Physics 212 Lecture 5 Electric Potential Energy Physics

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

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

Potential Energy 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 3

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

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

Example: Charge in External Field You hold a positively charged ball and walk due west in a region that contains an electric field directed due east. FE E FH dr 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 and WE > 0 and WE < 0 and WE > 0 Physics 212 Lecture 5, Slide 6

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

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

Calculate the change in potential energy for two point charges originally very far apart, moved to a separation of d. d q 1 q 2 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 Physics 212 Lecture 5, Slide 9

Example: Getting the signs right Case A Case B d 2 d 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 2 d. Which configuration has the highest potential energy? A) Case A B) Case B 22 Physics 212 Lecture 5, Slide 10

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

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

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? Q 2 d (superposition) d q Q 1 d 25 Physics 212 Lecture 5, Slide 13

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 ? Q d Q Work (by me) to bring in first charge: d d Q W 1 = 0 Work (by me) to bring in second charge : Work (by me) to bring in third charge : 27 Physics 212 Lecture 5, Slide 14

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

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

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

Example: Potential Energy Changes A positive charge q is placed at x=0 and a negative charge -2 q 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? A) B) C) D) 37 q -2 q X=0 X=d x 0 1 2 3 Physics 212 Lecture 5, Slide 18

Example: Potential Energy Changes 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&D A&D -2 q B C X=d D x Let’s calculate the positions of A and B Physics 212 Lecture 5, Slide 19

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

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

Summary For a pair of charges: r q 1 Just evaluate q 2 (We usually choose U = 0 to be where the charges are far apart) For a collection of charges: Sum up for all pairs Physics 212 Lecture 5, Slide 22