Last Time emphasis on E-field. Potential of spherical conductor. Quick quiz. Connected spheres. Varying E-fields on conductor.

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Lst Time emphsis on Efiel Electric flux through surfce Guss lw: Totl electric flux through close surfce proportionl to chrge enclose Q " E = E = 4$k e Q % o Chrge istribution on conuctors Chrge

Foun E = k e Q / in the ril irection. Wht is the electric potentil of the conuctor? V ( ) "V () = $ "E s Integrl long some pth, from point on surfce to inf.

18, 2006 Physics 208 Lecture 5 2 Quick quiz Connecte spheres V ( ) "V () = $ Er = $ k Q r r 2 = "k Q = k Q r So conucting sphere of rius crrying chrge Q is t potentil kq/ Since both must be t the sme

1 Lst Time emphsis on Efiel Electric flux through surfce Guss lw: Totl electric flux through close surfce proportionl to chrge enclose Q " E = E = 4$k e Q % o Chrge istribution on conuctors Chrge ccumultes t ens/corners Lrge Efiel t ens/corners Tues. Sep. 18, 2006 Physics 208 Lecture 5 1 Potentil of sphericl conuctor Chrge resies on surfce, so this is like the sphericl chrge shell. Foun E = k e Q / in the ril irection. Wht is the electric potentil of the conuctor? V ( ) "V () = $ "E s Integrl long some pth, from point on surfce to inf. = $ E s ifficult pth esy pth Esy becuse is sme irection s E, E s = E r = Er Tues. Sep. 18, 2006 Physics 208 Lecture 5 2 Quick quiz Connecte spheres V ( ) "V () = $ Er = $ k Q r r 2 = "k Q = k Q r So conucting sphere of rius crrying chrge Q is t potentil kq/ Since both must be t the sme potentil, kq 1 1 = kq 2 " Q 1 Q 2 = 1 Chrge proportionl to rius Two conucting spheres of iff rii connecte by long conucting wire. Wht is pproximtely true of Q 1, Q 2? Q 1 Q 1 ) Q 2 >Q 1 B) Q 2 <Q 1 C) Q 2 =Q 1 Tues. Sep. 18, 2006 Physics 208 Lecture 5 3 Surfce chrge ensities? " 4 $ " 1 " 2 = 1 Electric fiel? Surfce chrge ensity proportionl to 1/ Since E = " Locl Efiel proportionl to 1/, 2 (1/rius of curvture) o Tues. Sep. 18, 2006 Physics 208 Lecture 5 4 Vrying Efiels on conuctor Electrogenic fish Dipole nerby conucting object Expect lrger electric fiels ner the smll en. Electric fiel pproximtely proportionl to 1/(locl rius of curvture). Lrge electric fiels t shrp points, just like squre (one numericlly previously) Fiels cn be so strong tht ir ionize n ions ccelerte. Some fish cn both generte n etect electric fiels. Fiel t nerby conucting boy quite complicte. Distorts fish ipole fiels. Smll chnges etecte by fish. Tues. Sep. 18, 2006 Physics 208 Lecture 5 5 Tues. Sep. 18, 2006 Physics 208 Lecture 5 6 1

How sensitive? Potentil n chrge White shrk Sny h to be relese from Sn Frncisco qurium Kept bumping into section of tnk 0.

ΔV=125 µv Hve shown tht conuctor hs n electric potentil, n tht potentil epens on its chrge For chrge conucting sphere: V ( ) "V () = k Q = k Q Electric potentil

When it hs totl chrge Q o, its electric potentil is V o.

epens on shpe C = cpcitnce Lrge cpcitnce: nee lots of chrge to chnge potentil Smll cpcitnce: smll chrge cn chnge potentil. Tues. Sep.

