Week 1:Jn 5 : Jn 1 Physics 1B scheule Winter 009. Instructor: D.N. Bsov bsov@ucs.eu Mon We Friy Lecture: the Electric fiel Lecture: Intro, 15.1-15.3 Lecture: The oulomb lw, Lecture: Electric Flux & Guss s lw Lecture: Guss lw/exmples OH This week only: Fri 4-5 pm, 6-7 pm 3: Jn 19 University Holiy Lecture: Potentil Quiz 1: chpter 15 4: Jn 6 5: Feb Lecture: cpcitnce Lecture: Electric current, Ohm s lw Lecture: cpcitor combintions Lecture: Resistivity, Electric power Quiz : chpter 16 Lecture: Resistors, series prllel 6: Feb 9 7: Feb 16 8: Feb 3 9: Mrch 10: Mrch 9 Lecture: Kirchhoff s rules University Holiy Lecture: current loop, solenoi Lecture: Fry s lw, Lenz s lw Lecture: Energy of the mgnetic fiel Lecture: R circuits Lecture: Mgnetism Lecture: Inuce EMF Lecture Inuctnce, Inuctors Lecture: A circuits Quiz 3: chpter 17 Lecture: torue on current loop, Ampere s lw Quiz 4: chpter 18-19 Quiz 5: chpter 19-0 Lecture: iscussion of the finl exm HW: h15: 1,10,11,13,15,17,0,4,7,8,30,3,36,38,43,46,48 T.A.:A: Zhoushen Hung h16: 1,3,5,8,1,15,19,,3,5,9,31,33,35,43,45,47,49,60 h17: 1,3,8,9,11,13,16,19,0,3,31,33,39,45,5,60 zhohung@physics.ucs.eu h18: 1,3,5,7,13,17,1,6,31,33,35, B: Anres Stergiou, h19: 1,3,8,9,11,15,19,,4,7,9,34,37,38,41,44,47,49,57,61 stergiou@physics.ucs.eu h0: 1,5,8,11,13,16,18,3,5,7,9,31,34,37,39, Quizzes: Finl exm: ll mteril in ch 15-1 HW problems, problems in clss, more 4 best out of 5 No mke-up uizzes for ny reson no mke up finl for ny reson Lst upte: Jn 15, 009
Potentil ifference n electric potentil [16.1] Recll physics 1A: PE Potentil energy ifference AB W AB Work one by conservtive force F x A pth from A to B
E Potentil ifference n electric potentil [16.1] Recll physics 1A: Physics 1B: + A B PE Potentil energy ifference PE AB AB W AB Work one by conservtive force F x A pth from A to B ue to moving chrge objects in n electric fiel PE AB W AB F ( E ) E Becuse force is opposite to the irection of chrge motion
E Potentil ifference n electric potentil [16.1] Recll physics 1A: Physics 1B: + V A B V B PE Potentil energy ifference PE V A AB AB W AB Work one by conservtive force F x A pth from A to B ue to moving chrge objects in n electric fiel PE PE AB W AB F ( E ) E Becuse force is opposite to the irection of chrge motion sign of chrge is importnt! The potentil ifference V between finl point B n initil point A: V B -V A is efine in terms of chnge of PE ivie by the mgnitue of the chrge. Sclr untity. Units 1V1J/1 PE V B V A E
Potentil ifference n electric potentil [16.1] Potentil: property of the spce ue to chrges + + + + + + + + + + x E V 1 V V V B V A PE V x --------------- The potentil energy is ue to the chrge intercting with the fiel. E + + + + + + + + + + + PE 1 PE + PE --------------- PE V B V A E Potentil-Depens only position in the fiel! Units (V) Potentil Energy- Depens on the interction of the fiel with chrge. Units (J) Relte by: PE V Both PE n V re reltive. Only ( PE n V) re importnt!
