Electromagnetic Induction
This domain covers the generation of EMF from a changing flux. Questions ask for Faraday's laws, Lenz's law, the EMF equation, and the meaning of self and mutual inductance.
Faraday's laws
- Whenever the magnetic flux linked with a coil changes, an EMF is induced in it.
- The magnitude of that EMF is proportional to the rate of change of flux linkage:
e = −N (dΦ/dt)
No change of flux means no EMF, however strong the field.
Lenz's law
The minus sign shows that the induced EMF drives a current whose own field opposes the change producing it. This is a statement of conservation of energy: mechanical work must be done to push a magnet into a coil.
Inductance
Self-inductance L is the flux linkage per ampere, measured in henry (1 H = 1 Wb-turn/A). It depends on the number of turns, core material and geometry, not on the applied voltage. Mutual inductance describes the EMF induced in one coil by a changing current in a neighbouring coil, the basis of the transformer.
Dynamically induced EMF
A conductor of length l moving at velocity v perpendicular to flux density B gives e = Blv, direction by Fleming's right-hand rule (generator rule).
Worked example
A 200-turn coil has its flux changed uniformly from 0.02 Wb to 0.06 Wb in 0.1 s. dΦ = 0.04 Wb; dΦ/dt = 0.04/0.1 = 0.4 Wb/s. e = N × 0.4 = 200 × 0.4 = 80 V.
Applications and traps
Generators, transformers, induction cookers and eddy-current brakes all rely on induction. Common errors: dropping the number of turns N, using flux instead of change in flux, ignoring the minus sign of Lenz's law when asked for direction, and confusing Fleming's right-hand rule with the left-hand motor rule.