Usully trnsferre from nother conucting object, leving opposite chrge behin cpcitor consists of two conuctors Conuctors genericlly clle pltes Chrge trnsferre between

2 How sensitive? Potentil n chrge White shrk Sny h to be relese from Sn Frncisco qurium Kept bumping into section of tnk volts electric potentil ifference mesure between two of the tnk's winows 125 microvolts! ΔV=125 µv Hve shown tht conuctor hs n electric potentil, n tht potentil epens on its chrge For chrge conucting sphere: V ( ) "V () = k Q = k Q Electric potentil proportionl to totl chrge Tues. Sep. 18, 2006 Physics 208 Lecture 5 7 Tues. Sep. 18, 2006 Physics 208 Lecture 5 8 Quick Quiz Cpcitnce Consier this conucting object. When it hs totl chrge Q o, its electric potentil is V o. When it hs chrge 2Q o, its electric potentil Electric potentil of ny conucting object proportionl to its totl chrge. V = 1 C Q. is V o B. is 2V o C. is 4V o D. epens on shpe C = cpcitnce Lrge cpcitnce: nee lots of chrge to chnge potentil Smll cpcitnce: smll chrge cn chnge potentil. Tues. Sep. 18, 2006 Physics 208 Lecture 5 9 Tues. Sep. 18, 2006 Physics 208 Lecture 5 10 Cpcitors Where i the chrge come from? Usully trnsferre from nother conucting object, leving opposite chrge behin cpcitor consists of two conuctors Conuctors genericlly clle pltes Chrge trnsferre between pltes Pltes crry equl n opposite chrges Potentil ifference between pltes proportionl to chrge trnsferre Q Tues. Sep. 18, 2006 Physics 208 Lecture 5 11 Definition of Cpcitnce Sme s for single conuctor "V = 1 C Q but ΔV = potentil ifference between pltes Q = chrge trnsferre between pltes The SI unit of cpcitnce is the fr (F) 1 Fr = 1 Coulomb / Volt This is very lrge unit: we typiclly see µf = 10 6 F, nf = 10 9 F, pf = F Tues. Sep. 18, 2006 Physics 208 Lecture

Sphericl cpcitor Chrge Q move from outer to inner sphere Guss lw sys E=kQ/r 2 until secon sphere Potentil ifference b "V = E s long pth shown b kq "V = = $kq 1 b r 2 r = kq % 1 $ 1 ( ' b * & ) C "V =

Chrge enclose by Gussin surfce Q=0 Flux through Gussin surfce=0, > Efiel=0 outsie nother Gussin surfce: Efiel zero insie outer con. Efiel zero outsie outer con. No flux > no chrge on outer surfce!

3 Sphericl cpcitor Chrge Q move from outer to inner sphere Guss lw sys E=kQ/r 2 until secon sphere Potentil ifference b "V = E s long pth shown b kq "V = = $kq 1 b r 2 r = kq % 1 $ 1 ( ' b * & ) C "V = k $ 1 1 ' & ) % b( 1 Pth to fin ΔV Gussin surfce to fin E Chrge istributions Q rrnge on inner/outer surfces of outer sphere. Chrge enclose by Gussin surfce Q=0 Flux through Gussin surfce=0, > Efiel=0 outsie nother Gussin surfce: Efiel zero insie outer con. Efiel zero outsie outer con. No flux > no chrge on outer surfce! Q Q Tues. Sep. 18, 2006 Physics 208 Lecture 5 13 Tues. Sep. 18, 2006 Physics 208 Lecture 5 14 Prllel plte cpcitor outer Chrge Q move from right conuctor to left conuctor Ech plte hs size Length x With = re = Wht is the potentil ifference? Chrge lies only on the surfce of conuctors. Ech plte hs inner, outer surfce These surfces behve s sheets of chrge, ech proucing n Efiel Q Q inner Tues. Sep. 18, 2006 Physics 208 Lecture 5 15 Qouter Q inner Q outer Totl Efiel = E left plte E right plte In between pltes, E left plte = " inner uter 2 o 2 o 2 o E right plte = " inner uter 2 o 2 o 2 o = E left plte E right plte right plte Q "V = E s = $ x left plte o $ o C "V = o Q inner Tues. Sep. 18, 2006 Physics 208 Lecture 5 16 Q E left plte E right plte = Q Where is the chrge? How i the chrge get there? Chrge istribution in t mtter for Electric fiel, potentil ifference, cpcitnce But wht is chrge ist? Foun Use Gussin surfce, cyliner w/encps of re E=0 insie conucting plte Electric flux thru surfce = " inner / o = by Guss lw So " inner / ll chrge on inner surfces, Efiel zero outsie Q Tues. Sep. 18, 2006 Physics 208 Lecture 5 17 Q Btter hs fixe electric potentil ifference cross its terminls Conucting pltes connecte to bttery terminls by conucting wires. ΔV pltes = ΔV bttery cross pltes Electrons move from negtive bttery terminl to Q plte from Q plte to positive bttery terminl This chrge motion requires work The bttery supplies the work ΔV Tues. Sep. 18, 2006 Physics 208 Lecture

100 µm Humn cpcitors Cell membrne: Empty spce seprting chrge fluis (conuctors) ~ 7 8 thick In combintion w/fluis, cts s prllelplte cpcitor Extrcellulr flui Tues. Sep.

