1. Christopher Crawford PHY 311 2014-03-24
§1.1.5, , Electric Current: continuity equation and conductance
Christopher Crawford
PHY 311

2. HW7 #2

3. 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

4. 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

5. Kirchoff’s laws: conservation principles
Conservation of energy: loop rule
Conservation of charge: node rule
Conservation of charge in a capacitor?

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

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

8. 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

9. 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