Electricity and Magnetism Electric Dipole Continuous Distribution of Charge
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1 Electricit nd Mgnetism Electric Dipole Continos Distribtion of Chrge Ln heridn De Anz College Jn 16, 2018
2 Lst time electric field lines electric field from point chrge net electric field from mn chrges effect of fields on chrges
3 Wrm Up Qestions Which epression relting force to electric field is correct? (A) F = m 0 E (B) E = q 0 F (C) F = q 0 E (D) F = E
4 Wrm Up Qestions Which epression relting force to electric field is correct? (A) F = m 0 E (B) E = q 0 F (C) F = q 0 E (D) F = E
5 Wrm Up Qestions Wht re the nits of electric field? (A) Nm (B) N/C (C) Nm 2 /C 2 (D) C/N
6 Wrm Up Qestions Wht re the nits of electric field? (A) Nm (B) N/C (C) Nm 2 /C 2 (D) C/N
7 C, nd object B hs chrge electric Wrmforces Upon Qestions the objects? 52F qba 1 = (d) q 3 = FAB µc, FBA q 2 = 2.00 µc, nd = m. The resltnt force eerted on q 3 is F net,3 = ( 1.04 i j) N. Wht is the electric field t the loction of q 3 de to the other two chrges? q 2 2 F 23 q 3 F 13 (A) ( 1.04 i j) N (B) ( 1.04 i j) N/C (C) ( i j) MN/C (D) ( 2.08 i j) N/C q 1 Figre (Emple 23.2) The Figre from erw & Jewett, pg 696, E 2.
8 C, nd object B hs chrge electric Wrmforces Upon Qestions the objects? 52F qba 1 = (d) q 3 = FAB µc, FBA q 2 = 2.00 µc, nd = m. The resltnt force eerted on q 3 is F net,3 = ( 1.04 i j) N. Wht is the electric field t the loction of q 3 de to the other two chrges? q 2 2 F 23 q 3 F 13 (A) ( 1.04 i j) N (B) ( 1.04 i j) N/C (C) ( i j) MN/C (D) ( 2.08 i j) N/C q 1 Figre (Emple 23.2) The Figre from erw & Jewett, pg 696, E 2.
9 Overview electric field of dipole continos distribtions of chrge
10 Electric Dipole electric dipole z A pir of chrges of eql mgnitde q bt opposite sign, We re sll inte seprted b distnce, d. tht re lrge compred tht z d.at sch lrg dipole moment: E ( ) proimtion, we cn neg r (+) E (+) p = qd ˆr E q 4 0 z where ˆr is nit vector z pointing from the negtive chrge to the positive r ( ) chrge. Up here the +q The prodct qd, wh field domintes. dipole, is the mgnitde p : of the dipole. (The ni + +q + d Dipole center q p Down here the q p : The direction of is t dipole, s indicted in
11 Electric Dipole 2 1 (Emple sin f2k 2 e 23.6, B) 5 E 1 1 E 2 5 k e Evlte the electric field from the dipole t point, which is t position (0, ). q 1 5 q 2 nd 5 b. 0 q q 2 0 b 2 1 sin 2 E 1 re (Emple 23.6) en the chrges in Figre 2 re of eql mgnitde eqidistnt from the origin, sittion becomes smmets shown here. r E 2 E q q
12 q sin f2k 0 q e b 2 1 sin 2 Electric Dipole (Emple 23.7) E 1 The -components of the electric field cncel ot, E = 0. -components: E = E 1, + E 2, E Also E 1, = E 2, ) in, - r E 2 q q
13 q sin f2k 0 q e b 2 1 sin 2 Electric Dipole (Emple 23.7) E 1 The -components of the electric field cncel ot, E = 0. -components: E = E 1, + E 2, ) in, - r E 2 E Also E 1, = E 2, ( ke q E = 2 = r 2 2k e q ( ) ) cos θ ( ) q q = 2k e q ( ) 3/2
14 0 Electric Dipole 0 q 2 0 (Emple 23.7) sin f2k 2 e b 2 1 sin 2 E 1 Wht hppens s we move infinitel fr from the dipole? ( >> ) E, r E 2 q q
15 0, Electric Dipole 0 q 2 0 (Emple 23.7) sin f2k 2 e b 2 1 sin 2 q r E 1 E 2 E q Wht hppens s we move infinitel fr from the dipole? ( >> ) The constnt in the denomintor hs less nd less ffect on the fnction. We cn see tht the field fnction pproches E fr = 2k e q 3 [ ] E lim E fr = lim = lim = 1 2k e q ( ) 3/2 2k e q 3 ( 3 ( ) k e q ) 3/2 2k e q 3
16 0, Electric Dipole 0 q 2 0 (Emple 23.7) sin f2k 2 e b 2 1 sin 2 q r E 1 E 2 E q Wht hppens s we move infinitel fr from the dipole? ( >> ) The constnt in the denomintor hs less nd less ffect on the fnction. We cn see tht the field fnction pproches E fr = 2k e q 3 [ ] E lim E fr = lim = lim = 1 2k e q ( ) 3/2 2k e q 3 2k e q ( 3 ( ) k e q 3 ) 3/2