18, 2006 Physics 208 Lecture 5 20 8 10 $9 m Chrges re / ions inste of electrons Chrge motion is through cell membrne (ion chnnels) rther thn through wire Otherwise, cts s cpcitor ~0.

4 100 µm Humn cpcitors Cell membrne: Empty spce seprting chrge fluis (conuctors) ~ 7 8 thick In combintion w/fluis, cts s prllelplte cpcitor Extrcellulr flui Tues. Sep. 18, 2006 Physics 208 Lecture Moeling cell membrne K Extrcellulr flui N Cl Ionic chrge t surfces of conucting fluis Cpcitnce: ΔV~0.1 V ( $12 F /m)4% $6 m = Tues. Sep. 18, 2006 Physics 208 Lecture $9 m Chrges re / ions inste of electrons Chrge motion is through cell membrne (ion chnnels) rther thn through wire Otherwise, cts s cpcitor ~0.1 V resting potentil 100 µm sphere surfce re ( ) 2 ~ 3x10 4 cm 2 = $11 F = 35pF ~0.1µF/cm 2 Cell membrne epolriztion Cell membrne s ielectric 78 K Extrcellulr flui N Cl ΔV~0.02 ΔV~0.1 V V Cell membrne cn reverse potentil by opening ion chnnels. Potentil chnge ~ 0.12 V (100 chnnels/µm 2 )x4π(50 µm) 2 =3.14x10 6 ion chnnels Ions flow through ion chnnels Chnnel spcing ~ 10xmembrne thickness (~ 100 chnnels / µm 2 ) How mny ions flow through ech chnnel? Chrge xfer require ΔQ=CΔV=(35 pf)(0.12v) =(35x10 12 C/V)(0.12V) = 4.2x10 12 Coulombs 1.6x10 19 C/ion > 2.6x10 7 ions flow 78 K Extrcellulr flui N Cl Membrne is not relly empty It hs molecules insie tht respon to mgnetic fiel. The molecules in the membrne cn be polrize Dielectric: insulting mterils cn respon to n electric fiel by generting n opposing fiel. Ion flow / chnnel =(2.6x10 7 ions) / 3.14x10 6 chnnels ~ 7 ions/chnnel Tues. Sep. 18, 2006 Physics 208 Lecture 5 21 Tues. Sep. 18, 2006 Physics 208 Lecture 5 22 Effect of Efiel on insultors If the molecules of the ielectric re nonpolr molecules, the electric fiel prouces some chrge seprtion This prouces n inuce ipole moment E=0 E Tues. Sep. 18, 2006 Physics 208 Lecture 5 23 Dielectrics in cpcitor n externl fiel cn polrize the ielectric The inuce electric fiel is opposite to the originl fiel The totl fiel n the potentil re lower thn w/o ielectric E = E 0 / κ n V = V 0 / κ E in The cpcitnce increses C = κ C 0 E 0 Tues. Sep. 18, 2006 Physics 208 Lecture

5 78 Cell membrne s ielectric K Extrcellulr flui N Cl C increses by fctor of times s much chrge neee to rech potentil Tues. Sep. 18, 2006 Physics 208 Lecture 5 25 Without ielectric, we foun 7 ions/chnnel were neee to epolrize the membrne. Suppose lipi bilyer hs ielectric constnt of 10. How my ions / chnnel neee?. 70 B. 7 C. 0.7 Work one n energy store During the chrging of cpcitor, when chrge q is on the pltes, the work neee to trnsfer further q from one plte to the other is: The totl work require to chrge the cpcitor is The energy store in ny cpcitor is: For prllel cpcitor: U = 1/2 ε o E 2 Tues. Sep. 18, 2006 Physics 208 Lecture

Physics Lecture 14: MON 29 SEP

Physics Lecture 14: MON 29 SEP Physics 2113 Physics 2113 Lecture 14: MON 29 SEP CH25: Cpcitnce Von Kleist ws le to store electricity in the jr. Unknowingly, he h ctully invente novel evice to store potentil ifference. The wter in the