Electromagnetic Induction: Faraday's and Lenz's Laws

Electromagnetic induction — the generation of an EMF by a changing magnetic flux — is one of the most important phenomena in physics. It is the principle behind generators, transformers, induction hobs, and wireless charging. Michael Faraday and Joseph Henry independently discovered the effect in 1831, and Faraday formulated the law that bears his name.

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Faraday's Law

Faraday's law states that the magnitude of the induced EMF is equal to the rate of change of flux linkage through the circuit:

ε = −N dΦ/dt = −d(NΦ)/dt

where:

• ε is the induced EMF (V)
• N is the number of turns
• dΦ/dt is the rate of change of magnetic flux (Wb s⁻¹)
• The negative sign represents Lenz's law (see below)

In many exam questions, the change is uniform over a time interval, so:

ε = NΔΦ / Δt

(taking the magnitude and applying Lenz's law separately for direction).

Worked Example

A coil of 200 turns has a flux through it that decreases uniformly from 5.0 × 10⁻³ Wb to 1.0 × 10⁻³ Wb in 0.020 s. What is the induced EMF?

ΔΦ = 5.0 × 10⁻³ − 1.0 × 10⁻³ = 4.0 × 10⁻³ Wb