Outline. Part 1, Topic 3 Separation of Charge and Electric Fields. Dr. Sven Achenbach - based on a script by Dr. Eric Salt - Outline

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1 S. Achench: PHYS 55 (P, Topic 3) Hnous p. Ouline slie # Cunell & Johnson Univesiy of Sskchewn Unegue Couse Phys 55 Inoucion o leciciy n Mgneism conucos & insulos pllel ple cpcios , 9.5 enegy in cpcio ielecics effec of ielecics on cpcince P, Topic 3 Sepion of Chge n lecic Fiels D. Sven Achench se on scip y D. ic Sl S. Achench S. Achench Phys55 3: Sepion of Chge lecic Fiels 3 Ouline slie # Cunell & Johnson sucue of n om 5 8. foce of cion / epulsion 9 8./4/5 shell heoem fining enegy levels ue o poin chge 9.//3 elecic fiel ue o poin chges elecic poenil in fiel se up y poin chges elecic fiel ue o unifomly chge plne elecic poenil ue o unifomly chge fiel 57 sucue of n om 8. foce of cion / epulsion 8./4/5 shell heoem 8.9 fining enegy levels ue o poin chge 9.//3 elecic fiel ue o poin chges 8.6 elecic poenil in fiel se up y poin chges 9.4 elecic fiel ue o unifomly chge plne 8.7 elecic poenil ue o unifomly chge fiel conucos & insulos 8.3 pllel ple cpcios 8.9, 9.5 enegy in cpcio 9.5 ielecics 9.5 effec of ielecics on cpcince 9.5 S. Achench Phys55 3: Sepion of Chge lecic Fiels S. Achench Phys55 3: Sepion of Chge lecic Fiels 4

2 S. Achench: PHYS 55 (P, Topic 3) Hnous p. Sucue of n Aom Sucue of n Aom Niels Boh Dnish physicis (885 96, Noel Pize in Physics 9) in 93 popose moel fo he hyogen om negively chge picle: clle n elecon posiively chge picle: clle poon Niels Boh Dnish physicis (885 96, Noel Pize in Physics 9) in 93 popose moel fo he hyogen om epesens icl epue fom clssicl ies enegy of n om cn hve only iscee vlues single phoon is emie in he nsiion (o qunum jump) fom one enegy level o nohe moel eplins he ehviou of hyogen (u oes no wok well fo ohe oms) moel, while impefec, eplins eleciciy mss of n.. elecon: g poon: g (much hevie!) neuon: g (no p of hyogen om!) Boh s moel n Plnck s ies on qunum enegy: eginning of qunum mechnics (evelope y Schöinge n Heiseneg, c. 95) S. Achench Phys55 3: Sepion of Chge lecic Fiels 5 S. Achench Phys55 3: Sepion of Chge lecic Fiels 7 Sucue of n Aom Sucue of n Aom Niels Boh Dnish physicis (885 96, Noel Pize in Physics 9) ene Moel hevie oms: nucleus me of poons n neuons in 93 popose moel fo he hyogen om epesens icl epue fom clssicl ies enegy of n om cn hve only iscee vlues in clssicl mechnics: elecon is le o oi he nucleus ny ius in Boh s moel: elecon is esice o cein ii neuons n poons fom he nucleus single phoon is emie in he nsiion (o qunum jump) fom one enegy level o nohe If n om is ome wih nohe om / elecon / phoon, enegy will ge nsfee o he ome om: some enegy will e convee o elecic poenil cee y he elecon chnging ois (o lge ius) emine is nsfee o kineic enegy (enie om inceses velociy) ii of he elecon, poon, n neuon e ll ou 5 m ius of he smlles oi n elecon cn hve is ou 5 m size of hyogen om S. Achench Phys55 3: Sepion of Chge lecic Fiels 6 S. Achench Phys55 3: Sepion of Chge lecic Fiels 8

3 S. Achench: PHYS 55 (P, Topic 3) Hnous p. 3 Foce of Acion / Repulsion sucue of n om 8. foce of cion / epulsion 8./4/5 shell heoem 8.9 fining enegy levels ue o poin chge 9.//3 elecic fiel ue o poin chges 8.6 elecic poenil in fiel se up y poin chges 9.4 elecic fiel ue o unifomly chge plne 8.7 elecic poenil ue o unifomly chge fiel conucos & insulos 8.3 pllel ple cpcios 8.9, 9.5 enegy in cpcio 9.5 ielecics 9.5 effec of ielecics on cpcince 9.5 Chles Augusin e Coulom pefome epeimens h eemine like chges epel unlike chges c foun h he foce eween wo chge ojecs is wih consn κ Nm /C (hee given o 3 significn figues) equion is known s Coulom s Lw picle, picle, conins ne chge conins ne chge F κ iecion of foce cn lwys e eemine y common sense.. mens solue vlue of.. e.g. if i is negive, i i S. Achench Phys55 3: Sepion of Chge lecic Fiels 9 S. Achench Phys55 3: Sepion of Chge lecic Fiels Foce of Acion / Repulsion Foce of Acion / Repulsion Chles Augusin e Coulom mple (Coulom s Lw) pefome epeimens h eemine like chges epel unlike chges c foun h he foce eween wo chge ojecs is picle, picle, conins ne chge conins ne chge F κ.. mens solue vlue of.. e.g. if i is negive, i i Fin he foce of cion eween wo picles if one hs ne chge of 3 6 C n he ohe hs ne chge of 7 6 C. The picles e loce mm p. wih foce F [Newons, N] cive, if n e opposie chge ne chge on s picle [Coulom, C] ne chge on n picle [Coulom, C] isnce eween picles [mees, m] consn κ Nm /C (hee given o 3 significn figues) S. Achench Phys55 3: Sepion of Chge lecic Fiels S. Achench Phys55 3: Sepion of Chge lecic Fiels

