Chapter 21: Electric Charge and Electric Field

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1 Chpte 1: Electic Chge nd Electic Field Electic Chge Ancient Gees ~ 600 BC Sttic electicit: electic chge vi fiction (see lso fig 1.1) (Attempted) pith bll demonsttion: inds of popeties objects with sme popet epel ech othe objects with diffeent popeties ttct ech othe both popeties e lws ceted togethe Benjmin Fnlin: inds of chges e positive nd negtive b convention, negtive chge ssocited with mbe Consevtion of Chge: The lgebic sum of ll the electic chges in n closed sstem is constnt. p1c1: 1

2 Conductos nd Insultos (Objects e usull chged b moving electic chge ound, the thn ceting o destoing chge.) Conducto: chge psses esil though the mteil > conductos contin chges which e fee to move Insulto: chge cnnot move (esil) though mteil Semiconducto: tnsition between insulto nd conducto, usull of inteest becuse of eotic electicl popeties p1c1:

3 Chging b induction (see lso fig 1.6). Electicl Foce on Neutl Insultos: Induced Polition (see fig 1.7, n.. ) p1c1: 3

4 Quntition nd Consevtion of Chge Micoscopic stuctue of mtte: Atoms (see fig 1.4) Nucleus most of mss positive chge composed of potons (ech hs chge e) nd neutons (no electic chge) obiting electons (ech hs chge e) Atoms tend to be chge neutl chge quntied: e C Chge tnsfe usull in the fom of ddition o emovl of electons. p1c1: 4

5 Coulomb s Lw A desciption of the intection between two (point) chges The mgnitude of the Foce eeted b one chge on the othe is popotionl to the mgnitude of ech of the chges is invesel popotionl to the sque of the distnce between the chges cts long line connecting the chges F Qq 1 N m πε 0 C N m C Unit of chge is the Coulomb, new tpe of quntit. How big is 1 coulomb? p1c1: 5

6 Anothe fom of Coulomb s Lw the foce eeted b Q ( souce chge ) on q ( test chge ) Qq F ˆ F Foce on q ˆ unit vecto, Q ˆ q F fom Q to q distnce, fom Q to q p1c1: 6

7 Coulomb s Lw: the foce eeted b Q on q q F Qq ˆ Fo sevel Souces F F 1 Electic Chge nd Electic Field (cont d) Q1q ˆ 1 i 1 F Q q ˆ i i i Qq ˆ Q ˆ Q 1 F ˆ 1 F F 1 q F 1 ˆ Q p1c1: 7

8 Anle geomet/dw digm clculte mgnitude of ech contibution clculte components of ech contibution F i Q iq i dd contibutions s vectos (dd component b component) A chge q 5.0 nc is t the oigin. A chge Q 1.0 nc is locted cm to the ight on the is nd nd Q 3.0 nc is locted 4 cm to the ight on the is. Wht is the net foce on q? p1c1: 8

9 Q 1.0 µc Geomet.3m q 4.0 µc.3m.4m Mgnitudes Q.0 µc Components Net Foce p1c1: 9

10 Emple: Compe the electic epulsion of two electons to thei gvittionl ttction F Qq vesus F G Mm p1c1: 10

11 Q Electic Field nd Electic foces Electic field is distubnce in spce esulting fom the pesence of (souce) chge, which eets foce on (test) chge. q P F ˆ Foce of intection Q ˆ E(t P) F (t P) / q Q q F(on q) qe(t q) Test chge senses the distubnce in spce ˆ Souce chge cetes distubnce in spce p1c1: 11

12 E E Q ˆ Field t P ˆ unit vecto, fom Q to P Q ˆ P E distnce, fom Q to P E Q p1c1: 1

13 p1c1: 13 Q 1 1 ˆ 1 Q ˆ Fo sevel Souces i i i i Q Q Q E E E ˆ ˆ ˆ Foce Lw: F qe E E E 1

14 Element Electic Field Emples: Wht is the electic field 30 cm fom 4nC chge? When 100 volt btte is connected coss two pllel conducting pltes 1 cm pt, the esulting chge configution poduces nel unifom electic field of mgnitude E 1.00E4 N/C. Compe the electic foce on n electon in this field with its weight. Wht is the cceletion of the electon? The electon is elesed fom est t the top plte. Wht is the finl speed of the electon s it hits the second plte? How long does it te the electon to tvel this distnce? p1c1: 14

15 Electic Field Clcultions Anle geomet/dw digm Electic Field Contibutions e diected w fom positive chges, towd negtive chges clculte mgnitude of ech contibution clculte components of ech contibution E i Q i i dd contibutions s vectos (dd component b component) p1c1: 15

16 Electic Dipole: two equl sie(q), opposite sign chges septed b distnce (l ). Detemine the electic field on the -is Q Geomet Mgnitudes Components Q Net Foce p1c1: 16

17 Field of n electic dipole Q E E 0 Q ( ) p ( ) >> 3 3 p 3 Q p1c1: 17

18 Line of chge: unifom line of chge (chge Q, l oiented long -is). Detemine the electic field on the -is see lso nimtion dqλd Geomet dq Q sinθ d Q λ cosθ Mgnitudes de dq λ d Components de de cosθ λ d p1c1: 18

19 p1c1: 19 Add Components ( ) E E Q E Q d de E λ λ λ λ chge : infinite line of,, 3 chge ll << >>

20 Net: infinite sheet of chge is composed of of seies of infinite lines of chges Loo cefull t elted tetboo emples of ing of chge, nd dis of chge. p1c1: 0

21 Electic Field due to n infinite sheet of chge sheet of chge composed of seies of infinite lines of chge σ chge pe e Geomet sinθ λ σ d cosθ θ Mgnitudes de λ σ d Components de de cosθ σ d p1c1: 1

22 p1c1: Add Components unifom electic field!! 4 1 ctn chge ll πε ε σ σπ π π σ σ σ d de E θ

23 Intection of n electic dipole with n electic field dipole in unifom electic field FqE q θ l p q F F qe F qe F i toque bout cente of τ τ F τ 0 pe sinθ i l F sinθ lqe sinθ i l F i sinθ dipole RHR! τ p E p1c1: 3

24 Wo done otting dipole in n electic field wtch diections of τ, θ n dθ dw τ dθ pe sinθ dθ l θ dθ p W θ θ 1 pe pe sinθ dθ cosθ pe cosθ 1 U U ( θ ) pe cosθ p E p1c1: 4

25 Lines of Foce Electic Field Lines: mens of visuliing the electic field A line in spce lws tngent to the electic field t ech point in spce concenttion give indiction of field stength diection give diection of electic field stt on positive chges, end on negtive chges electic field lines neve coss see figue 1.6, p1c1: 5

26 p1c1: 6

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