Exmple An electron in the picture tube of n oler TV set is ccelerte from rest through potentil ifference V 5000V by uniform electric fiel. Wht is the chnge in potentil energy of the electron? Wht is the spee of the electron s result of this ccelertion (ssume it strte from rest)? -e E r? efinition of electric potentil X
Potentil ue to point chrge [16.] E k e r PE V B V A E E k e r V k e r V k e r [E. 16.4] V0 t r The electric potentil or work per unit chrge reuire to move test chrge from infinity to istnce r from the positive point chrge s the positive chrge moves close to. Fig.16.5 Potentil is sclr
Potentil ue to point chrge [16.] In crystl of N + l - the istnce between the ions is 0.4 nm. Fin the potentil ue to l - t the position of the N +. Fin the electrosttic energy of the N + ue to the interction with l -. r0.4nm l - N + V 9 19 k e 9x10 ( 1.6x10 ) 6.0V 9 r (0.4x10 ) PEV 1.6x10-19 x-6.0-9.6x10-19 J Superposition principle: the totl electric potentil t P ue to multiple point chrges is the lgebric sum of the electric potentils ue to the iniviul chrges ELETRON VOLT (convenient unit for tomic physics) 1eV1.6x10-19 J PE-6.0 ev
Potentil ue to point chrge [16.] E k e r E k e r V k e r V k e r [E. 16.4] V0 t r Superposition principle: the totl electric potentil t P ue to multiple point chrges is the lgebric sum of the electric potentils ue to the iniviul chrges Fig.16.5 Potentil is sclr
Electric potentil: superposition [16.] Two chrges of + ech re plce t corners of n euilterl tringle, with sies of 10 cm. If the Electric fiel ue to ech chrge is 100 V/m t the A fin the potentil t A. E A 100 V/m 10 cm B A V t A ue to ech chrge k e E r k V e V r E 1 r V E 10V V totl V B A +V AV 0 V
ENERGY of HARGE DISTRIBUTION [16.] -/ How much energy is store in this sure chrge istribution? k W + 3 k W 4 k W ( ) 1 4 3 k W W W W + + + -/ W 1?
ENERGY of HARGE DISTRIBUTION [16.] Which of the chrge istributions is the most stble? (hs the lowest PE) + + + + - - - - 0 k k k k k k PE + + PE k 0 k k k k k k PE + + 4 k k PE + STABLE
Potentils n chrge conuctors [16.3] Work on chrge one by electric force: W- PE Points A n B: PE(V B -V A ) W-(V B -V A ) No net work is reuire to move chrges between two points t the sme V! Fig. 16-9 hrge conuctor: ll points on the surfce hve the sme V. Why? At euilibrium: E is perpeniculr to pth between A&B W0 V A V B The electric potentil is constnt everywhere on the surfce of chrge conuctor in euilibrium. The electric potentil is constnt everywhere insie conuctor n is eul to the vlue t the surfce.
Euipotentil surfces [16.4] An euipotentil surfce is surfce on which ll points re the sme potentil. It tkes no work to move prticle long n euipotentil surfce or line (ssume spee is constnt). E + The electric fiel t every point on n euipotentil surfce is perpeniculr to the surfce. Euipotentil surfces re normlly thought of s being imginry; but they my correspon to rel surfces (like the surfce of conuctor).
Euipotentil surfces: point chrge [16.4] + Point chrge: euipotentil surfces re ll spheres centere on the chrge. We represent these spheres with euipotentil lines. Note tht the fiel lines re perpeniculr to the euipotentil lines t every crossing.
Euipotentil surfces: point chrge [16.4] + Point chrge: euipotentil surfces re ll spheres centere on the chrge. We represent these spheres with euipotentil lines. Note tht the fiel lines re perpeniculr to the euipotentil lines t every crossing.
Euipotentil surfces: point chrge [16.4] + Point chrge: euipotentil surfces re ll spheres centere on the chrge. We represent these spheres with euipotentil lines. Note tht the fiel lines re perpeniculr to the euipotentil lines t every crossing.
Euipotentil surfces: ipole [16.4] Fig.16-10
pcitnce [16.6] pcitor evice for storing chrge n energy, cn be ischrge rpily to relese energy. Applictions mer flsh Defibrilltors Electronic evices omputer memories (store informtion) Mny more!