4 S. Achench: PHYS 55 (P, Topic 3) Hnous p. 4 Foce of Acion / Repulsion Foce of Acion / Repulsion Coulom s Lw Coulom is he moun of chge on ou elecons o poons (smlles unis of ne chge) i.e.: he chge pe elecon o poon is C / (6.4 8 ).6 9 C evelope epeimenlly using vey smll picles compe o isnce of sepion: «; «Coulom s Lw picle, picle, conins ne chge conins ne chge u Couloms Lw hols fo ny if he picles cn e ssume o e so smll () hey cn e consiee poins Coulom s Lw lso pplies he omic level S. Achench Phys55 3: Sepion of Chge lecic Fiels 3 consn κ is ele o nohe consn: C pemiiviy of fee spce ε 8.85 ; 4π κ N m Coulom s Lw κ F κ 4π ε S. Achench Phys55 3: Sepion of Chge lecic Fiels 5 4π ε Foce of Acion / Repulsion mple (Coulom s Lw) Fin he foce eween he elecon n poon in hyogen om. sucue of n om 8. foce of cion / epulsion 8./4/5 shell heoem 8.9 fining enegy levels ue o poin chge 9.//3 elecic fiel ue o poin chges 8.6 elecic poenil in fiel se up y poin chges 9.4 elecic fiel ue o unifomly chge plne 8.7 elecic poenil ue o unifomly chge fiel conucos & insulos 8.3 pllel ple cpcios 8.9, 9.5 enegy in cpcio 9.5 ielecics 9.5 effec of ielecics on cpcince 9.5 S. Achench Phys55 3: Sepion of Chge lecic Fiels 4 S. Achench Phys55 3: Sepion of Chge lecic Fiels 6

5 S. Achench: PHYS 55 (P, Topic 3) Hnous p. 5 Shell Theoem Shell Theoem A shell of unifom chge cs o epels chge picle h is ousie he shell s if he chge wee concene is cene Shell is cus on sphee conins unifomly isiue chge mple 3 (ene Shell Theoem) Two unifomly chge sphees hve ne chges of 7 C n 3 C. They e sepe in spce y m. Wh is he foce of epulsion? chge picle, conins ne chge (poin chge) sphee, cm conins ne chge sphee, 8 cm conins ne chge foce on poin chge is F κ if chge picle is loce insie shell of unifom chge: no ne foce on he picle fom he chge in he shell S. Achench Phys55 3: Sepion of Chge lecic Fiels 7 S. Achench Phys55 3: Sepion of Chge lecic Fiels 9 Shell Theoem Shell Theoem A shell of unifom chge cs o epels chge picle h is ousie he shell s if he chge wee concene is cene mple 4 (Chge in Plne) Fin he foce on chge A 7 C loce poin A. A m C Shell Theoem cn e eene o unifomly chge sphee (no jus shells): Any chge (no jus poin chges) ousie he sphee epeiences foce s if ll he chge ws concene he cene of he sphee. 6 m C S. Achench Phys55 3: Sepion of Chge lecic Fiels 8 S. Achench Phys55 3: Sepion of Chge lecic Fiels

6 S. Achench: PHYS 55 (P, Topic 3) Hnous p. 6 negy Levels ue o Poin Chge sucue of n om 8. foce of cion / epulsion 8./4/5 shell heoem 8.9 fining enegy levels ue o poin chge 9.//3 elecic fiel ue o poin chges 8.6 elecic poenil in fiel se up y poin chges 9.4 elecic fiel ue o unifomly chge plne 8.7 elecic poenil ue o unifomly chge fiel conucos & insulos 8.3 pllel ple cpcios 8.9, 9.5 enegy in cpcio 9.5 ielecics 9.5 effec of ielecics on cpcince 9.5 S. Achench Phys55 3: Sepion of Chge lecic Fiels lecic Fiel ue o Poin Chge elecic fiel veco v v F equipoenil line (i.e. consn volge) Coulom s Lw: Foce F on chge loce isnce fom chge ceing he elecic fiel κ F v F κ elecic fiel sengh S. Achench Phys55 3: Sepion of Chge lecic Fiels 3 F negy Levels ue o Poin Chge negy Levels ue o Poin Chge lecic Fiel ue o Poin Chge Fining negy Levels in n lecic Fiel elecic fiel veco v v F equipoenil line (i.e. consn volge) F The elecic poenil (volge) of poin wih espec o poin (i.e. ) cn e foun y clculing he wok equie o move es chge fom poin o. equipoenil line (i.e. consn volge) F wih F foce eee y he elecic fiel on chge es chge use o es he elecic fiel is so smll h i oes no ffec he fiel S. Achench Phys55 3: Sepion of Chge lecic Fiels mos impon ecision in his clculion: choice of ph (Fo he ph o e suile, he ngenil componen of he foce mus e known fo he enie ph.) S. Achench Phys55 3: Sepion of Chge lecic Fiels 4

7 S. Achench: PHYS 55 (P, Topic 3) Hnous p. 7 negy Levels ue o Poin Chge negy Levels ue o Poin Chge Fining negy Levels in n lecic Fiel Fining negy Levels in n lecic Fiel In his cse i mkes sense o follow fiel line ecuse foce long his ph given y Coulom Lw ngle eween foce n ph fiel line (chge) se on his fomul: fin in seps fin he sign using common sense fin he mgniue using he fomul fiel line (chge) fin in seps: fin he sign using common sense fin he mgniue using he fomul (ememe efiniion of volge in opic ) wih wok W eee o move es chge fom poin o gins he foce se up y he elecic fiel (cee y chge ) (wih isnce fom chge o poin ; isnce fom chge o poin ) W F W S. Achench Phys55 3: Sepion of Chge lecic Fiels 5 () sign (is posiive o negive?): is posiive if posiive wok is one y he move on he fiel in moving posiive chge fom poin o Hee: posiive chge ; > long fiel line: o lowe poenil neg. wok one y move will e negive fiel line poins in iecion fom highe o lowe elecic poenil Hee: poenil ops fom o will e negive (egless of he chge) S. Achench Phys55 3: Sepion of Chge lecic Fiels 7 negy Levels ue o Poin Chge negy Levels ue o Poin Chge Fining negy Levels in n lecic Fiel Fining negy Levels in n lecic Fiel W () F W wih n n consn : W () F F wih elecic fiel sengh : ( ) efine y elecic fiel sengh s funcion of (chge) S. Achench Phys55 3: Sepion of Chge lecic Fiels 6 fiel line se on his fomul: fin in seps fin he sign using common sense fin he mgniue using he fomul (chge) mgniue only (why woy ou sign of foce gin: clcule F/ wih I...I ) F( ) κ ( ) S. Achench Phys55 3: Sepion of Chge lecic Fiels 8 fiel line κ ; wih F (compe ove)

