Electromagnetic inductionAQA A-Level Physics: Revision notes

When the magnetic flux linkage through a circuit changes, an emf is induced in it. Simple experiments: moving a magnet into or out of a coil, moving a conductor across a field, switching a current on or off in a nearby coil. An emf appears only while the flux linkage is changing; the faster the change, the larger the emf, and a stationary magnet in a coil induces nothing.

Faraday's law: the magnitude of the induced emf is equal to the rate of change of magnetic flux linkage:

ε = N ΔΦ / Δt

If the flux density changes at a constant rate with area fixed, ε = NA ΔB/Δt. A graph of flux linkage against time has gradient equal to the emf.

Lenz's law: the direction of the induced emf (and current) is always such as to oppose the change that produces it. This is expressed by the minus sign in ε = −NΔΦ/Δt.

Example: pushing the north pole of a magnet into a coil induces a current that makes that end of the coil a north pole, which repels the magnet. Work is done against this repulsion and becomes electrical energy: Lenz's law is the conservation of energy.

A conductor of length l moving at speed v at right angles to a field B sweeps out area lvΔt in time Δt, so the flux cut is BlvΔt and

ε = Blv

Example: an aircraft wing of span 36 m at 250 m s⁻¹ in a vertical field of 4.5 × 10⁻⁵ T gives ε = 4.5 × 10⁻⁵ × 36 × 250 = 0.41 V.

For a coil of N turns and area A rotating at angular speed ω = 2πf, with θ = ωt measured from the plane perpendicular to the field,

NΦ = BAN cos ωt, so ε = BANω sin ωt

The emf is sinusoidal, with peak value ε₀ = BANω. It is a maximum when the plane of the coil is parallel to the field (flux linkage zero but changing fastest), and zero when the plane is perpendicular to the field (flux linkage maximum). Doubling the rotation rate doubles both the peak emf and the frequency.