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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
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Symmetries – Noether’s Theorem
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Continuous Symmetries
Discrete Symmetries
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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
P12: x1  x2
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?
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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 –
nd
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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
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Chemical
Mechanical
Light
Thermal
(battery)
– isn’t chemical just electric forces?
(piezoelectric, Van de Graaff)
(photocell)
(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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