8 S. Achench: PHYS 55 (P, Topic 3) Hnous p. 8 negy Levels ue o Poin Chge negy Levels ue o Poin Chge Fining negy Levels in n lecic Fiel ememe sic inegion lws n n, n heefoe κ ( ) fiel line hee: κ κ Wih negive sign: (chge) κ mple 5 Consie hyogen om wih is elecon emove (clle hyogen ion), i.e. single poon. Wh is if poin is on he noml oi ph of he elecon n poin is long isnce wy (e.g. inifinie)? 5.9 m S. Achench Phys55 3: Sepion of Chge lecic Fiels 9 S. Achench Phys55 3: Sepion of Chge lecic Fiels 3 negy Levels ue o Poin Chge negy Levels ue o Poin Chge Fining negy Levels in n lecic Fiel Impon fomul fo elecic poenil cee y poin chge : κ equipoenil line (chge (i.e. consn volge) concene poin) mple 6 Bse on esuls fom emple 5, how much wok is equie o emove n elecon fom hyogen om (ignoing he kineic enegy of he elecon)? poin wih espec o poin ( o ) Whee is ny poin on he cicumfeence of cicle wih ius n he cene n is ny poin on he cicumfeence of cicle wih ius n he cene. S. Achench Phys55 3: Sepion of Chge lecic Fiels 3 S. Achench Phys55 3: Sepion of Chge lecic Fiels 3

9 S. Achench: PHYS 55 (P, Topic 3) Hnous p. 9 lecic Fiel ue o Poin Chges sucue of n om 8. foce of cion / epulsion 8./4/5 shell heoem 8.9 lecic Fiel Lines fo (quliive skech) fining enegy levels ue o poin chge 9.//3 elecic fiel ue o poin chges 8.6 elecic poenil in fiel se up y poin chges 9.4 elecic fiel ue o unifomly chge plne 8.7 elecic poenil ue o unifomly chge fiel conucos & insulos 8.3 If pos. chge neg. chge hen fiel lines s on pos. chge (hee: ) & en on neg. chge (hee: ) pllel ple cpcios 8.9, 9.5 enegy in cpcio 9.5 ielecics 9.5 effec of ielecics on cpcince 9.5 S. Achench Phys55 3: Sepion of Chge lecic Fiels 33 S. Achench Phys55 3: Sepion of Chge lecic Fiels 35 lecic Fiel ue o Poin Chges ee Foces The elecic fiel poin is foun y plcing (posiive) es chge h poin n compuing he foce F eee y he fiel. In his cse, compue foces ue o n sepeely n supepose hem (summing up). κ v S. Achench Phys55 3: Sepion of Chge lecic Fiels 34 κ v v v v iecion wy fom pos. iecion ows neg. sucue of n om 8. foce of cion / epulsion 8./4/5 shell heoem 8.9 fining enegy levels ue o poin chge 9.//3 elecic fiel ue o poin chges 8.6 elecic poenil in fiel se up y poin chges 9.4 elecic fiel ue o unifomly chge plne 8.7 elecic poenil ue o unifomly chge fiel conucos & insulos 8.3 pllel ple cpcios 8.9, 9.5 enegy in cpcio 9.5 ielecics 9.5 effec of ielecics on cpcince 9.5 S. Achench Phys55 3: Sepion of Chge lecic Fiels 36

10 S. Achench: PHYS 55 (P, Topic 3) Hnous p. lecic Poenil in Fiel se up y Poin Chges lecic Poenil in Fiel se up y Poin Chges Fining negy Levels in n lecic Fiel The elecic poenil poin wih espec o poin ( ) is W W W W W W is wok o e one o move es chge fom poin o poin wih W p of W o e one o ovecome fiel ue o chge W p of W o e one o ovecome fiel ue o chge o in ohe wos: ue o ue o S. Achench Phys55 3: Sepion of Chge lecic Fiels 37 eemine mgniue of wok W pe uni chge W W W W, segmen, segmen, segmen Fining negy Levels in n lecic Fiel I) Clcule W / ( ue o ) choose ph o move fom iecly ows (Coulom s Lw) hen, on n c wih (W, segmen ) eemine sign of W : posiive ( ue o ) W ( ue o ) κ F( ) κ κ S. Achench Phys55 3: Sepion of Chge lecic Fiels 39 move in his iecion κ lecic Poenil in Fiel se up y Poin Chges lecic Poenil in Fiel se up y Poin Chges Fining negy Levels in n lecic Fiel I) Clcule W / ( ue o ) move in his iecion (Coul use fomul evelope ove κ, u will eplin in eil gin) choose ph o move fom o so h ngenil componen of foce is known es o move fom iecly (sigh) ows unil isnce o is ecuse ngenil componen of foce is given y Coulom s Lw hen, move on n c of ius o poin ecuse ngenil componen of foce (on his equipoenil line) is zeo n heefoe no wok one on his segmen Fining negy Levels in n lecic Fiel II) Clcule W / ( ue o ) choose ph o move fis, on n c wih (W, segmen ) hen, iecly ows (Coulom s Lw) eemine sign of W : e.g. negive, if posiive (common sense) eemine mgniue of wok W pe uni chge ( ue o ) κ eemine sign of W if is posiive (sn), n is posiive, wok o move up gins fiel is posiive S. Achench Phys55 3: Sepion of Chge lecic Fiels 38 S. Achench Phys55 3: Sepion of Chge lecic Fiels 4

