Fun with Capacitors - Part IIThis weekCapacitor CircuitsA ThunkerAnudder ThunkerMore on the Big CSo….Not All Capacitors are Created EqualSpherical CapacitorCalculate Potential Difference VContinuing…Slide 12Polar Materials (Water)Apply an Electric FieldAdding things up..Non-Polar MaterialSlide 17We can measure the C of a capacitor (later)How to Check ThisChecking the idea..Slide 21Messing with CapacitorsAnother CaseNo BatteryAnother Way to Think About ThisA Closer Look at this stuff..Remove the BatterySlip in a Dielectric Almost, but not quite, filling the spaceA little sheet from the past..Some more sheet…A Few slides back No BatteryFrom this last equationAnother lookAdd Dielectric to CapacitorWhat happens?SUMMARY OF RESULTSAPPLICATION OF GAUSS’ LAWNew Gauss for DielectricsFun with Capacitors - Part IIThis weekWednesdayYell at you about the exam.Capacitors IIFridayFinish CapsStart Current and ResistanceMondayQuiz – Caps & Current (Through Friday’s stuff)Capacitor CircuitsiiiiCCParallelCCSeries11A ThunkerIf a drop of liquid has capacitance 1.00 pF, what is its radius?Anudder ThunkerFind the equivalent capacitance between points a and b in the combination of capacitors shown in the figure.V(ab) same across eachMore on the Big CWe move a charge dq from the (-) plate to the (+) one.The (-) plate becomes more (-)The (+) plate becomes more (+).dW=Fd=dq x E x d+q-qE=0A/d+dqSo….22220202000002122)(12211CVCVCCQUordAqAdqqd qAdUWdqdAqd WAqEGau ssEddqd WQSorta like (1/2)mv2Not All Capacitors are Created EqualParallel PlateCylindricalSphericalSpherical Capacitor???4)(402020sur priserqrEqErqdGauss-AECalculate Potential Difference VdrrqVEdsVabplatepositiveplatenegative20..14(-) sign because E and ds are in OPPOSITE directions.Continuing…ababVqCababqbaqVrqrdrqVba00002044114)1(44Lost (-) sign due to switch of limits.DIELECTRICPolar Materials (Water)Apply an Electric FieldSome LOCAL ordering Large Scale OrderingAdding things up..- +Net effect REDUCES the fieldNon-Polar MaterialNon-Polar MaterialEffective Charge isREDUCEDWe can measure the C of a capacitor (later)C0 = Vacuum or air ValueC = With dielectric in placeC=C0 (we show this later)How to Check ThisCharge to V0 and then disconnect fromThe battery.C0V0Connect the two togetherVC0 will lose some charge to the capacitor with the dielectric.We can measure V with a voltmeter (later).Checking the idea..V0000002102010001 CVVCCCVVCVCqqqCVqVCqVCqNote: When two Capacitors are the same (No dielectric), then V=V0/2.Messing with Capacitors+ V-+ V-+-+-The battery means that thepotential difference acrossthe capacitor remains constant.For this case, we insert the dielectric but hold the voltage constant,q=CVsince C C0qC0VTHE EXTRA CHARGE COMES FROM THE BATTERY!Remember – We hold V constant with the battery.Another CaseWe charge the capacitor to a voltage V0.We disconnect the battery.We slip a dielectric in between the two plates.We look at the voltage across the capacitor to see what happens.No Battery+-+-q0qq0 =C0VoWhen the dielectric is inserted, no chargeis added so the charge must be the same.000000VVorVCqVCqVCqV0VAnother Way to Think About ThisThere is an original charge q on the capacitor.If you slide the dielectric into the capacitor, you are adding no additional STORED charge. Just moving some charge around in the dielectric material.If you short the capacitors with your fingers, only the original charge on the capacitor can burn your fingers to a crisp!The charge in q=CV must therefore be the free charge on the metal plates of the capacitor.A Closer Look at this stuff..Consider this virgin capacitor.No dielectric experience.Applied Voltage via a battery.C0000000VdAVCqdAC++++++++++++------------------V0q-qRemove the Battery++++++++++++------------------V0q-qThe Voltage across thecapacitor remains V0q remains the same aswell.The capacitor is fat (charged),dumb and happy.Slip in a DielectricAlmost, but not quite, filling the space++++++++++++------------------V0q-q- - - - - - - -+ + + + + +-q’+q’E0EE’ from inducedchargesGaussian Surface-0000....AqEqdgapsmallinAEA little sheet from the past..+++---q-q-q’ +q’AqAqEAqEdialectricsheetsheet00/00'2'22'20 2xEsheet 0Some more sheet…AqqEsoAqEAqEechdielectric0000arg''A Few slides backNo Battery+-+-q0qq=C0VoWhen the dielectric is inserted, no chargeis added so the charge must be the same.000000VVorVCqVCqVCqV0VFrom this last equation0000001EEEEVVthusdEVEdVandVVAnother look+-VodVAQdVEFieldElectricdAVVCQdACPlateParallel0000000000000Add Dielectric to Capacitor•Original Structure•Disconnect Battery•Slip in Dielectric+-Vo+-+-V0Note: Charge on plate does not change!What happens?0001VEdVanddVEE+-iiooPotential Difference is REDUCEDby insertion of dielectric. 00/CVQVQCCharge on plate is Unchanged!Capacitance increases by a factor of as we showed previouslySUMMARY OF RESULTS000EECCVVAPPLICATION OF GAUSS’ LAWqqqandAqEEAqqEAqE''00000New Gauss for
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