§7.1 EMF and Ohm’s Law Christopher Crawford PHY

Outline Noether’s theorem – symmetries & conserved currents Kirchoff’s rules– conservation of charge & energy Current element– charge element in motion Continuity equation – local conservation of charge Conductivitty– another material property Drude’s law– “bumper cars” Power dissipation Relaxation time Resistor– another electrical component Conductance = 1 / Resistance relation to conductivity = 1 / resistivity EMF– electromotive force Magnetic EMF– motivation for Faraday’s law 2

Symmetries – Noether’s Theorem Continuous Symmetries –space-time translation –rotational invariance –Lorentz boosts –gauge invariance Noether’s Theorem continuous symmetries correspond to conserved quantities –energy-momentum –angular momentum –center-of-momentum –electric charge Discrete Symmetries –parity P : x  -x –time T : t  -t –charge C : q  -q –particle exchange P 12 : x 1  x 2 Discrete Theorems –spin-statistics theorem –CPT theorem position symmetry conserved momentum

Kirchoff’s laws: conservation principles Conservation of energy: loop rule Conservation of charge: node rule – Conservation of charge in a capacitor? What lifts up the charges, and what slows them going down? 4

Conductivity – Drude model What limits the current in a cathode ray tube (CRT)? Drude model – effective drift velocity-dependent force Power dissipation – compare with field energy density Relaxation of a static charge distribution in a conductor 5

Resistor – 2 nd electrical component Conductance G (conductivity) = 1 / resistance R (resistivity) – Ratio of flux over flow – Power dissipated: flux x flow Compare with formulas for capacitance C Coming up … inductance L 6

Electromotive Force (EMF) Better name: electromotance The force that pushes electrons around a circuit – Chemical (battery) – isn’t chemical just electric forces? – Mechanical (piezoelectric, Van de Graaff) – Light (photocell) – Thermal(thermocouple) Magnetic analogy: magnetomotance and reluctance HW5 #3 – Hopkinson’s law (Rowland) 7

Motional EMF Precursor to Faraday’s law Write f = v x B as a magnetic flux law Magnetic force does no work! 8

Motional EMF General proof: 9