11 S. Achench: PHYS 55 (P, Topic 3) Hnous p. lecic Poenil in Fiel se up y Poin Chges Fining negy Levels in n lecic Fiel III) Supepose esuls fo W / ( ue o ) n W / ( ue o ) ( ue o ) ( ue o ) wih signs eemine using common sense sucue of n om 8. foce of cion / epulsion 8./4/5 shell heoem 8.9 fining enegy levels ue o poin chge 9.//3 elecic fiel ue o poin chges 8.6 elecic poenil in fiel se up y poin chges 9.4 elecic fiel ue o unifomly chge plne 8.7 elecic poenil ue o unifomly chge fiel conucos & insulos 8.3 pllel ple cpcios 8.9, 9.5 enegy in cpcio 9.5 ielecics 9.5 effec of ielecics on cpcince 9.5 S. Achench Phys55 3: Sepion of Chge lecic Fiels 4 S. Achench Phys55 3: Sepion of Chge lecic Fiels 43 lecic Poenil in Fiel se up y Poin Chges lecic Fiel ue o unifomly chge Plne mple 7 Fin fo 3 C n C. 3 m 4 m 4 m lecic Fiel Poin chge pe uni e is enoe σ [ sigm ] in unis C/m How song is he elecic fiel poin loce isnce fom he plne? plce es chge poin & clcule he foce F which he elecic fiel v ees on v F elecic fiel unifomly chge plne line pepenicul o plne F foce on eee y el. fiel ue o ecess chge in plne consie following smple geomey: S. Achench Phys55 3: Sepion of Chge lecic Fiels 4 S. Achench Phys55 3: Sepion of Chge lecic Fiels 44

12 S. Achench: PHYS 55 (P, Topic 3) Hnous p. lecic Fiel ue o unifomly chge Plne lecic Fiel ue o unifomly chge Plne lecic Fiel Poin smple geomey o clcule he foce: nnulus (fl ing, like wshe) in he chge plne wih is is going hough poin lecic Fiel Poin foce in iecion of he is going hough poin fom ny given e ΔA wihin he nnulus 3 κ ( σ ΔA) ( cos θ ) ΔF, fom ΔA ΔA θ θ Δ F Δ F enie foce ue o ll ecess chge in he enie nnulus e κ σ [ e of nnulus] cos ΔF, fom enie nnulus ( ) ( θ ) 3 How ig is his e of he enie nnulus s funcion of n θ? S. Achench Phys55 3: Sepion of Chge lecic Fiels 45 S. Achench Phys55 3: Sepion of Chge lecic Fiels 47 lecic Fiel ue o unifomly chge Plne lecic Fiel ue o unifomly chge Plne lecic Fiel Poin ΔA lecic Fiel Poin R smple geomey o clcule he foce: only consie chge in his nnulus y symmey, ne foce on mus e in iecion of he is (which lso goes hough poin ) θ θ Δ F Δ F inne ius R of he nnulus: R sin θ R sin θ wih R of he nnulus: θ cos θ sin R π/ θ π/ θ θ now consie smll e ΔA wihin he nnulus: foce ΔF eee on y chge in ΔA cc. o Coulom s Lw hs siewys componen (u his siewys componen ges compense y ohe coniuions oun he nnulus) jus he componen long he is ΔF is ulimely elevn cos θ ΔF ΔF Δ F κ ΔF cos θ κ ( σ ΔA) cos θ cos θ 3 κ ( σ ΔA) ( cos θ ) cos θ S. Achench Phys55 3: Sepion of Chge lecic Fiels 46 wih sin θ sin θ θ is θ cos θ R θ R cos θ e of enie nnulus eemine y R cos θ sin θ n R θ ( cos θ ) θ ( cos θ ) R θ S. Achench Phys55 3: Sepion of Chge lecic Fiels 48 θ R cosθ π/ θ θ

13 S. Achench: PHYS 55 (P, Topic 3) Hnous p. 3 lecic Fiel ue o unifomly chge Plne lecic Fiel ue o unifomly chge Plne lecic Fiel Poin R lecic Fiel Poin e A of enie nnulus: wih R cos θ sin θ n R θ ( cos θ ) R π/ θ π/ θ θ noice h he foce ΔF ue o ll ecess chge in he enie nnulus e ΔF κ σ π sin θ θ θ θ Δ F A π π R oue R inne π R R A ( R ) R R R ( R ) π ( R R) ( R) π ( ) π π 3 ( cos θ ) π sin θ cos θ π θ sin θ θ ( cos θ ) S. Achench Phys55 3: Sepion of Chge lecic Fiels 49 oes no epen on he isnce of he es chge fom he plne ol foce F ue o ll ecess chge in he e of he enie plne (no jus his nnulus) y summing ll foces of jcen nnuli wih θ fom o π / (9 ; infinie plne) F θ π θ ΔF θ θ π κ σ π sin θ θ κ σ π sin θ θ θ π κ σ π cos F π κ σ ( cos ) θ π θ S. Achench Phys55 3: Sepion of Chge lecic Fiels 5 lecic Fiel ue o unifomly chge Plne lecic Fiel ue o unifomly chge Plne susiuing e A of enie nnulus π A sin θ θ 3 cos θ in fomul (eive ove) fo enie foce in he enie nnulus e ΔF κ σ e of nnulus ΔF, fom enie nnulus elives ΔF o in sho lecic Fiel Poin ( ), fom enie nnulus ( [ ]) ( cos θ ) π κ σ 3 ( cos θ ) sin θ θ ΔF κ σ π sin θ θ S. Achench Phys55 3: Sepion of Chge lecic Fiels 5 3 ( cos θ ) 3 θ θ Δ F lecic Fiel Poin wih ol foce F ue o ll ecess chge in he e of he enie (infinie) plne F π κ σ elecic fiel sengh F π κ σ σ ε ; using efiniion κ : 4 π ε wih pemiiviy of fee spce (o: elecic consn) chge pe uni e σ in C/m (o chge ensiy) ε π κ unifomly chge plne S. Achench Phys55 3: Sepion of Chge lecic Fiels 5 C N m 8.85 F m using F F uni of cpcince in C /(N m)

