Electromagnetic induction
Section: Magnetic Fields | Syllabus: Cambridge A Level Physics (9702)
Magnetic Flux and Flux Linkage
Magnetic Flux (Φ): product of magnetic flux density and the area perpendicular to the field.
Φ = BAUnit: Weber (Wb). 1 Wb = 1 T m^2.
Magnetic Flux Linkage (NΦ): For a coil with N turns:
Flux Linkage = NΦ = BAN(if field is perpendicular to area)
If the field makes an angle θ with the normal to the area: Φ = BA cos θ.
Laws of Induction
Electromagnetic induction occurs when there is a change in magnetic flux linkage.
Faraday's Law
The magnitude of the induced e.m.f. is directly proportional to the rate of change of magnetic flux linkage.
E = (Δ(NΦ)/Δ t)Flux Cutting (Straight Wire)
For a straight conductor of length L moving at speed v perpendicular to a field B:
E = B L vLenz's Law
The direction of the induced e.m.f. (or current) is such that it produces effects to oppose the change causing it.
(This is a statement of conservation of energy).
E = -(Δ(NΦ)/Δ t)The minus sign represents Lenz's Law.
Eddy Currents and DampingIf a metal plate (e.g. aluminium disc) moves through a magnetic field, eddy currents are induced effectively "inside" the metal.
By Lenz's Law, these currents create magnetic fields that oppose the motion of the disc, causing a braking force. This is electromagnetic damping.
Factors Affecting Induced E.M.F.
To increase the induced e.m.f (and current):
- Move faster: Increases rate of change of flux.
- Stronger magnet: Increases B and thus flux Φ.
- More turns (N): Increases flux linkage.
A large flux does not mean a large e.m.f. It is the rate of change that matters. A constant high flux produces zero induced e.m.f.
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