Christopher Crawford PHY 311 2014-03-24 §1.1.5, 7.1.1-2, 8.1.1 Electric Current: continuity equation and conductance Christopher Crawford PHY 311 2014-03-24

HW7 #2

Outline Noether’s theorem – symmetries & conserved currents Kirchoff’s laws – conservation of charge & energy Current element – charge element in motion Continuity equation – local conservation of charge Conductivitty – another material property Drude model – “bumper cars” Power dissipation Relaxation time Resistor – another electrical component Conductance = 1 / Resistance relation to conductivity = 1 / resistivity

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 P12: x1  x2 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?

Current elements Analogous to charge elements – different dimensions Relations between charge / current and different dimensions – analogy: multi-lane highway – current flux

Continuity equation Local conservation of charge Current I is a flux; current density J = flux density 4-vector current

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

Resistor – 2nd 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, reluctance R