14 S. Achench: PHYS 55 (P, Topic 3) Hnous p. 4 lecic Fiel ue o unifomly chge Plne lecic Fiel ue o unifomly chge Plne mple 8 Wh is he elecic fiel sengh of fiel se up y chge infinie plne? The chge ensiy is σ μc / m. fiel lines unifomly chge plne mple Skech he elecic fiel se up y wo unifomly chge pllel plnes. One plne is posiively chge wih chge ensiy of σ 9 C / m. One plne is negively chge wih chge ensiy of σ 9 C / m. The plnes e sepe y cm. S. Achench Phys55 3: Sepion of Chge lecic Fiels 53 S. Achench Phys55 3: Sepion of Chge lecic Fiels 55 lecic Fiel ue o unifomly chge Plne lecic Fiel ue o unifomly chge Plne mple 9 Skech he elecic fiel se up y wo unifomly chge pllel plnes. Boh e posiively chge, one wih chge ensiy of 8 C / m n one wih 8 C / m. The plnes e sepe y m. unifomly chge plne σ 8 C / m m unifomly chge plne σ 8 C / m en view of plne mple fiel lines fiel sengh is 56.5 N/C fiel lines en view of plne fiel sengh is 56.5 N/C fiel sengh is fiels cncel plne plne fiel sengh is 3 N/C fiel sengh is fiels cncel S. Achench Phys55 3: Sepion of Chge lecic Fiels 54 S. Achench Phys55 3: Sepion of Chge lecic Fiels 56

15 S. Achench: PHYS 55 (P, Topic 3) Hnous p. 5 lecic Poenil ue o unifomly chge Fiel sucue of n om 8. foce of cion / epulsion 8./4/5 shell heoem 8.9 fining enegy levels ue o poin chge 9.//3 elecic fiel ue o poin chges 8.6 elecic poenil in fiel se up y poin chges 9.4 elecic fiel ue o unifomly chge plne 8.7 elecic poenil ue o unifomly chge fiel conucos & insulos 8.3 pllel ple cpcios 8.9, 9.5 enegy in cpcio 9.5 ielecics 9.5 effec of ielecics on cpcince 9.5 S. Achench Phys55 3: Sepion of Chge lecic Fiels 57 lecic Fiel se up y chge Plne mgniue of AB : AB is he iffeence in elecic poenil (Δ) eween equipoenil lines in n el. Fiel, sepe isnce Δ n pssing hough poins A n B (hee, A n B e on he sme fiel line) in ohe wos: Δ AB vege elecic fiel sengh is given A y Δ ove isnce Δ Δ Δ We ley eive h in he cse of unifomly chge plne, v σ he elecic fiel sengh is consn σ/(ε ) A ε σ AB A Δ Δ ε Noe: If poins A n B e no on he sme elecic fiel line, hen Δ is he isnce long he fiel line eween equipo. lines unning hough A & B. S. Achench Phys55 3: Sepion of Chge lecic Fiels 59 B A A B Δ unifomly chge plne lecic Poenil ue o unifomly chge Fiel lecic Poenil ue o unifomly chge Fiel lecic Fiel se up y chge Plne fiel lines pllel (ue o unifomly chge plne), hee: hoizonl equipoenil lines (consn volge lines; enegy conous) lwys pepenicul o fiel lines hee: pllel veicl lines B A A B unifomly chge plne mple A veicl plne conining he yis is unifomly chge n he chge ensiy is σ C / m. Wh is he elecic poenil of poin A wih espec o poin B if A is loce (,y,z) (m,m,m) n B (m,6m,m)? y (,,) A (,6,) B Now fin AB fo poins A n B on he sme fiel line, n loce isnces A n B fom he chge plne. sign of AB : lecic fiel lines poin ows lowe elecic poenil. hee, A is highe poenil hn B volge fom B o A ( AB ) is posiive S. Achench Phys55 3: Sepion of Chge lecic Fiels 58 S. Achench Phys55 3: Sepion of Chge lecic Fiels 6

16 S. Achench: PHYS 55 (P, Topic 3) Hnous p. 6 Conucos, Insulos n Semiconucos sucue of n om 8. foce of cion / epulsion 8./4/5 shell heoem 8.9 fining enegy levels ue o poin chge 9.//3 elecic fiel ue o poin chges 8.6 elecic poenil in fiel se up y poin chges 9.4 elecic fiel ue o unifomly chge plne 8.7 elecic poenil ue o unifomly chge fiel conucos & insulos 8.3 pllel ple cpcios 8.9, 9.5 enegy in cpcio 9.5 ielecics 9.5 effec of ielecics on cpcince 9.5 Noe: Conucos fee elecons cn move esily wihin he soli conuco, u cn no esily e emove fom he meil fily song elecic fiel equie o emove n elecon fom soli conuco (e.g. ou / m N / C fo Cu) enegy equie o emove n elecon fom soli conuco (e.g. fom coppe penny o wie) is ou 4.7 e fo Cu e (elecon vol): enegy o wok W equie o move he chge of elecon (C/(6.4 8 ) hough poenil iffeence of e.6 9 J hee: 4.7 e C/(6.4 8 ) 4.7 J/C J S. Achench Phys55 3: Sepion of Chge lecic Fiels 6 S. Achench Phys55 3: Sepion of Chge lecic Fiels 63 Conucos, Insulos n Semiconucos Conucos, Insulos n Semiconucos Conucos meils in which elecons will move feely une he influence of n (even vey smll) elecic fiel e.g. coppe (Cu), omic nume Z9 9 poons & 9 elecons (& eleciclly neul neuons) in coppe om soli coppe (e.g. wie) consiss of Cu oms nge so h coulomic foces eween poons & elecons hol neighoing oms in plce espie coulomic foces, oue elecons in ech om no ighly oun o h om oue elecons cn wne oun wihin he soli: fee elecons (some oms will empoily hve 8 oiing elecons, ohes 3) if conuco (e.g. coppe) soli (e.g. wie) is plce in n (even vey smll) elecic fiel fee elecons will e popelle long wie conuce chge S. Achench Phys55 3: Sepion of Chge lecic Fiels 6 wok funcion : enegy equie o emove n elecon fom n ojec (e.g. wie) some common conucos n hei wok funcions: lemen Conucos luminium 4.8 cmium 4.7 con 4.8 coppe 4.7 gol 5. ion 4.5 le 4.4 mgnesium 3.68 mecuy 4.5 silve 4.73 zinc 4.3 Wok Funcion [e] S. Achench Phys55 3: Sepion of Chge lecic Fiels 64

