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Physics 212 Lecture 5 Today's Concept: Electric Potential Energy Defined as Minus Work Done by Electric Field Physics 212 Lecture 5, Slide 1 Music Who is the Artist? A) Tito Puente B) Buena Vista Social Club C) Louis Prima D) Freddie Omar con su banda E) Los Hombres Calientes Cuban Jazz !! Thanks to Ry Cooder for bringing these guys to our attention !! Why ?? Cuban Jazz at Krannert (Ellnora) Friday night (10:30pm) Marc Ribot y Cubanos Postizos Remembering Arsenio Rodriguez FREE Physics 212 Lecture 5 Your Comments “This really seems like a rehash of mechanics with electric Right! Nothing charges instead of masses.” really new “Please discuss in lecture about how the point charges will affect the electric field in different situations where it has both same charge or where it has opposite charges. I am confused about this. Also, SIGNS! please go over the potential energy equation to refresh my memory.” “When solving for the potential energy, does r1 get subtracted from r2? or is it the other way around?” “Homework problem style examples would be helpful, the checkpoints felt too easy.” Example today: “Still generally confused on some questions about the calculation for CP 3 potential energy, like the third checkpoint.” Discussion Sections “Had there been office hours this week I definitely would have this week should help been there. I'm still not 100% sure about Gauss' Law.” WORKED EXAMPLES! “Labor Day Weekend and Physics must definitely have the same charge because the weekend kept pushing the homework and this prelecture from getting done.” 05 Physics 212 Lecture 5, Slide 3 r2 Recall from physics 211: W F dr WTOT K r1 F Object speeds up ( K > 0 ) dr W>0 F dr or W<0 Object slows down ( K < 0 ) F dr F W=0 Constant speed ( K = 0 ) dr 9 Physics 212 Lecture 5, Slide 4 Potential Energy U Wconservative If gravity does negative work, potential energy increases! Same idea for Coulomb force… if Coulomb force does negative work, potential energy increases. F + + x Coulomb force does negative work + + Potential energy increases 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 “Since potential energy is negative, the charge will try to increase its potential energy, bringing it to zero..” “It wants to go to a spot with less PE.” “constant potential energy would require no work to preform.” It will move in the same direction as F F Work done by force is positive x U = -Work is negative Nature wants things to move in such a way that PE decreases 34 Physics 212 Lecture 5, Slide 6 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 FH 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 Physics 212 Lecture 5, Slide 7 Not a conservative force. Conservative force: U = - WE Does not have any U. FE FH dr E B) WH > 0 and WE < 0 Is U positive or negative? A) Positive B) Negative 16 Physics 212 Lecture 5, Slide 8 Example: Getting the signs right Case A d Case B 2d 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 22 Physics 212 Lecture 5, Slide 9 Example: Getting the signs right q1q2 1 • As usual, choose U = 0 to be at infinity: U (r ) 4 0 r q2 1 Case A UA d 4 0 d Case B q2 1 UB 2d 4 0 2d U(r) UA > UB U(d) U(2d) 0 r 23 Physics 212 Lecture 5, Slide 10 Example: Two Point Charges Calculate the change in potential energy for two point charges originally very far apart moved to a separation of “d” d q1q2 U k 2 dr d r12 q1 q2 q1q2 1 q1q2 U k d 4 0 d Charged particles w/ same sign have an increase in potential energy when brought closer together. For point charges often choose r=infinity as “zero” potential energy. 19 Physics 212 Lecture 5, Slide 11 Checkpoint 1 A charge of +Q is fixed in space. A second charge of +q was first placed at a distance r1 away from +Q. Then it is moved to a new position at a distance R away from its starting point on a straight path. The final location of +q is at a distance r2 from +Q. What is the change in the potential energy of the charge +q in the process? 