Electricity and MagnetismParallel Plate CapacitorEnergy stored in CapacitorIn-Class DemoWhere is the energy stored?Electric CircuitsElectric CircuitsElectric CircuitsDielectricsDielectric DemoDielectric DemoMicroscopic viewMicroscopic viewMicroscopic viewMicroscopic viewMicroscopic viewMicroscopic viewDielectric ConstantDielectric ConstantDielectric ConstantDielectric Constant‘Puzzle’ Demo‘Puzzle’ Demo‘Puzzle’ Demo‘Puzzle’ Demo‘Puzzle’ Demo‘Puzzle’ Demo‘Puzzle’ Demo‘Puzzle’ DemoExperiment EFHow to get force?Mar 8 2002Electricity and Magnetism• Capacitors– Dielectric• Experiment EFMar 8 2002Parallel Plate Capacitorslope = 1/CVC=ε0A/dd smalld big•Change d–change C• Q constantV1V2Q0Qd bigger -> C smaller -> V bigger for fixed QMar 8 2002Energy stored in Capacitor• Can store more energy, if–Cbigger– V biggerMar 8 2002In-Class DemoC = 100µFVab=4000 VU= 800 Jthin wireMar 8 2002Where is the energy stored?• Energy is stored in Electric Field• E2gives Energy Density:• U/Volume = ½ e0E2+++++++++++------------Q+QdMar 8 2002Electric CircuitsCapacitorCWireVVoltage source (like LVPS)Mar 8 2002Electric Circuits• Two capacitors in parallel • V56= V23 = V14 (after capacitor is charged)• Q1/C1= Q2/C2= V14• Qtot= Q1 +Q2• Ctot= (Q1 +Q2 )/ V14 = C1+C2• Capacitors in parallel -> Capacitances add!V14C11423C256Mar 8 2002Electric Circuits• Two capacitors in series• V14= V23 + V56 • Q = Q1= Q2• Vtot= Q1/C1 +Q2/C2 = Q/(C1+C2)• 1/Ctot = 1/C1+1/C2• Inverse Capacitances add!C1V141423C256Mar 8 2002DielectricsIn your toolbox:• Parallel Plate Capacitor:– C = ε0A/d–Ex. A = 1m2, d=0.1mm -> C ~ 0.1µF• How do they do that?• Where to get a factor of 10000?2 cmC = 1000µFMar 8 2002Dielectric Demo• Start w/ charged capacitor• d big -> C small -> V large+++++++----------Q+QMar 8 2002Dielectric Demo• Start w/ charged capacitor• d big -> C small -> V large• Insert Glass plate•NowV much smaller • C bigger •But A and d unchanged !• Glass is a Dielectric+++++++----------Q+QMar 8 2002Microscopic viewRemember: Dipoles+-LDipole Moment p = q LE > 0+-+-+-+-+-+-+-E = 0Mar 8 2002Microscopic viewE > 0+-+-+-+-+-+-+-E = 0Def: Polarization P = n <p> = const. EDensity: #dipoles/volumeMar 8 2002Microscopic viewPolarization P = const. E = ε0χ E+++++++----------Q+QGlassMar 8 2002Microscopic viewPolarization P = const. E = ε0χ E+++++++----------Q+Q+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+--++-+-+-+-+-+-+-+-+-+-Mar 8 2002Microscopic viewInside: Charges compensate+++++++----------Q+Q+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+--++-+-+-+-+-+-+-+-+-Surface: Unbalanced Charges!+-Mar 8 2002Microscopic viewInside: Charges compensate+++++++----------Q+Q+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+--++-+-+-+-+-+-+-+-+-Surface: Unbalanced Charges!+-Surface layer:Thickness LSurface charges reduce field!Mar 8 2002Dielectric ConstantSurface charge densityPolarizationMar 8 2002Dielectric ConstantAdd contributions to EE from plates and E from Dielectric surface chargeK: Dielectric ConstantField w/o DielectricMar 8 2002Dielectric Constant• Dielectric reduces field E0(K > 1)– E = 1/K E0• Dielectric increases Capacitance– C = Q/V = Q/(E d) = K Q/(E0d)• This is how to make small capacitors with large C !Mar 8 2002Dielectric Constant•ExamplesMaterial KVacuum 1Air 1.0006Plexiglass 3.4Water 80.4Ethanol 23Ceramics ~5000Glass 5-10Similar to vacuumLarge!C in HVPSMar 8 2002‘Puzzle’ DemoCopper Glass-+Mar 8 2002‘Puzzle’ Demo+++++++++++++++++++++++-------------------------+++++Mar 8 2002‘Puzzle’ Demo+++++++++++++++++++++++-------------+++++------------Mar 8 2002‘Puzzle’ Demo+++++++++++++++++++++++-------------+++++------------Mar 8 2002‘Puzzle’ Demo+++++++++++++-------------Mar 8 2002‘Puzzle’ Demo+++++++++++++-------------Surfaces charges remain on Glass !Mar 8 2002‘Puzzle’ Demo+++++++++++++-------------Mar 8 2002‘Puzzle’ DemoMar 8 2002Experiment EFMMM2+-VVdAl Foil+Q-QMMM1HVPSHow do we measure ε0with this?MMM2+-VVdMar 8 2002Al Foil+Q-QMMM1HVPSQ = CV = ε0A/d VMar 8 2002How to get force?Balance unknown Force withknown Force -> Gravity!t:
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