17 S. Achench: PHYS 55 (P, Topic 3) Hnous p. 7 Conucos, Insulos n Semiconucos Conucos, Insulos n Semiconucos Conucos someimes ege s posiive ions in se of fee elecons loose escipion: implies siony coniion howeve, fee elecons oi nucleus n cn esily chnge he nucleus hey oi Semiconucos meils h hve few fee elecons solis wih elecicl conuciviy eween conuco & insulo e.g. silicon (Si), gemnium (Ge), gllium senie (GAs) conuco s se of elecons flowing oun posiive ions S. Achench Phys55 3: Sepion of Chge lecic Fiels 65 S. Achench Phys55 3: Sepion of Chge lecic Fiels 67 Conucos, Insulos n Semiconucos Insulos meils in which ll elecons e oun o eihe single om o few oms (pemnenly he sme few oms) elecons e no popelle even y song elecic fiel (unless hey e knocke ou, e.g. y collision wih nohe om) e.g. polymes (e.g. kelie) sucue of n om 8. foce of cion / epulsion 8./4/5 shell heoem 8.9 fining enegy levels ue o poin chge 9.//3 elecic fiel ue o poin chges 8.6 elecic poenil in fiel se up y poin chges 9.4 elecic fiel ue o unifomly chge plne 8.7 elecic poenil ue o unifomly chge fiel conucos & insulos 8.3 pllel ple cpcios 8.9, 9.5 enegy in cpcio 9.5 ielecics 9.5 effec of ielecics on cpcince 9.5 S. Achench Phys55 3: Sepion of Chge lecic Fiels 66 S. Achench Phys55 3: Sepion of Chge lecic Fiels 68

18 S. Achench: PHYS 55 (P, Topic 3) Hnous p. 8 Pllel Ple Cpcios Pllel Ple Cpcios Cpcios evice use in mny eleconic cicuis e.g. pevening mplifies fom going ino unsle oscillions viey of iffeen wys o uil cpcio consie pllel ple cpcio wo plell mel ples of sme size A l l sepion of ples («l ; «l ) minine y insuling meil eween ples ecess chge: in one ple; in he ohe (opposiely chge wih sme moun of chge) nges iself in conucive ples o unifom isiuion wih chge ensiy σ / A S. Achench Phys55 3: Sepion of Chge lecic Fiels 69 l ple l ple eminl Cpcince wih ; chges on ples volge coss he ples wih espec o ech ohe A, e & sepion of (ech) ple n wih (eive in opic ) A ε ε A ecess chge in ech ple is popoionl o volge coss ples C ε A consn of popoionliy is clle cpcince C C C m N m C C C C unis of C e Couloms/ols F F m N m J J C Unfounely, he symol C is use fo oh, he pmee of cpcince n he uni of chge Coulom S. Achench Phys55 3: Sepion of Chge lecic Fiels 7 Pllel Ple Cpcios lecic Fiel fiel eween ples: nely he sme s in unifomly chge (infinie) pllel plnes ecuse «l ; «l elecic fiel sengh fiel he ck of he ples & he en of he ples: much weke hn eween he ples (compe sie view skech) lmos enie enegy soe in he fiel eween he ples σ σ ε ε ε S. Achench Phys55 3: Sepion of Chge lecic Fiels 7 σ σ ε A A ple fiel ple lines eminls vey wek fiel lines ε A sucue of n om 8. foce of cion / epulsion 8./4/5 shell heoem 8.9 fining enegy levels ue o poin chge 9.//3 elecic fiel ue o poin chges 8.6 elecic poenil in fiel se up y poin chges 9.4 elecic fiel ue o unifomly chge plne 8.7 elecic poenil ue o unifomly chge fiel conucos & insulos 8.3 pllel ple cpcios 8.9, 9.5 enegy in cpcio 9.5 ielecics 9.5 effec of ielecics on cpcince 9.5 S. Achench Phys55 3: Sepion of Chge lecic Fiels 7

19 S. Achench: PHYS 55 (P, Topic 3) Hnous p. 9 negy in Cpcio negy in Cpcio y efiniion, moving n ojec wih consn foce F s hough isnce kes he enegy, o wok W F s (F s is he foce in he iecion of he movemen) Wok / negy in consn elecic fiel, foce eee y he fiel on chge is consn uing consn movemen of he chge e.g. moving chge hough isnce in he iecion of fiel line h hs consn fiel sengh equies he wok W ± (wih F/ ) S. Achench Phys55 3: Sepion of Chge lecic Fiels 73 Plne Ple now consie fiel se up y unifomly chge plne wih chge ensiy σ n elecic fiel sengh σ / (ε ) : moving es chge which is evenly spe ove n enie shee pllel o he plne fom he plne o isnce kes, gin, he wok σ W ε now consie he unifomly chge plne o e one ple of cpcio, n he shee conining is he ohe ple of he cpcio. mgniue of he wok o sepe he ples fom o is gin Noe: his ls equion is n ppoimion s infinie plnes hve een eplce y finie ples en view of unifomly chge plne S. Achench Phys55 3: Sepion of Chge lecic Fiels 75 σ W ε shee conining negy in Cpcio negy in Cpcio Unifomly chge Plne now consie fiel se up y unifomly chge plne wih chge ensiy σ n elecic fiel sengh σ / (ε ) : moving es chge isnce σ kes he wok W ± ± ε σ W ε now consie he sme cse, u chges / e move long sepe fiel lines fo he sme isnce Since he fiel sengh is he sme on oh lines, W on oh lines is he sme, n ol W is he sme s ove W σ σ ε ε σ ε S. Achench Phys55 3: Sepion of Chge lecic Fiels 74 en view of unifomly chge plne / / Cpcio ple now consie he sme cse, u he eess chges on he cpcio ples e n. (i.e. he es chge on ple is!) wok o sepe he ples is clely posiive (sepion of cing opposie chges) W W C σ σ A ε ε A ( C ) W C ε A C ( C ) C ε A S. Achench Phys55 3: Sepion of Chge lecic Fiels 76 C enegy soe in he fiel eween he ples of cpcio ple eminls C cpcince

