Physics 202, Lecture 2. Announcements

Transcription

1 Physcs 202, Lectue 2 Today s Topcs Announcements Electc Felds Moe on the Electc Foce (Coulomb s Law The Electc Feld Moton of Chaged Patcles n an Electc Feld Announcements Homewok Assgnment #1: WebAssgn (coesponds to Ch. 23 #5,10,12,15,19,26,42 Due Fday, Sept 14 at 10PM Futue assgnments wll be due Mondays at 10 PM. IMPORTANT: Exam polcy evson If you have an evenng class conflct, let us know ght away (now and we wll accommodate t. Recall exam dates: 10/1, 10/29, 11/26, 5:30-7 PM. 1

2 Coulomb s Law (Pont Chages Foce on 2 by 1 : Foce on 1 by 2 : F 12 = k e 1 2 F 21 = k e 1 2 Vecto decton of F: moe explctly 1 Foce on 2 by 1 : F12 = k 1 2 e 2 ( = k e n the above language: = 1 ˆ = ˆ ˆ ( Coulomb s Law: Multple chages Many pont chages: lnea supeposton Foce on chage 1: F 1 = F 1 = k 1 e 1 2 ˆ 1 Impotant: vecto sum 3 Moe explctly: F 1 = k 1 e 1 ( " = " k e 1 (

3 Coulomb s Law: Dstbutons Contnuous dstbutons of chage: dvde nto " # d Inteacton of pont chage wth contnuous dstbuton: F 1 = k e 1 $ d ˆ Lne segment (1 dmenson: Suface (2 dmensons: Volume (3 dmensons: d = dx d = da d = dv moe about ths shotly Popetes of the Electc Foce One of fou fundamental foces: Stong >Electomagnetc > weak >> gavty Magntude: Popotonal to 1/ : doubled ¼ F Decton: epulsve fo lke sgns, attactve fo opposte sgns A consevatve foce (wok ndependent of path: W = " f ke12 F d = A potental enegy can be defned. (Topc of Ch. 25 k 1 e 2 U = f ke12 + = ( U f ( U 3

4 The Electc Feld Ognal (Coulomb s vew of electc foce apples electc foce on 0 (acton at a dstance F = k e 0 Foce on chage always popotonal to stength of that chage ˆ 0 F Moden vew of electc foce: s the souce of an electc feld E The electc feld E apples a foce on 0 F = 0 k e ˆ = 2 0 E E : souce chage 0 : test chage E ndependent of 0 Asde: Vecto and Scala Felds The feld concept s extemely useful n physcs, both conceptually and fo pactcal puposes Usng the concept of the electc feld, one can map the electc feld anywhee n space poduced by any abtay chage dstbuton What s a feld? A feld epesents some physcal uantty (e.g., tempeatue, wnd speed, foce It can be a scala feld (e.g., tempeatue feld It can be a vecto feld (e.g., electc feld It can be a tenso feld (e.g., spacetme cuvatue 4

5 A Scala Feld These solated tempeatues sample the scala feld (you only lean the tempeatue at the pont you choose, but T s defned eveywhee (x, y A Vecto Feld Pehaps moe nteestng to know whch way the wnd s blowng That would eue a vecto feld (you lean both wnd speed and decton 5

6 The Electc Feld, Recap Chage souces an electc feld E E( = k e ˆ Moe geneally, E( = k e ( " " 2 " = k e (chage at ogn ( " " 3 P " P Multple souces: E( = k e 2 ˆ Contnuous dstbutons: E( d = k ˆ e (moe geneal E( = k ( " e # " 3 E( d( = k # " e " 3 Vsualzng the Electc Feld Consde the electc feld of a postve pont chage at the ogn: vecto map map feld lnes + chage + chg + + Magntude: length of aows Magntude: local densty of lnes 6

7 Rules fo Feld Lnes Popety 1. Feld lnes can stat o temnate only on chages, neve empty space. Popety 2. Feld lnes of pont chage go off to nfnty. (tue fo any localzed dstbuton wth nonzeo net chage Popety 3. Feld lnes ognate on postve chages, temnate on negatve chages. Popety 4. No two feld lnes eve coss, even when multple chages pesent. Example: Pont-Lke Chages E( = k e ˆ E( = k e ˆ + - 7

8 Example: Two Chaged Patcles + and + + and - Two Chaged Patcles 8

9 Example: Unfomly Chaged Sphee A unfomly chaged sphee has a adus R and total chage Q, fnd the electc feld outsde the sphee. See notes (to be posted on web z E(x,y,z=? R y Doable but complcated wth the conventonal method Please pevew Ch. 24 Gauss Law befoe Tuesday x 9