1. Christopher Crawford PHY 417 2015-02-25
§7.2 Faraday’s law
Christopher Crawford
PHY 417

2. 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

3. Review– 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)

4. Motional EMF Precursor to Faraday’s law
Write f = v x B as a magnetic flux law
Magnetic force does no work!

5. Motional EMF
General proof:

6. Faraday’s law – THREE experiments

7. Example: AC generator

8. Example: solenoid and ring
What is I(t) in the ring?
Which direction?
Levitation of ring
Permanent for superconductors

9. THREE Ampère-like laws
Ampère’s law Vector potential Faraday’s law
Relation between E and A: will need to revisit electric potential!

10. Mutual Inductance Overlapping solenoid and ring: mutual inductance M
Self-inductance L

11. Inductance – 1 of THREE components
Capacitor Resistor Inductor
Each the ratio of FLUX / FLOW
Units:
Complex impedance:

12. Example – LR-circuit

13. Magnetic field energy
Work against the “back-EMF” is stored in the magnetic field
It acts as “electrical inertia” to keep current moving