17 0 Big-O Nottion 0 q 2 0 (Emple 23.7) sin f2k 2 e b 2 1 sin 2 E 1 >> Recll tht f () = O(g()) if > k. f () g() C E, r E 2 q q
18 0 Big-O Nottion 0 q 2 0 (Emple 23.7) sin f2k 2 e b 2 1 sin 2 E 1 E >> Recll tht f () = O(g()) if > k. E E fr = = 2k e q ( ) 3/2 2k e q 3 f () g() C ( ( ) ) 2 3/2 + 1, q r E 2 q Choosing k = we cn see: E 1 E fr 2 > 2 ( ) Therefore, E = O 2ke q or simpl O( 3 ). 3
19 Electric Dipole (Emple 23.7) As we move w from the dipole (red line, r 3 ) the E-field flls off fster thn it does for point chrge (ble line, r 2 ). dipole, 1 r 3 point chrge, 1 r 2 The negtive chrge prtill shields the effect of the positive chrge nd vice vers.
20 Continos distribtion of chrge In previos emple, we dded p the field from ech point chrge. Bt wht bot the cse of chrged object, like plte or wire? In jst -1 Colomb of chrge, there re more thn qintillion ecess electrons!
21 Continos distribtion of chrge In previos emple, we dded p the field from ech point chrge. Bt wht bot the cse of chrged object, like plte or wire? In jst -1 Colomb of chrge, there re more thn qintillion ecess electrons! Yo do not wnt to dd p the effect of ech one b one.
22 Continos distribtion of chrge In previos emple, we dded p the field from ech point chrge. Bt wht bot the cse of chrged object, like plte or wire? In jst -1 Colomb of chrge, there re more thn qintillion ecess electrons! Yo do not wnt to dd p the effect of ech one b one. oltion: tret the chrge s continos distribtion with some chrge densit.
23 Chrge Densit chrge densit The mont of chrge in per nit volme of n object. (Here volme cold be volme, re, or length) B convention, different smbols cn be sed in different cses: smbol description I nits λ chrge per nit length C m 1 σ chrge per nit re C m 2 ρ chrge per nit volme C m 3 For wire, sll se chrge per length. For plte, chrge per re.
24 nt from the chrges or lt Continos chnges in distribtion re- of chrge (E. 23.7) d Rod l t e t e A rod of length l, hs niform positive chrge per nit length λ nd totl chrge Q. Clclte the electric field t point tht is locted long the long is of the rod nd distnce from one end. E d Figre (Emple 23.7) The electric field t de to niforml chrged rod ling long the is.
25 Continos distribtion of chrge d Rod l t E e t Figre (Emple 23.7) The electric field t e We need to dd p the chrge of ech little prticle d. Ech de to niforml chrged rod ling long the is. hs chrge λ d. e ther from To be perfectl the chrge ccrte, distribtion. we wold mke the length of d 0. contined d This is n integrl: λ λ d
26 ged Rod Continos distribtion of chrge (E. 23.7) th l tht rom E rge ent ke dq Figre E = (Emple 23.7) The electric field t ite de to niforml chrged 2 rod ling long the is. l+ me 1 = k e rther from the chrge distribtion. 2 λ d contined d
27 ged Rod Continos distribtion of chrge (E. 23.7) th l tht rom E rge ent ke dq Figre E = (Emple 23.7) The electric field t ite de to niforml chrged 2 rod ling long the is. l+ me 1 = k e rther from the chrge distribtion. 2 λ d [ ] l+ contined = k e λ = k e Q l d 1 ( 1 1 l + ) = k eq (l + )
28 of niform chrge integrl Qestion of step 4. is of smmetr, s de, replce r 2 with dding component (b) (c) The figre here shows three noncondcting rods, one circlr nd cos,bt is identi vrible. two stright. Replce Ech hs niform chrge of mgnitde Q long its Fig r s, rond top hlf the nd cir- nother long its bottom hlf. For ech rod, wht is the direction of the line net of smmetr. electric field t point? () oint is on n etension of the line of chrge. (b) is on line of smmetr of the line of chrge, t perpendiclr distnce from tht line. (c) me s (b)ecept tht is not on For () it is: rods, one circlr nd two (A) p nitde Q long its top hlf od, wht is the direction of (B) down (C) left (D) right Q Q () (b) (c) 1 ge 590, Hllid, Resnick, Wlker.
