Electricity & Magnetism Lecture 5: Electric Potential Energy

Transcription

1 Electricity & Magnetism Lecture 5: Electric Potential Energy Toay... Ø Ø Ø Ø Recap of Unit 19 graing This unit s (21) wri=en Homework Electric PotenDal Energy Unit 21 session GravitaDonal an Electrical PE Electricity & MagneDsm Lecture 5, Slie 1

2 Stuff you aske about: Ø Ø recap all the formulas so far an how they can be use in ifficult quesdons please. An o so perhaps every 5 lectures (if we have Dme) because a lot are popping up. I'll buy a ozen onuts for the class if nee be. In the first prelecture quesdon: where i gravity come from? Isn't gravity perpenicular to the modon, thus has no effect. Ø An on't we have a 10minute break at 1.20? My scheule says so ;( There s now a irectory of Main Points You can take a break, if you want. :) Electricity & MagneDsm Lecture 5, Slie 2

3 CheckPoint Result: EPE of Point Charge A charge of +Q is fixe in space. A secon charge of +q was first place at a istance r 1 away from +Q. Then it was move along a straight line to a new posidon at a istance R away from its stardng posidon. The final locadon of +q is at a istance r 2 from +Q. What is the change in the potendal energy of charge +q uring this process? A. kqq/r B. kqqr/r 1 2 C. kqqr/r 2 2 D. kqq((1/r 2 )- (1/r 1 )) E. kqq((1/r 1 )- (1/r 2 )) kqq/r is the poten2al at a point so the ifference in these two poten2als will be foun by oing kqq((1/r2)- (1/r1)) Since the par2cle is move away from the fixe charge, the poten2al energy must increase. The part 1/r1-1/r2 woul yiel a posi2ve answer because 1/r1>1/r2 Electricity & MagneDsm Lecture 5, Slie 12

4 CheckPoint Result: EPE of Point Charge A charge of +Q is fixe in space. A secon charge of +q was first place at a istance r 1 away from +Q. Then it was move along a straight line to a new posidon at a istance R away from its stardng posidon. The final locadon of +q is at a istance r 2 from +Q. What is the change in the potendal energy of charge +q uring this process? A. kqq/r B. kqqr/r 1 2 C. kqqr/r 2 2 D. kqq((1/r 2 )- (1/r 1 )) E. kqq((1/r 1 )- (1/r 2 )) Note: +q moves AWAY from +Q. Its Poten2al energy MUST DECREASE ΔU < 0 Electricity & MagneDsm Lecture 5, Slie 13

5 W = R~r 2 ~r 1 ~F ~r Recall from Mechanics: F r W > 0 Object spees up ( ΔK > 0 ) or F r F r W < 0 Object slows own ( ΔK < 0 ) F r W = 0 Constant spee ( ΔK = 0 ) Electricity & MagneDsm Lecture 5, Slie 3

6 Dot Prouct (review) If you know A an B in rectangular coorinates, then you can fin the angle between them.

7 Potential Energy If gravity oes negadve work, potendal energy increases! Same iea for Coulomb force if Coulomb force oes negadve work, potendal energy increases. + + F + + Δx Coulomb force oes nega2ve work Poten2al energy increases Electricity & MagneDsm Lecture 5, Slie 4

8 CheckPoint: Motion of Point Charge Electric Fiel A charge is release from rest in a region of electric fiel. The charge will start to move A) In a irec:on that makes its poten:al energy increase. B) In a irec:on that makes its poten:al energy ecrease. C) Along a path of constant poten:al energy. It will move in the same irec:on as F F Work one by force is posi:ve Δx ΔU = Work is nega:ve Nature wants things to move in such a way that PE ecreases Electricity & MagneDsm Lecture 5, Slie 5

9 Clicker Question You hol a posidvely charge ball an walk ue west in a region that contains an electric fiel irecte ue east. East F E F H r West W H is the work one by the han on the ball W E is the work one by the electric fiel on the ball Which of the following statements is true: A) W H > 0 an W E > 0 B) W H > 0 an W E < 0 C) W H < 0 an W E < 0 D) W H < 0 an W E > 0 Electricity & MagneDsm Lecture 5, Slie 6

10 Clicker Question ConservaDve force: ΔU = W E Not a conservadve force. Does not have any ΔU. E F E F H r B) W H > 0 an W E < 0 Is ΔU posidve or negadve? A) PosiDve B) NegaDve Electricity & MagneDsm Lecture 5, Slie 7