20 S. Achench: PHYS 55 (P, Topic 3) Hnous p. negy in Cpcio Cpcio ple enegy ws clcule y sing wih oh ples ogehe n hen focing hem p o isnce while ples whee ogehe: pos. chge on ple is supeimpose on neg. chge on ple no ecess chge no elecic fiel when seping he ples: elecic fiel eween ples is cee (n vey smll fiel ehin he ples ecuse ples e no n infinie plne) enegy soe in he cpcio is elly soe in he elecic fiel eween he ples ple eminls sucue of n om 8. foce of cion / epulsion 8./4/5 shell heoem 8.9 fining enegy levels ue o poin chge 9.//3 elecic fiel ue o poin chges 8.6 elecic poenil in fiel se up y poin chges 9.4 elecic fiel ue o unifomly chge plne 8.7 elecic poenil ue o unifomly chge fiel conucos & insulos 8.3 pllel ple cpcios 8.9, 9.5 enegy in cpcio 9.5 ielecics 9.5 effec of ielecics on cpcince 9.5 S. Achench Phys55 3: Sepion of Chge lecic Fiels 77 S. Achench Phys55 3: Sepion of Chge lecic Fiels 79 negy in Cpcio Dielecics mple Chge is slowly move, iny moun ime, fom one ple of cpcio o he ohe. As he chge is move, he volge uils up ccoing o he gph. ) Wh is he cpcince of he cpcio? [vols] [μc] ) How much enegy is soe in he elecic fiel eween he ples of he cpcio when hee is n ecess chge of µc on one of he ples? 3) How much enegy is soe in he elecic fiel eween he ples of he cpcio when he volge coss he ples is 3? 4 3 Cpcince Michel Fy: nglish chemis & physicis, evelope concep of cpcince (see ove): eemine h he ecess chge on ple in cpcio is popoionl o he volge coss he ples clle he consn of popoionliy he cpcince C C uni of cpcince C nme fe him: F F Coulom / ol foun h he consn of popoionliy (cpcince) epens on ype of meil use o sepe he ples (when epeimening wih cpcios in ou 837) e.g. ppe inse of i eween he ples inceses he cpcince y fco of 3.5 S. Achench Phys55 3: Sepion of Chge lecic Fiels 78 S. Achench Phys55 3: Sepion of Chge lecic Fiels 8

21 S. Achench: PHYS 55 (P, Topic 3) Hnous p. Dielecics Dielecics slope cpcince Dielecic Consn i eween he ples ppe eween he ples slope is smlle cpcince is igge cpcince fo i (o vcuum) eween he ples ε A C cpcince fo ppe eween he ples ε ε A C ε, ppe 3.5 Poliy ypes of ielecics fom n omic viewpoin pol nonpol foun h he consn of popoionliy (cpcince) epens on ype of meil use o sepe he ples (when epeimening wih cpcios in ou 837) e.g. ppe inse of i eween he ples inceses he cpcince y fco of 3.5 (in gph, he slope (/cpcince) is 3.5 smlle fo ppe) S. Achench Phys55 3: Sepion of Chge lecic Fiels 8 S. Achench Phys55 3: Sepion of Chge lecic Fiels 83 Dielecics Dielecics Dielecic Consn Nonpol Dielecics ε is clle he elive pemiiviy of meil while nginees (ngineeing es) use ε, Physiciss (Physics es) use κ s n equivlen: ε κ oh e ienicl, oh e uniless [] κ is clle he ielecic consn of meil consns fo some useful meils: meil ε k [] i.54 polysyene.6 ppe 3.5 uy mic 5.4 pocelin 6.5 ini cemic 3 cpcince fo i (o vcuum) eween he ples ε A C cpcince fo ppe eween he ples ε ε A C ε, ppe 3.5 nonpol ielecics e insulos elecons e oun o single om o cluse of oms & cnno move fom one cluse o he ne pplying he shell heoem o he elecons, hey ppe s poin chge loce cene of he nucleus nucleus iself is opposiely chge (cluses of) oms ppe s neully (un)chge ojecs S. Achench Phys55 3: Sepion of Chge lecic Fiels 8 S. Achench Phys55 3: Sepion of Chge lecic Fiels 84