1 Qq 1 Qq A. kQq/R B. kQqR/r12 C. kQqR/r22 U initial U final D. kQq(1/r2 - 1/r1) E. kQq(1/r1 - 1/r2) 4 0 r1 4 0 r2 “It is inversely proportional to the first radius.” Qq 1 1 “Simple conservation of energy problem: final U U f U i potential minus initial potential should equal 4 0 r2 r1 change. ” Note: +q moves AWAY from +Q. “1/r1 will be larger then 1/r2 and this must be Its Potential energy MUST DECREASE positive” 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? Q2 d d qQ1 1 qQ2 1 U 4 0 d 4 0 d (superposition) Q1 q 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. A) 0 Q 2 Q 1 B) U 4 0 d 3 Q2 Q2 1 C) U 2 4 d d d W Wi 0 40 d 2 D) U 3 Q 1 4 0 d 3 Q2 Q2 1 U E) U 6 40 d 4 0 d Q d Q Work to bring in first charge: W1 = 0 1 Q2 Work to bring in second charge : W2 40 d 1 Q2 1 Q2 2 Q2 Work to bring in third charge : W3 40 d 40 d 40 d 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? 2 A) 0 Q Q2 1 B) U 1 4 d 1 Q2 0 d d W Wi 40 d 2 Q 1 C) U 1 4 d 0 2 D)U 2 Q 1 U 1 Q2 4 0 d Q2 1 40 d E) U 2 1 Q d Q 4 0 d Work to bring in first charge: W1 = 0 1 Q2 Work to bring in second charge : W2 40 d 1 Q2 1 Q2 Work to bring in third charge : W3 0 40 d 40 d 29 Physics 212 Lecture 5, Slide 15 Checkpoint 2 Two charges which are equal in magnitude, but opposite in sign, are place at equal distances from point A. If a third charge is added to the system and placed at point A, how does the electric potential energy of the charge collection change? A. Increases B. decreases C. doesn’t change D. The answer depends on the sign of the third charge “inserting another charge is going to increase the magnitude of the potential energy.” “No matter what the sign is the potential energy would be a positive number minus a negative number minus another negative number. ” “the change in potential is found by adding another kqq/r term. this term is dependent on the sign of the new charge.“ 31 Physics 212 Lecture 5, Slide 16 Checkpoint 3 You start with two point charges separated by some distance. The charge of the first is positive. The charge of the second is negative and its magnitude is twice as large as that of the first. Is it possible to find a place to which you can bring a third charge in from infinity without changing the total potential energy of the system? A. YES, as long as the third charge is positive B. YES as long as the third charge is negative C. YES, no matter what the third charge is D. NO “The positive third charge will cancel out the negative charge.“ “It doesn't matter what the sign is. Place the new charge twice the distance from the - as the + charge. It doesn't matter what the sign is because the U added to the system will now be zero.” “Adding a third charge that is opposite to at least one other charge will cause a change in potential energy” 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 -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? q -2q x X=0 X=d A) 0 B) 1 C) 2 D) 3 37 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 -2q A X=0 B C D x X=d A) A&B B) A&C C) B&C Let’s calculate the positions of A and B D) B&D E) A&D 40 Physics 212 Lecture 5, Slide 19 Lets work out where A is r d q -2q A X=0 x X=d 1 Qq 1 2Qq U 40 r 40 r d Set U = 0 1 2 r rd Makes Sense! rd Q is twice as far from -2q as it is from +q 43 Physics 212 Lecture 5, Slide 20 Lets work out where B is r d-r q -2q x X=0 B X=d 1 2 Setting U = 0 r d r 2r d r d r 3 Makes Sense! Q is twice as far from -2q as it is from +q Physics 212 Lecture 5, Slide 21 46 Summary For a pair of charges: r q1q2 Just evaluate U k q1 q2 r (We usually choose U = 0 to be where the charges are far apart) For a collection of charges: q1q2 Sum up U k for all pairs r Physics 212 Lecture 5, Slide 22