Electromagnetic induction (A-level only): Faraday’s and Lenz’s laws.

The idea

Faraday’s law states that the magnitude of an induced emf equals the rate of change of magnetic flux linkage, so a faster change or more turns gives a larger emf. Lenz’s law states that the induced emf drives a current whose magnetic effect opposes the change producing it, which is a consequence of energy conservation. For example, pushing a magnet towards a coil induces a current whose field repels the approaching pole, so work must be done against that repulsion and electrical energy is transferred. Pulling the magnet away reverses the induced current, which now attracts the receding pole. The laws apply to generators, transformers, induction braking and search coils, and they explain the direction as well as the size of an induced emf.

What earns the marks

• Faraday’s law: the magnitude of the induced emf is proportional to the rate of change of magnetic flux linkage, ε = −N ΔΦ/Δt for a coil of N turns.
• Flux linkage is NΦ, where Φ = BA cos θ for a uniform field through a flat coil, so changing B, A or the angle θ changes the linkage.
• Lenz’s law: the induced current flows in a direction that opposes the change in flux linkage that produced it.
• Lenz’s law follows from conservation of energy because the induced current transfers energy and work must be done against the opposing force or torque.
• A qualitative direction question is answered by identifying the change in flux linkage, then choosing the induced current direction whose field opposes that change.
• A quantitative question uses the magnitude relationship and treats the minus sign as a direction indicator rather than a numerical size.

Common mistakes and how to put them right

• Treating the minus sign in ε = −N ΔΦ/Δt as making the emf negative in magnitude calculations.

  Put it right: The correct approach is to calculate the magnitude from the rate of change and use Lenz’s law separately for direction.

• Confusing magnetic flux Φ with flux linkage NΦ.

  Put it right: Multiply the flux through one turn by the number of turns before finding the rate of change.

• Stating that the induced current opposes the magnetic field itself rather than the change in flux linkage.

  Put it right: Say it opposes the change, so the induced field may be in the same direction as the original field when that field is decreasing.

Exam tips

• When asked for the direction of an induced current, first state whether the flux linkage is increasing or decreasing, then apply Lenz’s law to choose the current direction.
• Show the substitution into ε = N ΔΦ/Δt with consistent units, and keep the magnitude separate from the direction discussion.
• Use energy conservation to justify Lenz’s law in explanation questions, referring to the work done against the opposing force or torque.