Prllel plte cpcitor two infinite plnes of chrge re A seprte by istnce where << A, crry chrge +, - + + + + + + + + + + + + ----------------- A +/A+σ -/A-σ The chrges re t the inner surfce of the cpcitor
Fiel insie the cpcitor pltes By superposition of fiels ue to sheet of chrge E in σ ε o E + E - E out 0 A /Aσ + + + + + + + + + + + + ----------------- E out 0 σ σ E in E + +E - ε ε o 0
E fiel outsie the cpcitor using Guss s Lw use cyliner s the Gussin surfce, ens of the cyliner prllel to A, sies perpeniculr to A E out A + + + + + + + + + + + + Φ E 0 E εo E 0 out out A ----------------- E out A The chrge in the Gussin surfce is zero. The E fiel outsie the cpcitor is zero
E fiel insie the cpcitor using Guss s Lw E out 0 + + + + + + + + + + + + E in ----------------- Φ E A E E in in ε σ Aε ε o o o
pcitnce [16.6] Prllel plte cpcitor - - - - - + + + + +
ircuit Digrm: Wire conuctor Voltge source + - V pcitnce [16.6] conuctor cpcitor + - Q V [ oulomb] [ Volt] 1F - - - - - + + + + + Work is one to seprte chrges: pcitors stores electricl energy
ircuit Digrm: Wire conuctor A Voltge source Guss lw: Prllel plte cpcitor [16.7] + - V E conuctor o σ ε Aε o cpcitor + - + - V V Q V [ oulomb] [ Volt] Aε rerrnge o A ε o to increse : V Increse A Decrese 1F E fiel increses with chrge ensity
Prllel plte cpcitor [16.7] Exmple: A prllel plte cpcitor with pltes ech with re 1.0 m seprte by istnce of 1.0 mm hols +,-, 10-6 ) Fin the cpcitnce. - V A1 m 1mm b) Fin the E fiel ) Fin V cross the pltes E V Aε o Aε o E 1 1(8.9 x10 ) 9 0.001 6 110 x 1 (1)(8.9 x10 ) 8.9x10 F 8.9nF 5 1.1x10 / V m 5 3 1.110(110 ) 1.110 x x x V
Thin film cpcitors Metl film seprte by thin insultors A ε o metl insultor Metl Mking the re lrge n the insulting gp smll increses
Energy store in chrge cpcitor [16.9] A + V Q V Energy store U 1 - Q V 1 ( ) V Q prllel plte cpcitor U A ε o 1 Aε 0 ( E ) U 1 ε 0E A
Unerstning cpcitors Suppose the cpcitor shown here is chrge to Q n then the bttery is isconnecte. Now suppose I pull the pltes further prt so tht the finl seprtion is 1. + + + + ----- 1 + + + + ----- How o the untities Q, U,, V, E chnge? U 1 Q V Q: U: : V: E: const: no wy for chrge to leve. increses.. energy to system by seprting ecreses.. since energy, but Q remins sme increses.. since, but Q remins sme remins the sme... epens only on chrge ensity Q U V Q 1 1 V 1 V 1 U 1 1 U
Unerstning cpcitors Suppose the bttery (V) is kept ttche to the cpcitor. Agin pull the pltes prt from to 1. How o the untities Q, U,, V, E chnge? V + + + + ----- 1 + + + + ----- V : V: Q: E: U: ecreses (cpcitnce epens only on geometry) must sty the sme - the bttery forces it to be V must ecrese, QV chrge flows off the plte V D must ecrese ( E, E ) 1 must ecrese ( U V ) E σ 0 Q V ε A 0 1 E 1 1 1 E U 1 1 U
ombintions of cpcitors [16.8] pcitors connecte in series n prllel + - Voltge source ircuit igrm resistor cpcitor V R V onuctor
Prllel cpcitors [16.8] Fig. 16-17 Both cpcitors re t sme potentil: Totl chrge: e V V1 V 1+ 1 V + V 1 V + V e V V + 1