11 Example: Two Point Charges Calculate the change in potendal energy for two point charges originally very far apart move to a separadon of q 1 q 2 Charge pardcles with the same sign have an increase in potendal energy when brought closer together. ε is another epsilon For point charges open choose r = infinity as zero potendal energy. Electricity & MagneDsm Lecture 5, Slie 8

12 Clicker Question Case A Case B 2 In case A two negadve charges which are equal in magnitue are separate by a istance. In case B the same charges are separate by a istance 2. Which configuradon has the highest potendal energy? A) Case A B) Case B Electricity & MagneDsm Lecture 5, Slie 9

13 Clicker Question Discussion As usual, choose U = 0 to be at infinity: Case A Case B U(r) 2 U A > U B U() U(2) 0 r Electricity & MagneDsm Lecture 5, Slie 10

14 Potential Energy of Many Charges Two charges are separate by a istance. What is the change in potendal energy when a thir charge q is brought from far away to a istance from the original two charges? Q 2 (superposidon) Q 1 q Electricity & MagneDsm Lecture 5, Slie 14

15 Potential Energy of Many Charges What is the total energy require to bring in three iendcal charges, from infinitely far away to the points on an equilateral triangle shown. A) 0 B) Q C) D) E) Q Work to bring in first charge: W 1 = 0 Work to bring in secon charge : Q Work to bring in thir charge : Electricity & MagneDsm Lecture 5, Slie 15

16 Potential Energy of Many Charges Suppose one of the charges is negadve. Now what is the total energy require to bring the three charges in infinitely far away? Q 2 A) 0 B) C) D) E) 1 Q Q Work to bring in first charge: W 1 = 0 Work to bring in secon charge : Work to bring in thir charge : Electricity & MagneDsm Lecture 5, Slie 16

17 CheckPoint: EPE of a System of Point Charges 1 Two charges which are equal in magnitue, but opposite in sign, are place at equal istances from point A as shown. If a thir charge is ae to the system an place at point A, how oes the electric potendal energy of the charge collecdon change? A. PotenDal energy increases B. PotenDal energy ecreases C. PotenDal energy oes not change D. The answer epens on the sign of the thir charge If the new charge has a poten2al energy cause by charge 1 equal to charge 2, when we sum them up, it will a up to 0, resul2ng in no change in total poten2al energy. thir charge will a kq 1 q 3 / an kq 2 q 3 / to the total U, unless q 3 is zero, it will efinitely change the total poten2al energy of the system. Electricity & MagneDsm Lecture 5, Slie 17

18 CheckPoint: EPE of a System of Point Charges 2 Two point charges are separate by some istance as shown. The charge of the first is posidve. The charge of the secon is negadve an its magnitue is twice as large as the first. Is it possible fin a place to bring a thir charge in from infinity without changing the total potendal energy of the system? A. YES, as long as the thir charge is posidve B. YES, as long as the thir charge is negadve C. YES, no ma=er what the sign of the thir charge D. NO HOW? LET S DO THE CALCULATION! As long as the thir charge is twice as far from the larger negative charge as it is the smaller positive charge, the total potential energy of the system will be unaffecte. The potential energies the thir charge will contribute to the system have opposite signs but NOT equal magnitues. So the net potential energy will not equal 0. Electricity & MagneDsm Lecture 5, Slie 18

19 Example A posidve charge q is place at x = 0 an a negadve charge 2q is place at x =. At how many ifferent places along the x axis coul another posidve charge be place without changing the total potendal energy of the system? A) 0 B) 1 C) 2 D) 3 Q X = 0 2Q X = x Electricity & MagneDsm Lecture 5, Slie 19

20 Example At which two places can a posidve charge be place without changing the total potendal energy of the system? Q 2Q A X = 0 B C X = D x A) A & B B) A & C C) B & C D) B & D E) A & D Let s calculate the posidons of A an B Electricity & MagneDsm Lecture 5, Slie 20

21 Lets work out where A is r A Q X = 0 2Q X = x Set ΔU = 0 Makes Sense! Q is twice as far from 2q as it is from +q Electricity & MagneDsm Lecture 5, Slie 21

22 Lets work out where B is r r Q X = 0 B 2Q X = x Serng ΔU = 0 Makes Sense! Q is twice as far from 2q as it is from +q Electricity & MagneDsm Lecture 5, Slie 22

23 What about D? Can you prove that is not possible to put another charge at posidon D without changing U? r Q X = 0 2Q X = D x 1 r+ = 2 r (r must be posidve)

24 Summary For a pair of charges: r Just evaluate Q 1 Q 2 (We usually choose U = 0 to be where the charges are far apart) For a collecdon of charges: Sum up for all pairs Electricity & MagneDsm Lecture 5, Slie 23