Physics 2112 Unit 5: Electric Potential Energy
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1 Physics 11 Unit 5: Electric Potential Energy Toay s Concept: Electric Potential Energy Unit 5, Slie 1
2 Stuff you aske about: I on't like this return to mechanics an the potential energy concept, but this is conceptually easier. Can't wait to see it in class. Want to see examples worke out. Concepts were a lot easier to unerstan compare to the previous section. Please o an example of the best way to sort out the values of potential energy in a complex system. motion of a point charge in an electric fiel relating to potential energy nees more elaboration the only thing I in't get out of this lecture was: the way a point charge woul move if release from rest in a region containing an electric fiel. How o electric fiels affect point charges?? very much like the potential energy lecture in mechanics. its interesting to see how similar the charges can be to what we saw in mechanics Potential energy of a system of point charges is confusing. Coul we go over this please? one well (: Unit 5, Slie
3 Where we re heae. Force 111 Energy 11 E Fiel??? Unit 5, Slie 3
4 Recall from Mechanics: W r = F r r 1 W = DK TOT F r W > Object spees up ( DK > ) or F r F r W < Object slows own ( DK < ) F r W = Constant spee ( DK = ) Unit 5, Slie 4
5 Prelecture Question Masses M 1 an M are initially separate by a istance R a. Mass M is now move further away from mass M 1 such that their final separation is R b. Which of the following statements best escribes the work W ab one by the force of gravity on M as it moves from R a to R b? A. W ab > B. W ab = C. W ab < Unit 5, Slie 5
6 Potential Energy DU W conservati If gravity oes negative work, potential energy increases! ve Same iea for Coulomb force if Coulomb force oes negative work, potential energy increases. + + F + Dx Coulomb force oes negative work Potential energy increases Unit 5, Slie 6
7 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 irection that makes its potential energy increase. B) In a irection that makes its potential energy ecrease. C) Along a path of constant potential energy. It will move in the same irection as F F Work one by force is positive Dx DU = Work is negative Nature wants things to move in such a way that PE ecreases Unit 5, Slie 7
8 Question You hol a positively charge ball an walk ue east in a region that contains an electric fiel irecte ue west. E F E F H r 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 > an W E > B) W H > an W E < C) W H < an W E < D) W H < an W E > Unit 5, Slie 8
9 Question Conservative force: DU = W E Not a conservative force. Does not have any DU. E F E F H r B) W H > an W E < Is DU positive or negative? A) Positive B) Negative Unit 5, Slie 9
10 Two Point Charges Calculate the change in potential energy for two point charges originally very far apart move to a separation of DU = k q1q r 1 r q1q DU = k (Charge particles with the same sign have an increase in potential energy when brought closer together.) q 1 For point charges often choose r = infinity as zero potential energy. q1q U = k q Unit 5, Slie 1
11 Prelecture Question In case A two opposite charges which are equal in magnitue are separate by a istance. In case B the same charges are separate by a istance. Which configuration has the highest potential energy? A) Case A B) Case B Case A Case B Unit 5, Slie 11
12 Clicker Question In case A two negative charges which are equal in magnitue are separate by a istance. In case B the same charges are separate by a istance. Which configuration has the highest potential energy? A) Case A B) Case B Case A Case B Unit 5, Slie 1
13 Case A Case B Clicker Question Discussion q 1 U A = r 4 U B U( r) = q 1 = q1q 1 r U(r) U A > U B U() U() r Unit 5, Slie 13
14 Example 5.1 (Velocity after a long time) The two charges shown below are hel in place an then release. What is their final velocity after they have move a great istance apart? = 1cm q 1 q m 1 = 5X1-1 kg q 1 = +6nC m = 7X1-1 kg q = +8nC Unit 5, Slie 14
15 Pause to connect to 111 When we sai The ball has mgh of potential energy. we really meant The ball-earth system has mgh of potential energy. Why coul we ignore earth? Why can t we ignore the other charges now? Unit 5, Slie 15
16 CheckPoint: 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 position at a istance R away from its starting position. The final location of +q is at a istance r from +Q. What is the change in the potential energy of the two charges uring this process? A. kqq/r B. kqqr/r 1 C. kqqr/r D. kqq((1/r )-(1/r 1 )) E. kqq((1/r 1 )-(1/r )) Unit 5, Slie 16
17 CheckPoint Result: EPE of Point Charge What is the change in the potential energy of the two charges uring this process? A. kqq/r B. kqqr/r 1 C. kqqr/r D. kqq((1/r )-(1/r 1 )) E. kqq((1/r 1 )-(1/r )) D) The change in potential energy = final potential energy - initial potential energy. E) the change in potential energy is given as an integral with respect to the raius so there will be two raii in the equation an the change is negative so the before raius an after raius flip. Unit 5, Slie 17
18 CheckPoint Result: EPE of Point Charge What is the change in the potential energy of charge +q uring this process? U 1 = 1 Qq r 1 U = 1 Qq r DU U U 1 = Qq 1 1 r r1 Note: +q moves AWAY from +Q. Its Potential energy MUST DECREASE DU < Electricity & Magnetism Lecture 5, Slie 18
