§7.1 EMF and Ohm’s Law

Christopher CrawfordPHY 417

2015-02-23

Outline• Noether’s theorem – symmetries & conserved currents

Kirchoff’s rules – conservation of charge & energyCurrent element – charge element in motionContinuity equation – local conservation of charge

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• Conductivitty – another material propertyDrude’s law – “bumper cars”Power dissipationRelaxation time

• Resistor – another electrical componentConductance = 1 / Resistancerelation to conductivity = 1 / resistivity

• EMF – electromotive forceMagnetic EMF – motivation for Faraday’s law

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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?

• What lifts up the charges, and what slows them going down?

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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

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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

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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)

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Motional EMF• Precursor to Faraday’s law• Write f = v x B as a magnetic flux law

• Magnetic force does no work!

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Motional EMF• General proof:

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