iclicker Quiz a) True b) False Theoretical physics: the eternal quest for a missing minus sign and/or a factor of two. Which will be an issue today?

Transcription

1 Clce Quz I egsteed my quz tansmtte va the couse webste (not on the clce.com webste. I ealze that untl I do so, my quz scoes wll not be ecoded. a Tue b False Theoetcal hyscs: the etenal quest fo a mssng mnus sgn and/o a facto of two. Whch wll be an ssue today?

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3 Electc monooles We sometmes efe to the total chage Q of an etended chaged object as ts monoole moment. When you bac fa enough away, any chaged object, egadless of ts shae, loos le a smle ont chage. In the eesson fo the electc feld of a monoole, the vecto ognates fom the cente of chage. E Q

4 You have an nsulatng od wth small shees at each end. On one shee you lace a chage Q and on the othe a chage -Q. Ths od s laced nto a unfom electc feld n the + decton. It s laced such that the mdont of the od s fed and cannot move but the od can otate about that ont. Befly descbe how the od mght esond f ostoned at some andom oentaton and eleased. assumng t s a ostvely chaged feld The od should otate clocwse untl the od s algned along the y- as. The od would otate because the shee wth the -Q chage would be ulled towads the + decton and the +Q shee would be eelled fom the + decton. The ostve Q end would ont towads the decton of the feld lnes. That s, f the -Q end wee the bac of an aow, and the +Q was the head, the aow would ont the same way as the feld lnes. Ths confguaton s called an electc dole

5 Electc dole moment aq Whee a s the seaaton between the q and the +q. The decton of s fom the negatve chage to the ostve chage. Sometmes we call the dstance d athe than a An electc dole wll feel a toque f thee s a comonent of eendcula to the electc feld.

6 Electc doles Equal and ooste chages of magntude Q = Q + = Q. + onts fom the negatve chage to the ostve chage. We now as What s the electc feld oduced by a dole? Defne dole moment: Q Le +, the dole moment vecto always onts fom the negatve chage to the ostve chage. E E E Q ( Q ( Lmt : 0 and Q such that Q s constant.

7 Dole n a unfom feld

8 An electcally neutal dole s laced n an etenal feld. In whch stuaton(s s the net foce on the dole zeo?. A. C. E Moe than one of the above s coect

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10 HW -1. Two chaged atcles wth chages of ±q = [01] C ae seaated by a dstance of a = 0.80 nm. (a What s the dole moment of ths chage a? (b Usng the dole aomaton (d << a, what s magntude of the electc feld at a oston along* the dole as whch s a dstance of d = cm away fom the chage a? [(a 5: ; 8: C m (b ; N/C] *Hnt: You wll fnd the fomula n the study gude. How does t dffe fom the tet? Geneal devaton at end of esentaton.

11 Moe Imotant dole facts: They ae common n many dsclnes They have no net chage but They do ceate an Electc Feld that Falls off as 1/³. (It eally s 1/³ not 1/²! You can use the bnomal eanson to get these fomulae.

12 a z What s the Electc feld at a dstance z along the z as due to a dsc wth a suface chage Q whch s evenly dstbuted.

13 Calculatng the electc foce/feld due to a contnuous chage dstbuton dq E qdq df q e q lm q 0 e dq de dq dq

14 ( ( d L qq qdq df e / / ( L L e d L qq df F d L Q d dq 4 / ( ( ( ( / 1 / 1 1 / / L qq L L L L L qq L L L qq L qq e e e L L e

15 The hemshee shown s chaged unfomly wth a ostve suface chage densty. At the ogn, what decton s the electc feld? A. + decton B. +y decton C. +z decton D. Somethng else not along a,y, o z as E. Zeo magntude thus no decton

16 -. A unfomly chaged ng of adus 11.6 cm has a total chage of Q = [0] C. What s the magntude of the electc feld on the as of the ng at a dstance of 4.81 cm fom the cente of the ng? [1.00; 1.60 N/C]

17 Fnd E at the cente of a hemshecal shell of unfom chage densty.

18 In the acet What does t mean to ntegate?

19 Shecal Coodnates sn( sn( sn( cos( sn( cos( cos( sn( y z z z y

20 Shecal Aea d d z da d d sn( d d sn( z cos(

21 Shecal Aea d d a d ad da sn( shecal atchwo a dz dz a dz da sn( sn( sn( tomato slces cones d a ad da sn( oange slces d a da sn( z a a a z

