Chapter 21: Electric Charge and Electric Field

Transcription

1 Chpte : lectc Chge nd lectc Feld lectc Chge Known b ncent Geeks s el s 600 BC Sttc electct: electc chge v fcton (see lso fg.) (Attempted) pth bll demo nd/o scotch tpe demo: knds of popetes objects wth sme tpe of popet epel ech othe objects wth dffeent tpes of popetes ttct ech othe both popetes e lws ceted togethe Benjmn Fnkln: knds of chges e postve nd negtve b conventon, negtve chge ssocted wth mbe (plstc) Consevton of Chge: The lgebc sum of ll the electc chges n n closed sstem s constnt. pc: Quntzton nd Consevton of Chge Mcoscopc stuctue of mtte: Atoms Nucleus most of mss postve chge composed of potons (ech hs chge +e) neutons (no electc chge) obtng electons (ech hs chge e) Atoms tend to be chge neutl Ions hve lost (posttve) o gned (negtve) electons chge quntzed: e (63)0-9 C Chge tnsfe usull n the fom of ddton o emovl of electons. pc:

2 pplcton: lse pnte Applng negtve chge to the photosenstve dum Lse neutlzng the negtve chge on the photoeceptve dum to fom n electosttc mge. Meltng tone onto ppe usng het nd pessue. mges souce: use:dle Mhlko CC-BY-AS 3.0 pc: 3 TYU Stctl spekng, does the (now postvel chged) plstc od wegh moe, less o ectl the sme fte t ws chged b ubbng t wth fu (comped to when t ws not chged). ) moe ) less 3) sme 4) huh? Stctl spekng, does the (now negtvel chged) glss od wegh moe, less o ectl the sme fte t ws chged b ubbng t wth slk (comped to when t ws not chged). ) moe ) less 3) sme 4) huh? pc: 4

3 Conductos nd Insultos (Objects e usull chged b movng electc chge ound, the thn cetng o destong chge.) Conducto: chge psses esl though the mtel > conductos contn chges whch e fee to move Insulto: chge cnnot move (esl) though mtel Semconducto: tnston between nsulto nd conducto, usull of nteest becuse of eotc electcl popetes pc: 5 Chgng b nducton (see nmton ). Usng negtve chge nd conducton pth to gound to nduce postve chge on the sphee lectcl Foce on Neutl Insultos: Induced Polzton Wh would thee be net foce? Fle:lectoscope_showng_nducton.png Publc Domn pc: 6

4 TYU Two lghtweght metl sphees ech hng fom n nsultng thed. One hs net negtve chge, the othe hs no net chge. If the sphees e close togethe but do not touch, wll the ) ttct ech othe ) epel ech othe 3) eet no foce on ech othe The sphees e now llowed to touch. Afte touchng wll the ) ttct ech othe ) epel ech othe 3) eet no foce on ech othe pc: 7 Coulomb s Lw An ntecton between two (pont) chges F on b F b on The mgntude of the Foce eeted b one chge on the othe s popotonl to the mgntude of ech of the chges s nvesel popotonl to the sque of the dstnce between the chges cts long lne connectng the chges Fk q q b whee k N m /C N m /C Altente fomulton of constnts: k 4πǫ 0 whee ǫ C / N m k(0 7 N s /C )c ϵ 0 s the pemttvt of fee spce pc: 8

5 Unt of chge s the Coulomb, new tpe of quntt. How bg s coulomb? Compe the mgntude of the electosttc epulson to the gvttonl ttcton between two potons. Repet fo two electons. pc: 9 Anothe fom of Coulomb s Lw the foce eeted b Q ( souce chge ) on q ( test chge ) F Q on q k Qq q F F Q pc: 0

6 lectc Chge nd lectc Feld (cont d) Coulomb s Lw: the foce eeted b Q on q Qq q F k ˆ Q ˆ Fo sevel Souces F F Qq k ˆ + F + L Q q k ˆ Qq + k ˆ + L Q F ˆ F F q F ˆ Q pc: Poblem-Solvng Stteg. Set up Sketch Coodntes Identf oles of chges (souce vs ecpent of foce) ecute Clculte Foce Mgntudes Fee Bod Dgm(s), nlze geomet Clculte Foce Component contbutons, then sum Note: Wtch Unts N, C, m Contnuous chge dstbutons: sum becomes ntegl plot Smmetes pc:

7 Anlze geomet/dw dgm (set up fee-bod dgm!) clculte mgntude of ech contbuton k Q q clculte components of ech contbuton (wtch dectons!) dd contbutons s vectos (dd component b component) Two pont chges e locted n the s. A chge Q.0 nc s locted.0 cm to the ght of the ogn nd Q 3.0 nc s locted 4.0 cm fom to the ght of the ogn. Detemne the net foce these chges eet on thd q 5.0 nc locted t the ogn. F pc: 3 Q.0 µc.3m q 4.0 µc.4m.3m Q.0 µc pc: 4

8 TYU In the pevous emple, suppose the bottom chge wee eplced wth.0 µc chge. In ths cse the net foce on q would be ) n the postve -decton ) n the negtve -decton 3) n the postve -decton 4) n the negtve -decton 5) zeo.3m.3m Q.0 µc.4m q 4.0 µc Q.0 µc pc: 5 lectc Feld () nd lectc foces dstubnce n spce esultng fom the pesence of (souce) chge Q ˆ eets foce on (test) chge. q F Foce of ntecton Q ˆ P Souce chge cetes dstubnce n spce (t P) F(t P) / q q Q F( on q) q(t q) ˆ Test chge senses the dstubnce n spce The electc foce on chge s eeted b the electc feld ceted b othe chges lectc feld obsevtons F 0 q 0 stctl spekng lm q 0 0 F 0 q 0 so Fq nlog F g m g pc: 6