22 S. Achench: PHYS 55 (P, Topic 3) Hnous p. Dielecics Dielecics Nonpol Dielecics nonpol ielecics e insulos elecons e oun o single om o cluse of oms & cnno move fom one cluse o he ne pplying he shell heoem o he elecons, hey ppe s poin chge loce cene of he nucleus nucleus iself is opposiely chge (cluses of) oms ppe s neully (un)chge ojecs elecon oi chnges une impc of n elecic fiel : oi is shife upsem he fiel elecons cn sill e ege poin chge, u poin oes no line up wih nucleus nymoe (cluses of) oms now look like ipole: neg. chge one en; pos. chge ohe en; no ne chge S. Achench Phys55 3: Sepion of Chge lecic Fiels 85 Pol Dielecics molecules of pol ielecics hve pemnen elecic ipole (no only une he impc of n elecic fiel) in sence of n elecic fiel: molecules nomly oiene no ne chge in ny sip of he meil in pesence of n elecic fiel: fiel ens o line up he molecules elonge he ipoles (effec ofen negligile) S. Achench Phys55 3: Sepion of Chge lecic Fiels 87 ege of meil no ne chge ne negive chge ege of meil ne posiive chge Dielecics Dielecics Nonpol Dielecics in lock of meil, hese ipols my look like his no ne chge in cene of meil en zones wih ne chge, epening on elecic fiel ege of meil ne negive chge no ne chge ielecic ne posiive chge ege of meil Pol Dielecics molecules of pol ielecics hve pemnen elecic ipole (no only une he impc of n elecic fiel) in sence of n elecic fiel: molecules nomly oiene no ne chge in ny sip of he meil in pesence of n elecic fiel: fiel ens o line up he molecules elonge he ipoles (effec ofen negligile) in fiel of sme sengh, pol ielecics pouce gee mouns of ecess chge he sies hn nonpol ieleics pol ielecics hve lge ielecic consn κ o elive pemiiviy ε S. Achench Phys55 3: Sepion of Chge lecic Fiels 86 S. Achench Phys55 3: Sepion of Chge lecic Fiels 88

23 S. Achench: PHYS 55 (P, Topic 3) Hnous p. 3 ffec of Dielecics on Cpcince sucue of n om 8. foce of cion / epulsion 8./4/5 shell heoem 8.9 fining enegy levels ue o poin chge 9.//3 elecic fiel ue o poin chges 8.6 elecic poenil in fiel se up y poin chges 9.4 elecic fiel ue o unifomly chge plne 8.7 elecic poenil ue o unifomly chge fiel conucos & insulos 8.3 pllel ple cpcios 8.9, 9.5 enegy in cpcio 9.5 ielecics 9.5 effec of ielecics on cpcince 9.5 S. Achench Phys55 3: Sepion of Chge lecic Fiels 89 ffecive Chge wih P cul chge on one ple D chge on one sie of ielecic eff effecive chge on one ple wih ielecic in cpcio gp σ eff effecive chge ensiy in he fiel A e of one ple isnce eween ples s epline efoe, eff P D cpcio ple (pos. chge) S. Achench Phys55 3: Sepion of Chge lecic Fiels 9 shee of neg. chge sepe in ielecic ielecic el. fiel sengh in he gp eween cpcio ples ws σ /ε since eff < P, elecic fiel is smlle when ielecic is in he gp shee of pos. chge sepe in ielecic σ eff cpcio ple (neg. chge) ε eff A σ eff eff A ε ffec of Dielecics on Cpcince ffec of Dielecics on Cpcince ffecive Chge ielecic (pol o nonpol) in he gp of pllel ple cpcio euces he elecic fiel in he gp ecuse he effecive chge on ech ple of he cpcio hs een euce y he chge on he sies of he ielecic cpcio ple (pos. chge) chge on he sies of he ielecic is physiclly sepe fom he ples, u eemely close cn e consiee o e in he ples fo pupose of clculions shee of neg. chge sepe in ielecic ielecic shee of pos. chge sepe in ielecic cpcio ple (neg. chge) ffecive Chge cpcio cpcio wih ple ple P cul chge on one ple (pos. chge) (neg. chge) D chge on one sie of ielecic ielecic eff effecive chge on one ple wih ielecic in cpcio gp σ eff effecive chge ensiy in he fiel A e of one ple isnce eween ples shee of shee of neg. chge pos. chge eff sepe in sepe in using, ielecic ielecic A ε he volge coss he eminls of cpcio h hs ielecic in he gp is A eff eff ε A ε eff ε A S. Achench Phys55 3: Sepion of Chge lecic Fiels 9 S. Achench Phys55 3: Sepion of Chge lecic Fiels 9

24 S. Achench: PHYS 55 (P, Topic 3) Hnous p. 4 ffec of Dielecics on Cpcince ffec of Dielecics on Cpcince ffecive Chge cpcio wih P cul chge on one ple ple (pos. chge) D chge on one sie of ielecic ielecic eff effecive chge on one ple wih ielecic in cpcio gp σ eff effecive chge ensiy in he fiel A e of one ple isnce eween ples shee of neg. chge sepe in Fy s epeimens showe h ielecic he cul chge on ple of he cpcio is ε A P ε ε A wih eff heefoe P ε eff enge o P D D P A ε ( ε ) S. Achench Phys55 3: Sepion of Chge lecic Fiels 93 eff eff ε eff shee of pos. chge sepe in ielecic eff cpcio ple (neg. chge) mple 3 A pllel ple cpcio is uil wih polysyene eween he ples. The isnce eween he ples is 5 m, n he e of ech ple is. m. The ples of he cpcio e opposiely chge wih he sme moun of chge. The moun of chge is such h he volge coss he ples is. ) Wh is he cpcince of he cpcio? ) Wh is he moun of chge (of couse, h mens ecess chge) on ech ple? 3) Wh is he elecic fiel sengh eween he ples of he cpcio? 4) Wh is he chge in he hin shee of he ielecic h is igh ne o ple of he cpcio? S. Achench Phys55 3: Sepion of Chge lecic Fiels 95 ffec of Dielecics on Cpcince Cpcince mos impon equion o eleconics eles cul chge on ple P o he volge coss he ples ε A P ε cpcio ple (pos. chge) Fy efine he cpcince C o e he consn h eles P o cpcince C in pllel ple cpcio wih ielecic (wih ε κ) in he gp is C ε ε A P C Noe: Wheneve we use he equion C, efes o he cul chge P on one ple i.e. C inclues ε S. Achench Phys55 3: Sepion of Chge lecic Fiels 94 shee of neg. chge sepe in ielecic ielecic shee of pos. chge sepe in ielecic cpcio ple (neg. chge)