22 Olde altenate sldes follow

23 , Fo ( ( ( ( y y a a Q y a y a Q Q Q Q E j j E E E E Off-as dole feld Seway.6

24 E ( / 1 / 1 ( 1 ( ( aq a Q a a Q a a Q a a Q Q Q Q E E E On-as dole feld Bnomal aomaton +Q -Q E d = a ( s f s s

25 ( E Ty usng the geneal dole fomula (only fo the usts among you 0 ( ( and y y y j j j E j Peendcula case ( and E On-as case

26 Moments of a dstbuton (eta detals fo usts (If you tell anyone that I mentoned ths, I ll deny t! Monoole moment (scala q ( dv dq Dole moment (vecto ( dv Quaduole ~ moment (ola an- tenso ~ Q ( I ( dv Choose ogn at the cente of chage (le cente of mass The electc feld of a chage dstbuton can be eessed as a sees eanson nvolvng successvely hghe moments of the dstbuton. E q ( ~ ~ 5( Q Q 4...

27 Thee s a egon nea the ogn of a coodnate system that you ae told contans chages. You ae not able to see them but have been ased to lean as much about them as ossble. In you eementaton you lace a test chage at thee ostons a dstance d fom the ogn and detemne the decton of the electc feld. Along the ostve as the feld onts n the + decton. Along the negatve as t also onts n the + decton. On the y as howeve t onts n the negatve decton. Consde ths esult and suggest what you mght be able to say about the chages nea the ogn. It would seem fom ths nfomaton that thee ae at least two chages nea the ogn, one ostve and one negatve. It may be sad that thee s a ostve and a negatve chage esent n the cluste. The ostve chage would be close to the + decton than the negatve chage. Ths would elan the decton of the feld stayng consstent n the + decton on ethe sde of the as. Along the y as the feld would be movng n the - decton because the electc feld lne fom the ostve chage on the ght would be movng towads the negatve chage on the left.

28 It could be two chages ght net to each othe. Thee would be a negatve chage on the left sde, and a ostve chage on the ght. Ths would cause a test chage on the ght to move ght, away fom the ostve chage, and the test chage on the left to be attacted towads the ostve chage. The test chage laced on the y as would be ushed left, because t s slghtly attacted by the negatve chage, and slghtly eelled by the ostve one. The y-coodnate's would cancel out. I beleve that the only way fo ths to be ossble s fo thee to be equal numbes of ostve and negatve chages.

29 Electc Feld Lnes The decton of the Electc feld s the decton the foce on a ostve test chage would be at a gven ont f a chage wee esent. The decton of the Electc feld lnes show the decton of the feld. The densty of the feld lnes tells how stong the feld s (how much foce a ostve test chage would feel Feld lnes always stat and end on a chage.

30 Whch s a vald eesentaton of feld lnes when no chages ae esent n the vewed aea?: e Moe than one ae vald

31 See nteactve alet at htt://lectueonlne.cl.msu.edu/~mm/alst/alets.htm

32 Indvdual queston: The hemshee shown s chaged unfomly wth a ostve suface chage densty. At the ogn, what decton s the electc feld? A. + decton B. +y decton C. +z decton D. Somethng else not along a,y, o z as E. Zeo magntude thus no decton

33 Shecal Volume d d d dv d d d dv sn( d d dv sn( d d dv dz z a dv ( shecal atchwo cones oange slces tomato slces sn( z z d

34 How do I fnd the suface aea?

35 Futue

36 Flu Bucet 1 wll catch moe wate than bucet Aea vecto 1 Defne an Aea vecto eendcula to the suface. The moe that vecto s lned u wth the an, the moe an gets nto the bucet. If ths vecto s eendcula to the an, no an gets nto the bucet.

37 E Electc Flu A E A cos E suface da The net flu though a suface s the numbe of lnes leavng the suface mnus the numbe of lnes enteng the suface.

38 A cylndcal ece of nsulatng mateal s laced n an etenal electc feld, as shown. The net electc flu assng though the suface of the cylnde s A. ostve. B. negatve. C. zeo.