9 lectc feld of pont chge Q k ˆ Feld t P ˆ unt vecto, fom Q to P dstnce, Q k fom Q to P Q ˆ P lectc Felds t vous ponts due to postve nd due to negtve chge pc: 7 Fo sevel Souces + + L Q Q k ˆ + k ˆ Q k ˆ + L Q ˆ Q ˆ Foce Lw: Fq pc: 8

10 lectc Feld mples: Wht s the mgntude of the electc feld t pont.00 m fom 4.00 nc pont chge? A nc pont chge s locted t the ogn. Wht s the electc feld ( vecto!) t the pont (.0m, -.60m)? pc: 9 When 00 volt btte s connected coss two pllel conductng pltes cm pt, the esultng chge confguton poduces nel unfom electc feld of mgntude.004 N/C. Compe the electc foce on n electon n ths feld wth ts weght. Wht s the cceleton of the electon? The electon s elesed fom est t the top plte. Wht s the fnl speed of the electon s t hts the second plte? How long does t tke the electon to tvel ths dstnce? pc: 0

11 TYU A negtve chge moves on stght lne dectl towds postve chge. Whch spects of the electc foce on the negtve chge wll emn constnt s t moves? ) mgntude ) decton 3) both 4) nethe A negtve chge moves long ccle centeed on postve chge. Whch spects of the electc foce on the negtve chge wll emn constnt s t moves? ) mgntude ) decton 3) both 4) nethe pc: lectc Chge nd lectc Feld (cont d) Coulomb s Lw: the foce eeted b Q on q Qq q F k ˆ Q ˆ Fo sevel Souces F F Qq k ˆ + F + L Q q k ˆ Qq + k ˆ + L Q F ˆ F F q F ˆ Q pc:

12 Poblem-Solvng Stteg. Set up Sketch Coodntes Identf oles of chges (souce vs ecpent of foce) ecute Clculte Foce Mgntudes Fee Bod Dgm(s), nlze geomet Clculte Foce Component contbutons, then sum Note: Wtch Unts N, C, m Contnuous chge dstbutons: sum becomes ntegl plot Smmetes pc: 3 lectc Dpole: two equl sze(q), opposte sgn chges septed b dstnce (l ). Detemne the electc feld fo ponts on the -s +Q Q pc: 4

13 Feld of n electc dpole +Q 0 k k Q ( + ) p ( + ) 3 3 p k >> 3 dpole Q pc: 5 lectc Feld Clcultons Anlze geomet/dw dgm lectc Feld Contbutons e dected w fom postve chges, towd negtve chges clculte mgntude of ech contbuton clculte components of ech contbuton k Q dd contbutons s vectos (dd component b component) pc: 6

14 lectc Dpole: two equl sze(q), opposte sgn chges septed b dstnce (l ). Detemne the electc feld fo ponts on the -s +Q Q pc: 7 Feld of n electc dpole +Q 0 k k Q ( + ) p ( + ) 3 3 p k >> 3 dpole Q pc: 8

15 Lne of chge: unfom lne of chge (chge Q, l oented long -s). Detemne the electc feld on the -s see lso nmton dqλd Geomet dq d Q snθ + Q λ cosθ Mgntudes d dq k k λ d + Components d d cosθ λ d k + + pc: 9 Add Components k d Q k, kλ, λ d ( + ) kλ kq + + mpotnt lmts ll chge 3 >> << nfnte lne of chge : kλ pc: 30

16 TYU In the pevous emple, suppose the bottom hlf of the lne of chge wee negtve nsted of postve. In ths cse the electc feld t the pont P would be ) n the postve -decton ) n the negtve -decton 3) n the postve -decton 4) n the negtve -decton 5) zeo P pc: 3 Net: nfnte sheet of chge s composed of of sees of nfnte lnes of chges Look cefull t elted tetbook emples of ng of chge, dsk of chge. pc: 3

17 lectc Feld due to n nfnte sheet of chge sheet of chge composed of sees of nfnte lnes of chge whee σ chge pe e dvde plne nto sees of nfntesmll wde stpes ( lnes of chge) Geomet snθ λ σ dz z z cosθ + z θ Mgntudes Components kλ d d kσ dz z kσ dz d cosθ + z z + + pc: 33 Add Components z z d ll chge kσdz z + kσ ctn z π π kσ kσπ σ k ε 0 unfom electc feld!! z 4 πε0 + two oppostel chged sheets z θ pc: 34

18 Lnes of Foce lectc Feld Lnes: mens of vsulzng the electc feld A lne n spce lws tngent to the electc feld t ech pont n spce concentton gve ndcton of feld stength decton gve decton of electc feld stt on postve chges, end on negtve chges electc feld lnes neve coss see fgue.6, pc: pc: 36

19 TYU If the electc feld lnes n egon of spce e stght lnes, wll chged ptcle elesed fom est be long feld lne? ) es ) no 3) ethe, depends upon ddtonl fctos pc: 37 Intecton of n electc dpole wth n electc feld dpole n unfom electc feld F+q θ +q l p q z F q F 0 toque bout cente of dpole τ τ F RHR! l l τ z F snθ + F snθ lq snθ p snθ τ p pc: 38

20 Wok done ottng dpole n n electc feld wtch dectons of τ, θ n dθ dw τ dθ p snθ dθ l θ dθ p z W θ θ p snθ dθ p cosθ p cosθ U U ( θ ) p cosθ p pc: 39 TYU An electc dpole s plced n egon of unfom electc feld, wth the dpole pontng n the decton opposte of tht of the electc feld. The dpole s ) n stble equlbum ) n unstble equlbum 3) not n equlbum pc: 40