Transcript Fundamental nuclear symmetries meet classical electrodynamic

§7.2 Faraday’s law
Christopher Crawford
PHY 417
2015-02-25
Outline
• Motional EMF – from Lorenz force law
• Faraday’s law – THREE experiments, one result
– EMF, Lenz’ law, special relativity
– Examples: AC generator, solenoid & ring, SC levitation
• Differential form – THREE Ampère-like laws, one form
– Magnetic vector potential: potential momentum
• Mutual inductance – transformers, inductors
– Example: overlapping solenoids
• Inductor – THREE electrical devices, one calculation
– Example: L–R circuit
• Magnetic field energy – back EMF or “electrical inertia”
– Compare: electrical field energy
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Review– Electromotive Force (EMF)
• Better name: electromotance
• The force that pushes electrons around a circuit
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–
–
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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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Faraday’s law – THREE experiments
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Example: AC generator
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Example: solenoid and ring
• What is I(t) in the ring?
• Which direction?
• Levitation of ring
• Permanent for
superconductors
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THREE Ampère-like laws
Ampère’s law
Vector potential
Faraday’s law
•Relation between E and A: will need to revisit electric potential!
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Mutual Inductance
• Overlapping solenoid and ring: mutual inductance M
• Self-inductance L
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Inductance – 1 of THREE components
Capacitor
Resistor
Inductor
• Each the ratio of FLUX / FLOW
• Units:
• Complex impedance:
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Example – LR-circuit
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Magnetic field energy
• Work against the “back-EMF” is stored in the magnetic field
• It acts as “electrical inertia” to keep current moving
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