29 of niform chrge integrl Qestion of step 4. is of smmetr, s de, replce r 2 with dding component (b) (c) The figre here shows three noncondcting rods, one circlr nd cos,bt is identi vrible. two stright. Replce Ech hs niform chrge of mgnitde Q long its Fig r s, rond top hlf the nd cir- nother long its bottom hlf. For ech rod, wht is the direction of the line net of smmetr. electric field t point? () oint is on n etension of the line of chrge. (b) is on line of smmetr of the line of chrge, t perpendiclr distnce from tht line. (c) me s (b)ecept tht is not on For () it is: (A) p rods, one circlr nd two nitde Q long its top hlf od, wht is the direction of (B) down (C) left (D) right Q Q () (b) (c) 1 ge 590, Hllid, Resnick, Wlker.
30 of niform chrge integrl Qestion of step 4. is of smmetr, s de, replce r 2 with dding component (b) (c) The figre here shows three noncondcting rods, one circlr nd cos,bt is identi vrible. two stright. Replce Ech hs niform chrge of mgnitde Q long its Fig r s, rond top hlf the nd cir- nother long its bottom hlf. For ech rod, wht is the direction of the line net of smmetr. electric field t point? () oint is on n etension of the line of chrge. (b) is on line of smmetr of the line of chrge, t perpendiclr distnce from tht line. (c) me s (b)ecept tht is not on For (b) it is: rods, one circlr nd two (A) p nitde Q long its top hlf od, wht is the direction of (B) down (C) left (D) right Q Q () (b) (c) 1 ge 590, Hllid, Resnick, Wlker.
31 of niform chrge integrl Qestion of step 4. is of smmetr, s de, replce r 2 with dding component (b) (c) The figre here shows three noncondcting rods, one circlr nd cos,bt is identi vrible. two stright. Replce Ech hs niform chrge of mgnitde Q long its Fig r s, rond top hlf the nd cir- nother long its bottom hlf. For ech rod, wht is the direction of the line net of smmetr. electric field t point? () oint is on n etension of the line of chrge. (b) is on line of smmetr of the line of chrge, t perpendiclr distnce from tht line. (c) me s (b)ecept tht is not on For (b) it is: rods, one circlr nd two (A) p nitde Q long its top hlf od, wht is the direction of (B) down (C) left (D) right Q Q () (b) (c) 1 ge 590, Hllid, Resnick, Wlker.
32 of niform chrge integrl Qestion of step 4. is of smmetr, s de, replce r 2 with dding component (b) (c) The figre here shows three noncondcting rods, one circlr nd cos,bt is identi vrible. two stright. Replce Ech hs niform chrge of mgnitde Q long its Fig r s, rond top hlf the nd cir- nother long its bottom hlf. For ech rod, wht is the direction of the line net of smmetr. electric field t point? () oint is on n etension of the line of chrge. (b) is on line of smmetr of the line of chrge, t perpendiclr distnce from tht line. (c) me s (b)ecept tht is not on For (c) it is: rods, one circlr nd two (A) p nitde Q long its top hlf od, wht is the direction of (B) down (C) left (D) right Q Q () (b) (c) 1 ge 590, Hllid, Resnick, Wlker.
33 of niform chrge integrl Qestion of step 4. is of smmetr, s de, replce r 2 with dding component (b) (c) The figre here shows three noncondcting rods, one circlr nd cos,bt is identi vrible. two stright. Replce Ech hs niform chrge of mgnitde Q long its Fig r s, rond top hlf the nd cir- nother long its bottom hlf. For ech rod, wht is the direction of the line net of smmetr. electric field t point? () oint is on n etension of the line of chrge. (b) is on line of smmetr of the line of chrge, t perpendiclr distnce from tht line. (c) me s (b)ecept tht is not on For (c) it is: rods, one circlr nd two nitde Q long its top hlf od, wht is the direction of (A) p (B) down (C) left (D) right Q Q () (b) (c) 1 ge 590, Hllid, Resnick, Wlker.
34 mmr electric dipole field electric fields of chrge distribtion Homework Collected homework 1, posted online, de on Mond, Jn 22. erw & Jewett: Ch 23, onwrd from pge 716. robs: 45, 71, 84
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