4.5 Electromagnetic Induction

Faraday's Law of Induction

A changing magnetic flux through a loop induces an EMF: ε = -N(ΔΦ/Δt), where Φ = B·A·cos(θ). Flux can change by varying the field strength, the area of the loop, or the angle between B and the area vector. More loops (N) or faster changes produce a larger induced EMF.

Lenz's Law: Direction of Induced Current

The negative sign in Faraday's Law reflects Lenz's Law: the induced current flows in the direction that opposes the change in flux causing it. This is a consequence of conservation of energy — the induced magnetic field resists the original change, requiring work to be done to induce the current.

Motional EMF and Generators

When a conducting rod of length L moves with velocity v through field B, it generates a motional EMF = BLv, as moving charges experience a magnetic force. This principle underlies generators, where mechanical rotation of a coil in a magnetic field continuously changes flux, producing alternating EMF.

Key terms

Faraday's Law

ε = -N(ΔΦ/Δt); induced EMF is proportional to the rate of change of magnetic flux through a loop.

Magnetic flux (Φ)

Φ = B·A·cos(θ), a measure of the magnetic field passing through a given area.

Lenz's Law

The induced current flows in a direction that opposes the change in flux that created it, consistent with conservation of energy.

Motional EMF

EMF induced in a moving conductor: ε = BLv, where L is the rod's length and v is its velocity through field B.

Generator

A device that converts mechanical energy into electrical energy by rotating a coil in a magnetic field, inducing an alternating EMF.

Try an AP-style question

What does Faraday's law state?

1. Current is proportional to voltage
2. A constant field always induces a current
3. Charges create magnetic fields
4. A changing magnetic flux induces an emf