You Comments I'm thinking of changing my majo to physics, not because I'm amazing at it, just because it seems inteesting an I enjoy it. Shoul I switch? I thooughly looke though the pelectue this time aoun an things mae so much moe sense! I in't finish my homewok fo this week. :( WHY AM I BAD AT THIS In the powe points uing lectue can the clicke questions be in a lage font? they ae extemely ifficult to see fom the back Thee's this eally hot guy who sits a few seats away fom me. I want to talk to him, but I'm woie that I'm out of his league. I mean, he's totally gogeous, an I'm just kin of aveagelooking. What shoul I o? Okay, so lots of people ene up asking what epsilon naught was a few lectues ago, but I'm assuming that most of us wee awae it was a constant. But what oes epsilon naught epesent (as unimpotant as it might be fo this couse) Why oes the pelectue sometimes uses K an sometimes uses /4piE? FINALLY SOMETHING THAT MAKES SENSE!! what fequency ae ou Iclickes suppose to be on? like o 3 iffeent ones wok. an the only one that has a title thing in oom 4 is phys... Electicity & Magnetism Lectue 5, Slie
Physics Lectue 5 Toay s Concept: Electic Potential Enegy 5 Electicity & Magnetism Lectue 5, Slie
Recall fom physics : Wok (Mechanics Review) W = F W = K TOT F W > (e.g. W gavity on object oppe) o F F W < (e.g. W gavity on ball going up) F W = (e.g. W gavity on moving hoizontally) 7 Electicity & Magnetism Lectue 5, Slie 3
Potential Enegy This lectue was confusing between the negative an positive wok an then the negative an positive wok, I eally in't unestan it. U W consevati ve If gavity oes negative wok, potential enegy inceases! Same iea fo Coulomb foce if Coulomb foce oes negative wok, potential enegy inceases. + + F + + x Coulomb foce oes negative wok Potential enegy inceases 8 Electicity & Magnetism Lectue 5, Slie 4
CheckPoint 4 A chage is elease fom est in a egion of electic fiel. The chage will stat to move A) In a iection that makes its potential enegy incease. B) In a iection that makes its potential enegy ecease. C) Along a path of constant potential enegy. Simila to gavity. The object always wants to fall (o to have less potential enegy). It will move in the same iection as F x F Wok one by foce is positive U = Wok is negative Natue wants things to move in such a way that PE eceases Electicity & Magnetism Lectue 5, Slie 5
Clicke uestion You hol a positively chage ball an walk ue east in a egion that contains an electic fiel iecte ue west. E F E F H W H is the wok one by the han on the ball W E is the wok one by the electic fiel on the ball Which of the following statements is tue: A) W H > an W E > B) W H > an W E < C) W H < an W E < D) W H < an W E > Electicity & Magnetism Lectue 5, Slie 6
Clicke uestion Consevative foce: U = W E E F E F H B) W H > an W E < Is U positive, negative o zeo? A) Positive B) Negative C) Zeo 4 Electicity & Magnetism Lectue 5, Slie 7
Example: Two Point Chages Calculate the change in potential enegy fo two point chages oiginally vey fa apat move to a sepaation of 6 U F = f i = F x k qq x x qq = kq q = k = Chage paticles with the same sign have an incease in potential enegy when bought close togethe. Fo point chages often choose = infinity as zeo potential enegy. q x=- q q q x= Electicity & Magnetism Lectue 5, Slie 8
Clicke uestion Case A Case B In case A two negative chages which ae equal in magnitue ae sepaate by a istance. In case B the same chages ae sepaate by a istance. Which configuation has the highest potential enegy? A) Case A B) Case B 8 Electicity & Magnetism Lectue 5, Slie 9
Clicke uestion Discussion As usual, choose U = to be at infinity: Case A Case B U() q U A = 4 U B U( ) = qq q = U A > U B U() U() 9 Electicity & Magnetism Lectue 5, Slie
An Remembe U is just a numbe (not a vecto) U DOES have a sign U() U A U A > U B U B U B > U C U C U C > U D U D Physics Lectue 5, Slie
CheckPoint A chage +q is move fom position to position, What is the change in potential enegy? A kq B kqr C R D kq E kq kqr U = kq U = kq 3 Fin the PE fo each position an subtact fom. k,, an q ae constant thoughout the poblem. U U U = kq Note: +q moves AWAY fom +. Its Potential enegy MUST DECREASE U < Electicity & Magnetism Lectue 5, Slie
Potential Enegy of Many Chages Two chages ae sepaate by a istance. What is the change in potential enegy when a thi chage q is bought fom fa away to a istance fom the oiginal two chages? U = q + q 4 (supeposition) q 6 Electicity & Magnetism Lectue 5, Slie 3
Potential Enegy of Many Chages What is the total enegy equie to bing in thee ientical chages, fom infinitely fa away to the points on an equilateal tiangle shown. A) B) C) D) U = U = U = 3 E) U = 6 W = W i 3 = 3 U = + Wok by E to bing in fist chage: W = Wok by E to bing in secon chage : Wok by E to bing in thi chage : W W 3 = = = 3 Electicity & Magnetism Lectue 5, Slie 4
Potential Enegy of Many Chages Suppose one of the chages is negative. Now what is the total enegy equie to bing the thee chages in infinitely fa away? A) B) U = + C) U = D) U = + E) U = 3 W = W U i = + = 33 Wok by E to bing in fist chage: W = Wok by E to bing in secon chage : W = + Wok by E to bing in thi chage : W = + 3 = Electicity & Magnetism Lectue 5, Slie 5
CheckPoint Two chages with equal magnitue but opposite sign ae locate at equal istances fom the point labele A If a thi chage is bought in fom fa away to point A, how oes the potential enegy of the collection of chages change? 36 Inceases Deceases Same Depens on sign of chage A B C D C) The ae pat of potential enegy fom a thi chage cancels out, egaless of the sign.. D) The sign of the thi chage woul etemine the sign of the oveall potential enegy when the foces on all 3 chages ae ae. Electicity & Magnetism Lectue 5, Slie 6
CheckPoint 3 A positive chage is place on the ight sie of a negative chage. The magnitue of the negative chage is twice that of the positive chage. Is thee any (finite) location that a thi chage can be place such that the total potential enegy of the system oes not change? C) If the chage is place twice as fa fom the geate negative chage as fom the smalle positive chage, then it shoul wok. D) A chage will always ceate a foce to the othe chages no matte how fa away the chage is. Futhemoe, afte looking at the potential enegy gaph,the gaph neve eaches only appoaches it. LET S DO THE CALCULATION! 38 Electicity & Magnetism Lectue 5, Slie 7
Example A positive chage q is place at x = an a negative chage q is place at x =. At how many iffeent places along the x axis coul anothe positive chage be place without changing the total potential enegy of the system? A) B) C) D) 3 X = X = x 4 Electicity & Magnetism Lectue 5, Slie 8
Example At which two places can a positive chage be place without changing the total potential enegy of the system? A B C D X = 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 43 Electicity & Magnetism Lectue 5, Slie 9
Lets wok out whee A is A X = X = x U = + q q + Set U = = + = Makes Sense! is twice as fa fom q as it is fom +q 45 Electicity & Magnetism Lectue 5, Slie
Lets wok out whee B is X = B X = x Setting U = = = = 3 Makes Sense! is twice as fa fom q as it is fom +q 5 Electicity & Magnetism Lectue 5, Slie
Summay Fo a pai of chages: qq = k Just evaluate U (We usually choose U = to be whee the chages ae fa apat) Sum up Fo a collection of chages: qq U = k fo all pais Electicity & Magnetism Lectue 5, Slie