19 Potential Energy of Many Charges Two charges are separate by a istance. What is the change in potential energy when a thir charge q is brought from far away to a istance from the original two charges? DU = qq 1 + qq 1 1 Q (superposition) Don t ouble count No sines an cosines Q 1 q Electricity & Magnetism Lecture 5, Slie 19
20 Potential Energy of Many Charges What is the total work by the electric fiel when three ientical charges by brought from infinitely far away to the points on an equilateral triangle. A) B) C) D) W W W = = + Q 1 Q Q = 3 1 Q DU = W con = +3k Q Q E) W = + 3 Q 1 Q Work to bring in first charge: W 1 = Work to bring in secon charge : Work to bring in thir charge : W W 3 1 Q = 1 Q = 1 Q = Q Electricity & Magnetism Lecture 5, Slie
21 Potential Energy of Many Charges What is the total work by the outsie force when it brings three ientical charges from infinitely far away to the points on an equilateral triangle? A) B) C) D) W = W = + Q 1 Q Q 1 W = 3 Q 1 Q E) W = + 3 Q Q Electricity & Magnetism Lecture 5, Slie 1
22 Potential Energy of Many Charges Now lets say the secon charge is negative. Now what is the total work one by the fiel to bring the three charges in? A) B) C) D) Q 1 W = + 1 Q 1 W = 1 Q 1 W = + Q E) Q 1 Q Q W = 1 W = W i 1 Q = + 1 Q DU = DU Q = k Work to bring in first charge: W 1 = Work to bring in secon charge : W 1 Q = + Work to bring in thir charge : W = + 1 Q 1 Q 3 = Unit 5, Slie
23 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 potential energy of the charge collection change? A. Potential energy increases B. Potential energy ecreases C. Potential energy oes not change D. The answer epens on the sign of the thir charge Unit 5, Slie 3
24 CheckPoint: EPE of a System of Point Charges 1 If a thir charge is ae to the system an place at point A, how oes the electric potential energy of the charge collection change? A. Potential energy increases B. Potential energy ecreases C. Potential energy oes not change D. The answer epens on the sign of the thir charge A) If a positive charge is ae, then the overall potential energy will become more positive. If a negative charge is ae, then the overall potential energy will still become more positive. So it oes not matter what charge it is, the overall energy will increase either way. C) Since the original two charges are opposite in irection with equal magnitue in potential energy (ue to their equal magnitue an istance), no matter what sign charge goes at point A, the potential energies will cancel out an be left with the initial potential energy between the two original charges. D) If a positive charge is place at A, the potential energy woul be negative an viceversa if a negative charge is place at A Unit 5, Slie 4
25 CheckPoint: EPE of a System of Point Charges Two point charges are separate by some istance as shown. The charge of the first is positive. The charge of the secon is negative 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 potential energy of the system? A. YES, as long as the thir charge is positive B. YES, as long as the thir charge is negative C. YES, no matter what the sign of the thir charge D. NO Unit 5, Slie 5
26 CheckPoint: EPE of a System of Point Charges Is it possible fin a place to bring a thir charge in from infinity without changing the total potential energy of the system? A. YES, as long as the thir charge is positive B. YES, as long as the thir charge is negative C. YES, no matter what the sign of the thir charge D. NO A) If the thir charge approaches the positive charge, the total potential energy can stay at its original state. C) there will be a point in space where the potential energy of the thir charge will be zero from the other two charges so yes, it is possible an it wont matter what's the sign of the actual charge is D) it is not possible because the only reason it i not change the total potential energy in the last Checkpoint is because the two original charges ha the SAME MAGNITUDE an therefore were able to cancel each other's potential energies out. The fact that these have DIFFERENT magnitues makes that impossible. LET S DO THE CALCULATION! Unit 5, Slie 6
27 Example 5. A positive charge q is place at x = an a negative charge q is place at x =. At how many ifferent places along the x axis coul another positive charge be place without changing the total potential energy of the system? A) B) 1 C) D) 3 Q X = Q X = x Unit 5, Slie 7
28 Example At which two places can a positive charge be place without changing the total potential energy of the system? Q A B C D X = Q X = x A) A & B B) A & C C) B & C D) B & D E) A & D Let s calculate the positions of A an B Unit 5, Slie 8
29 Lets work out where A is r A Q X = Q X = x DU = + 1 Qq 1 r Qq r + Set DU = 1 r = r + Makes Sense! Q is twice as far from q as it is from +q r = Unit 5, Slie 9
30 Lets work out where B is r r Q X = B Q X = x Setting DU = 1 r = r r = r Makes Sense! Q is twice as far from q as it is from +q r = 3 Electricity & Magnetism Lecture 5, Slie 3
31 CheckPoint: EPE of a System of Point Charges Two point charges are separate by some istance as shown. The charge of the first is positive. The charge of the secon is negative 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 potential energy of the system? A. YES, as long as the thir charge is positive B. YES, as long as the thir charge is negative C. YES, no matter what the sign of the thir charge D. NO Unit 5, Slie 31
32 Summary For a pair of charges: q1q = k r Just evaluate U (We usually choose U = to be where the charges are far apart) r Q 1 Q Sum up For a collection of charges: q1q U = k r for all pairs Unit 5, Slie 3
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