Last time…Parallel plate capacitorSlide 3What is the potential difference?What is the capacitance?Quick QuizWork done to charge a capacitorEnergy stored in a capacitorSlide 9Human capacitorsModeling a cell membraneCell membrane depolarizationCharge motionElectric CurrentSlide 15Current in a wireBut experiment says…Charge motion with collisionsSlide 19ResistorsSlide 21Current conservationSlide 23Resistors in SeriesSlide 25Slide 26Resistors in ParallelSlide 28Quick QuizHow did the charge get transferred?Capacitors in ParallelCapacitors in SeriesEnergy densityCurrent DensityWhat is the drift velocity?Slide 36Charge Carrier Motion in a ConductorSlide 38ResistanceQuick Quiz 1Electrical PowerCell membrane as dielectricEffect of E-field on insulatorsDielectrics in a capacitorSlide 45Charge distributionsSpherical capacitorPowerPoint PresentationElectric Dipole alignmentPolar MoleculesHow to build CapacitorsCapacitance of Parallel Plate CapacitorSlide 53Charge, Field, Potential DifferenceHuman capacitors: cell membranesSlide 56Ion channelsHow much charge flow?Slide 59Capacitance and DielectricsCharge distribution on conductorsCapacitors with DielectricsDielectrics – An Atomic ViewThe Electric FieldElectric field and potentialPotential from electric fieldQuick Quiz 3Electric Potential - Uniform FieldElectric field from potentialEquipotential linesElectric Field and equipotential lines for + and - point chargesSlide 72Slide 73Slide 74Slide 75Drift SpeedHow small is the drift velocity?Work done and energy storedDrift VelocitySlide 80Slide 81Producing an electric currentSlide 83ResistivityTues. Oct. 11, 2007 Physics 208 Lecture 12 1Last time…Potential and electric fieldCapacitors € dr l V=Vo € dr l € dr l Friday Honors Lecture: Prof. R. Moss, PhysiologyDetecting the body’s electrical signalsFriday Honors Lecture: Prof. R. Moss, PhysiologyDetecting the body’s electrical signals€ ΔV =1CQTues. Oct. 11, 2007 Physics 208 Lecture 12 2Parallel plate capacitorCharge Q moved from right conductor to left conductorEach plate has size Length x Width = Area = APlate surfaces behave as sheets of charge, each producing E-field+Q-QdinnerouterTues. Oct. 11, 2007 Physics 208 Lecture 12 3Parallel plate capacitorCharge only on inner surfaces of plates.E-field inside superposition of E-field from each plate.Constant E-field inside capacitor.+-dTues. Oct. 11, 2007 Physics 208 Lecture 12 4What is the potential difference?Electric field between platesUniform electric field-Q+Qd+++++++++++++++---------------Etotal€ Eleft+ Eright= η /2εo+ η /2εo= η /εoPotential difference = V+-V-= (1/q)x(- work to move + charge from + to minus plate)€ = 1/q( )× − −qEd( )( )ΔV = Ed = η d /εo= QdεoA ⎛ ⎝ ⎜ ⎞ ⎠ ⎟Tues. Oct. 11, 2007 Physics 208 Lecture 12 5What is the capacitance?+Q-Qd€ ΔV = V+−V−= QdεoA ⎛ ⎝ ⎜ ⎞ ⎠ ⎟€ ΔV = Q/C€ C =εoAdThis is a geometrical factorTues. Oct. 11, 2007 Physics 208 Lecture 12 6An isolated parallel plate capacitor with spacing d has charge q. The plates are pulled a small distance further apart. Which of the following describe situation after motion?A) The charge decreasesB) The capacitance increasesC) The electric field increasesD) The voltage between the plates increasesE) None of these+q-q++++----dpullpullE= q/(0A) E constantV= Ed V increasesC = 0A/d C decreases!Quick QuizTues. Oct. 11, 2007 Physics 208 Lecture 12 7Requires work to transfer charge dq from one plate:Total work required = sum of incremental work:Work done to charge a capacitor€ dW = ΔVdq =qCdq€ dW = ΔVdq =qCdq€ W =qC0Q∫dq =Q22C€ W =qC0Q∫dq =Q22CTues. Oct. 11, 2007 Physics 208 Lecture 12 8Energy stored = work doneExample: parallel plate capacitorEnergy stored in a capacitor€ U =Q22C=12QΔV =12C ΔV( )2€ U =Q22C=12QΔV =12C ΔV( )2€ U =12Ad( )εoE2€ U =12Ad( )εoE2Energy density depends only on field strength€ U / Ad( )=12εoE2Tues. Oct. 11, 2007 Physics 208 Lecture 12 9An isolated parallel plate capacitor has a charge q. The plates are then pulled further apart. What happens to the energy stored in the capacitor?1) Increases2) Decreases3) Stays the same+q-q++++----dpullpullQuick QuizTues. Oct. 11, 2007 Physics 208 Lecture 12 10Human capacitorsCell membrane:‘Empty space’ separating charged fluids (conductors)~ 7 - 8 nm thickIn combination w/fluids, acts as parallel-plate capacitorCytoplasmExtracellular fluidPlasma membrane100 µmTues. Oct. 11, 2007 Physics 208 Lecture 12 11Modeling a cell membraneCharges are +/- ions instead of electronsCharge motion is through cell membrane (ion channels) rather than through wireOtherwise, acts as a capacitor~0.1 V ‘resting’ potentialCytoplasmExtracellular fluidPlasma membraneNa+Cl-K+A--- - - - -++ + + + +7-8 nmV~0.1 VIonic charge at surfaces of conducting fluidsCapacitance:€ εoAd=8.85 ×10−12F /m( )4π 50 ×10−6m( )28 ×10−9m= 3.5 ×10−11F = 35 pF100 µm sphere surface area~ 3x10-4 cm2~0.1µF/cm2Tues. Oct. 11, 2007 Physics 208 Lecture 12 12Cell membrane depolarizationCell membrane can reverse potential by opening ion channels.Potential change ~ 0.12 VIons flow through ion channels Channel spacing ~ 10x membrane thickness (~ 100 channels / µm2 )CytoplasmExtracellular fluidPlasma membraneNa+Cl-K+A--- - - - -++ + + + +7-8 nmV~0.1 V++ + + + +-- - - - -V~-0.02 VCharge xfer required Q=CV=(35FpF)(0.12V) =(35x10-12 C/V)(0.12V)= 4.2x10-12 Coulombs1.6x10-19 C/ion -> 2.6x107 ions flow This is an electric current!This is an electric current!Tues. Oct. 11, 2007 Physics 208 Lecture 12 13Charge motionCell membrane capacitor: ~70 ions flow through each ion channel to depolarize membraneOccurs in ~ 1 ms = 0.001 sec.This is a current, units of Coulombs / sec1 Coulomb / sec = 1 AmpTues. Oct. 11, 2007 Physics 208 Lecture 12 14Electric CurrentElectric current = I = amount of charge per unit time flowing through a plane perpendicular to charge motionSI unit: ampere 1 A = 1 C / sDepends on sign of charge:+ charge particles: current in direction of particle motion is positive- charge particles:current in direction of particle motion is negativeTues. Oct. 11, 2007 Physics 208 Lecture 12 15Quick QuizAn infinite number of positively charged particles are uniformly distributed throughout an otherwise empty infinite space. A spatially uniform positive electric
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