7 1 EMF and Ohms Law Christopher Crawford

Outline • Noether’s theorem Kirchoff’s rules Current element Continuity equation – symmetries & conserved

Symmetries – Noether’s Theorem • – – • • Continuous Symmetries Discrete Symmetries –

Kirchoff’s laws: conservation principles • Conservation of energy: loop rule • Conservation of charge:

Conductivity – Drude model • What limits the current in a cathode ray tube

Resistor – nd 2 electrical component • Conductance G (conductivity) = 1 / resistance

Electromotive Force (EMF) • Better name: electromotance • The force that pushes electrons around

Motional EMF • Precursor to Faraday’s law • Write f = v x B

Slides: 9

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§ 7. 1 EMF and Ohm’s Law Christopher Crawford PHY 417 2015 -02 -23

Outline • Noether’s theorem Kirchoff’s rules Current element Continuity equation – symmetries & conserved currents – conservation of charge & energy – charge element in motion – local conservation of charge • • Conductivitty Drude’s law Power dissipation Relaxation time – another material property – “bumper cars” • 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 Discrete Symmetries – – space-time translation rotational invariance Lorentz boosts gauge invariance Noether’s Theorem parity� P : x -x time T : t -t charge C : q -q particle exchange P 12: x 1 x 2 continuous symmetries • correspond to conserved quantities – energy-momentum – angular momentum – center-of-momentum – electric charge 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 – nd 2 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 Mechanical Light Thermal (battery) – isn’t chemical just electric forces? (piezoelectric, Van de Graaff) (photocell) (thermocouple) • Magnetic analogy: magnetomotance and reluctance HW 5 #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