Prllel cpcitors [16.8] For N cpcitors in prllel: e 1+ +... N Both cpcitors re t sme potentil: Totl chrge: e V V1 V 1+ 1 V + V 1 V + V e V V + 1
pcitors in series [16.8] V 1 + - + - V 1 e V 1 V V1+ V + 1 V 1 ( + ) e 1 1 the chrge on both cpcitors in series is 1 1 1 1 1 1 1 + + +... e 1 e 1 N
ombintions of cpcitors [16.8] Wht is the euivlent cpcitnce, e, of the combintion shown? o e o 1 1 1 1 1 + 1 e + 3
34. Fin the euivlent cpcitnce. X series 6µF X 1 1 1 4 1 + series 4 8 4 6 e 4.00+.00+6.001.00 µf
34. Fin the chrge on ech cpcitor. 1 X X 3 4 series 6µF V 1 1 V4x10-6 (36)1.44x10-4 Vx10-6 (36)0.7x10-4 3 4 series V6x10-6 (36).16x10-4
ombintions of cpcitors [16.8] V 0 Wht is the reltionship between V 0 n V in the systems shown below? +Q (Are A) +Q (Are A) /4 V /4 -Q -Q conuctor The electric fiel in the conuctor 0. The electric fiel everywhere else is: E Q/(Aε 0 ) To fin the potentil ifference, integrte the electric fiel: V E 0 V E + 0 + 4 1 V E E 4
ombintions of cpcitors [16.8] Problem 16-4. Fin the euivlent cpcitnce between n b. X X 1 1 1 1 + 7 5 35/1 ser ser.9µ F 4.0 µf.9 µf 6.0 µf b e 4.0+.9+6.0 1.9 µf
ombintions of cpcitors [16.8] Two ienticl cpcitors. chrge one cpcitor t 10 V, isconnect, connect the chrge cpcitor to the unchrge cpcitor. Wht is the voltge rop cross the ech cpcitor? One wy to o this problem: is constnt but ivie between the two cpcitors + V 0 10V - / -/ the chrge on ech cpcitor is reuce by fol thus the voltge cross ech cpcitor is reuce by fol / -/ V V V o
ombintions of cpcitors [16.8] Two ienticl cpcitors. chrge one cpcitor t 10 V, isconnect, connect the chrge cpcitor to the unchrge cpcitor. Wht is the voltge rop cross the ech cpcitor? Another wy to o this problem is constnt but is plce on n euivlent cpcitor + V o 10V - e V The voltge is reuce by fol V V e o
pcitors with ielectrics [16.8] 600µF Dielectric mteril insultors such s pper, glss plstic, cermic. Dielectric Strength - is the electric fiel t which conuction occurs through the mteril 1F ielectric mteril + -
pcitors with ielectrics [16.8] Fig.16-3 V V o κ Potentil ue to chrge ecreses by κ κ ielectric constnt (imensionless)
pcitors with ielectrics [16.8] Originlly + Vo o - A ielectric + - V V κ o κ V o pcitnce increses
pcitors with ielectrics [16.8] Originlly + - Vo o A ielectric + - V κ o V E κ E o V o E Electric fiel ecreses (when not connecte to bttery) κ
pcitors with ielectrics [16.8] Originlly + - Vo o A ielectric + - V κ o E o E κε A εa Eo ε κε o Permittivity is increse (ompre to vcuum) κ
pcitors with ielectrics [16.8] Exmple: A prllel plte cpcitor consists of metl sheets (A 1.0m ) seprte by Teflon sheet (κ.1) with thickness of 0.005 mm. () fin the cpcitnce. (b) Fin the mximum voltge. The mximum electric fiel cross Teflon is 60x10 6 V/m. this is its ielectric strength. () Κ.1 0.005m A0.5m κεo A 3.7 10 6 x F 1.1(8.8 10 )(1.0) x 0.005x10 (b) 6 3 3 Vmx E 60x10 (0.005x10 ) 300V s
pcitors with ielectrics summry [16.8] + o o V o - o V o - E PE κ o V κov o κ V V o Eo 1 1 V κ Vo κpe o