Electricity and MagnetismRecapWork and Electrostatic ForceFES is conservative!Electric Potential EnergyElectric Potential EnergyElectric PotentialElectric PotentialElectric Potential for many chargesElectric Potential for many chargesElectrical potentialsExample: Capacitor platesExample: Capacitor platesExample: Capacitor platesDemo: Ping-Pong BallDemo: Ping-Pong BallDemo: Ping-Pong BallDemo: Ping-Pong BallTrick question: Why does it start?ApplicationsApplicationsConductorsConductivityConductivityIn-Class DemoIn-Class DemoImportant applicationConductivityConductorsConductorsFeb 25 2002Electricity and Magnetism•Today– Electric Potential Energy– Electric Potential– Example of calculation– Practical applications– Conductors, Isolators and Semi-ConductorsFeb 25 2002Recap• Work in the Electrostatic Field• Electrostatic Potential Energy• Electrostatic PotentialFeb 25 2002Work and Electrostatic Force+Qba+qCharge q at point a in Coulomb field of QHow much work to move to point b?Feb 25 2002+Qadlr+qαbFESis conservative!Feb 25 2002Electric Potential Energy• Note: What we used was the fact that Coulomb Force is radial (i.e. F || r)– all radial forces are conservative (e.g. Gravity)Feb 25 2002Electric Potential Energy• Potential Energy for two charges• Can only observe differences in potential– often set U( ) = 0 or U(earth) = 0– U(r) energy needed to bring q,Q together from infinity8Feb 25 2002Electric Potential• Electric Potential Energy proportional to q•Define V = U/q• Electric Potential V: – Units are Volt [V] = [J/C]V = U/qFeb 25 2002Electric Potential• Note: because V = U/q -> U = V q– for a given V, U can be positive or negative, depending on sign of q•Example:Single ChargeFeb 25 2002Electric Potential for many charges• Superposition principle....• Sum of scalars, not vectors!• Integral for continous distributionsV(r) = Σ1/(4πε0) Qi/riFeb 25 2002Electric Potential for many charges• Electric potential depends on charges that create field, not the test charge!• V tells us how much energy a charged object can aquire when moving from a to bV(r) = Σ1/(4πε0) Qi/riFeb 25 2002Electrical potentials• Battery: 1.5 V• Power outlet: 120 V• HV power line: 106V• Accelerators: 108V• Thunderstorm: 108 VFeb 25 2002Example: Capacitor plates• Deposite opposite charges on plates• What is the Electric Potential?– What does E look like?•Move charge +q from a to b+++++++++++-----------ba+qxaxbxaxbx=0xx=dFeb 25 2002Example: Capacitor plates+++++++++++-----------ba+qxaxbx=0xx=dFeb 25 2002Example: Capacitor plates+++++++++++-----------ba+qxaxbxV(x)xx=0xU(x,q)0q>0q<0x=dFeb 25 2002Demo: Ping-Pong Ball+++--------------+++++++++++q>0Feb 25 2002Demo: Ping-Pong Ball+++++++++++-----------q>0+++++xV(x)0xxU(x,q)q>0Feb 25 2002Demo: Ping-Pong Ball+++++++++++-----------q<0xV(x)0xxU(x,q)-----Feb 25 2002Demo: Ping-Pong Ball• Field not perfectly uniform:– Net Force on Dipole+++++++++++-----------+++---xV(x)0Feb 25 2002Trick question: Why does it start?xV(x)0+++++++++++-----------+++---Slope dV/dx~ E ~ F !Feb 25 2002Applications+++++++++++-----------+qVelocity vd• Energy for single particle (e.g. electron) small•Often measured in ‘Electron Volt’[eV]• Energy aquired by particle of charge 10-19C going through ∆V=1V• Independent of dFeb 25 2002ApplicationsRelativistic Heavy Ion ColliderCathode Ray TubeRHIC∆VEkin~ 10 keV (104eV) Ekin~ 100 GeV (1011eV)Feb 25 2002Conductors• Important for next few weeks– Electrical Circuits• Why are some materials conductive?– All materials contain electrical charges!Feb 25 2002ConductivityMicroscopic viewMetal: e-can move around freelyU(x)e-xxInsulator: e-stuck in placeU(x)e-Feb 25 2002ConductivityxU(x)e-• How can we get charges ‘unstuck’?– Give them enough energy to jump out of potential wellsFeb 25 2002In-Class DemoCharged Ions+++++++++++++ElectroscopeFeb 25 2002In-Class DemoIons discharge ElectroscopeCharged Ions++++++++ElectroscopeFeb 25 2002Important applicationxU(x)∆U ~ 0.5 eV• Semi-conductor– # of charges controllable (by T and V)–At T=0oC Ekin~ 1/40 eV– Basis of all Electronic Circuits (e.g. Computers)Feb 25 2002Conductivity• Note: Usually, charge carried by electrons, but not always– ‘holes’ (i.e. missing electrons) in semi-conductorsFeb 25 2002Conductors•E = 0 inside – otherwise charges would move• No charges inside –Gauss• E perpendicular to surface– otherwise charges on surface would move• Potential is constant on conductorFeb 25 2002Conductors• Potential is constant on