to be at infinity: U(r) 0 r d Case A U(d) 2d Case B U(2d) U A > U B 23

12. Physics 212 Lecture 5, Slide 12 Checkpoint 1 34 A B C D E Note: +q moves AWAY from +Q. Its potential energy MUST DECREASE  U < 0

13. Physics 212 Lecture 5, Slide 13 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? Q1Q1Q1Q1 Q2Q2Q2Q2 25 (superposition) d q d d

14. Physics 212 Lecture 5, Slide 14 Potential Energy of Many ChargesQQ d Q 27 dd Work (by me) to bring in second charge : Work (by me) to bring in first charge: W 1 = 0 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 ?

15. Physics 212 Lecture 5, Slide 15 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? A) 0 B) C) D) E) QQ d -Q 29 dd Work to bring in third charge : Work to bring in first charge: W 1 = 0 1 Work to bring in second charge : 3 2

16. Physics 212 Lecture 5, Slide 16 Checkpoint 2 31 A B C D A B C D

17. Physics 212 Lecture 5, Slide 17 Checkpoint 3 34 LET’S DO THE CALCULATION !!

18. Physics 212 Lecture 5, Slide 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? 37 q -2q x X=0 X=d A)0 B)1 C)2 D)3

19. Physics 212 Lecture 5, Slide 19 Example: Potential Energy Changes At which two places can a positive charge be placed without changing the total potential energy of the system? 40 q -2q A BC D x X=0 X=d A)A & B B)A & C C)B & C D)B & D E)A & D Let’s calculate the positions of A and B

20. Physics 212 Lecture 5, Slide 20 Lets work out where A is 43 q -2q A x X=0 X=d d r Set  U = 0 Makes Sense! Q is twice as far from -2q as it is from +q

21. Physics 212 Lecture 5, Slide 21 Lets work out where B is 46 q -2q B x X=0 X=d d - r r Setting  U = 0 Makes Sense! Q is twice as far from -2q as it is from +q

22. Physics 212 Lecture 5, Slide 22 Summary q1q1 q2q2 r For a pair of charges: For a collection of charges: Sum up for all pairs Just evaluate (We usually choose U = 0 to be where the charges are far apart)