Electricity and MagnetismDielectricsMicroscopic viewDielectric ConstantElectric CurrentElectric CurrentElectric CurrentElectric CurrentIn-Class Demo IIn-Class Demo IIn-Class Demo IIn-Class Demo IIIn-Class Demo IIIn-Class Demo IIIIn-Class Demo IIIResistivityResistivityReminder: GravityResistivityResistivityResistivityResistivityResistivityResistivityResistivityResistivityResistivityEnergy conservationResistanceResistanceIn-Class DemoIn-Class DemoIn-Class DemoMar 11 2002Electricity and Magnetism•Today– Electric current– Resitivity/Resistance– Ohm’s LawMar 11 2002DielectricsIn your toolbox:2 cmC = 1000µF• Parallel Plate Capacitor:– C = ε0A/d–Ex. A = 1m2, d=0.1mm C ~ 0.1µF• C can be increased with Dielectric– C = K ε0A/d– K: Dielectric ConstantMar 11 2002Microscopic viewInside: Charges compensate+++++++----------Q+Q+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+--++-+-+-+-+-+-+-+-+-Surface: Unbalanced Charges!+-Surface layer:Thickness LSurface charges reduce field!Mar 11 2002Dielectric Constant•ExamplesMaterial KVacuum 1Air 1.0006Plexiglass 3.4Water 80.4Ethanol 23Ceramics ~5000Glass 5-10Similar to vacuumLarge!C in HVPSMar 11 2002Electric Current• So far: Electrostatics– Look at situation where charges don’t move– E = 0 in conductors• otherwise mobile charges would move!• Now we look at moving charges!– Electric currents– |E| > 0 possible in conductorMar 11 2002Electric CurrentE+q+q+q+q-q-q-q-qArea ACurrent I: Net amount of charge passing through conductor per unit timeMar 11 2002Electric Current• Electric Current I:– I = dQ/dt•Units:– [I] = C/s = A (Ampere)• 1 A = 1.6 1019qe/s•I is a scalar, connected to given conductorMar 11 2002Electric Current• Current I = dQ/dt has a direction– Convention: Direction of flow of positive charges– In our circuits, I carried by electrons• To get a current:– Need mobile charges– Need |E| > 0 (Potential difference)Mar 11 2002In-Class Demo ICharged Ions+++++++++++++ElectroscopeMar 11 2002In-Class Demo IIons discharge ElectroscopeCharged Ions++++++++ElectroscopeMar 11 2002In-Class Demo INeutral molecules:Pos. and neg. charges move together -> No current!Ions:Pos. and neg. charges move separately -> Current |I| > 0 !Mar 11 2002In-Class Demo IIVoltage sourceGlassLead IonsLight BulbSolid glass: Potential charge carriers are stuck!Mar 11 2002In-Class Demo IIVoltage sourceGlassLight BulbMolten glass: Charge carriers become mobile ->Current flows -> Bulb lights up!Mar 11 2002In-Class Demo III110 VDistilled WaterLight BulbWill the bulb light up? NONo light -> No current -> No mobile charges!Mar 11 2002In-Class Demo III110 VDistilled WaterAdd NaCl: Dissociates into Na+and Cl-Charge carriers are available -> Current flows ->Bulb lights upLight BulbMar 11 2002Resistivity• To get a current, we needed – mobile charge carriers– a Potential difference• What determines magnitude of I ?• -> Microscopic analysisMar 11 2002Resistivity• Consider an electron in a conductor:e-EEquation of motion: medv/dt = qeEFor |E| > 0, |v| increases all the time (|v| -> infinity)Consider analogy with GravityMar 11 2002Reminder: Gravityv-f vm gEquation of motion: m dv/dt = m g -f vFriction grows with |v|, limits maximal velocity v<vmax( m g = f vmax)Mar 11 2002Resistivitye-Where does friction come from?Metal: Electrons move through lattice of atomsLattice: Thermal vibrations, average position fixedElectrons: Light! Bounce around...Mar 11 2002<v>= vD> 0Resistivity|E|=0 |E|>0If |E| > 0: Electron accelerated between scatteringsOn average: Electron moves in –E direction<v>=0Mar 11 2002Resistivity• Interplay of scattering and acceleration gives an average velocity vD•vDis called ‘Drift velocity’• Similar to terminal velocity for parachuting:For dv/dt = 0 -> vD= (qeE) / fFrictionEquation of motion: medv/dt = qeE –f vSteady StateMar 11 2002Resistivity• How fast do the electrons move?– Thermal speed is big: vth~ 106m/s– Drift velocity is small: vD~ 10-3m/s• How long do I have to wait when switching on the light?– ∆t = 10m/vD= 104s ~ 3 hours!?!–No, ∆t = 10m/c = 3*10-7s• All electrons in conductor start to move, as soon as E> 0Mar 11 2002Resistivity• What determines magnitude of current I?• Connect macroscopic description (I) with microscopic descriptionMar 11 2002ResistivityE-qvDLAabvD* dtHow big is the current I?I = dQ/dt = 1/dt * (Charge going through A)= 1/dt * q * nq*(A vDdt) = q nqA vD= q nqvDAVolumeCharges/VolumeMar 11 2002ResistivityE-qvDLAabvD* dtI = q nqvDAAreaVelocityCharges/VolumeVelocity * Area: Flux! (like flow of water)Def: J = q nqvDCurrent Density ([J] = A/m2 )Then I = J AMar 11 2002ResistivityE-qvDLAabvD* dtHow does J = q nqvDdepend on the Field E ?Remember: vD= (qeE) / f -> J = q2nq/f E J = 1/ρ E; ρ = f /(q2nq)constantResistivityρ= f /(q2nq): ResistivityUnits: [ρ] = V/m m2/A = m V/A = m ΩMaterialρ [m Ω]Glass <1010Pure Water 2*105Carbon 3.5*105Silicon 2300Sea Water 0.2Gold 2.4*10-8Copper 1.7*10-8InsulatorSemiconductorConductorOhmMar 11 2002Mar 11 2002Energy conservation• We spend energy to apply potential difference• But velocity of charges doesn’t increase• Where does the energy go?•‘Friction’ of electrons moving through conductor causes heatMar 11 2002ResistanceLAabDefine R = V/I : ResistanceJ = 1/ρ E and I = J A -> I = R V for R = ρ L /AV = Va–Vb= E LMar 11 2002ResistanceR = ρ L /A = f/(nqq2) L/A• How can we change Resistance?– generally, want low resistance (lose less energy to heat)– Make Area A big–Make lengthL short–Make f small!•Demo....Mar 11 2002In-Class Demo Light bulbVoltagesourceMar 11 2002In-Class Demo VoltagesourceLight bulbLiquid Nitrogen (T ~ -200oC) Wire cold -> less resistance -> more current -> bulb burns brighterMar 11 2002In-Class Demoe-e-•T high•Big vibration• Electrons bounced around•T low• Less vibration• Electrons move through lattice