Lenz’s Law & the Direction of Induction

You’ll be able to

Use Lenz’s law to determine the direction of an induced current
Explain Lenz’s law as a consequence of energy conservation
Apply the induced-current-opposes-change idea to magnets and loops

Nature pushes back

Faraday’s law gives the size of an induced EMF; Lenz’s law gives its direction. The rule: an induced current always flows in the direction that opposes the change in flux that produced it. If the flux through a loop is increasing, the induced current creates its own field to oppose the increase; if the flux is decreasing, the induced current tries to maintain it. The induced current is always fighting to keep things the way they were — a kind of electromagnetic inertia.

Lenz’s law is energy conservation

Why must the induced current oppose the change? Conservation of energy. Imagine pushing a magnet toward a loop and suppose the induced current helped the magnet along instead of resisting it — the magnet would accelerate on its own, creating kinetic energy and electrical energy from nothing. That is impossible. So the loop must repel an approaching magnet and attract a retreating one, always resisting your push or pull. The work you do against that opposition is exactly the electrical energy generated.

Lenz’s law (the minus sign)

EMF = − N · (ΔΦ / Δt)

The negative sign encodes Lenz’s law: the induced EMF (and current) opposes the change in flux. It is the mathematical statement that induction resists whatever is changing.

Worked example

The north pole of a bar magnet is pushed toward a conducting loop. Determine the direction of the loop’s response and explain why.

1.As the north pole approaches, the magnetic flux through the loop increases.
2.By Lenz’s law, the induced current opposes this increase, so it creates a magnetic field pointing back out toward the magnet.
3.That makes the loop’s near face act like a north pole, which repels the incoming north pole of the magnet.
4.You must do work pushing against this repulsion; that work becomes the electrical energy of the induced current.

Answer: The loop’s near face becomes a north pole and repels the approaching magnet — opposing the increasing flux, exactly as energy conservation requires.

Checkpoint

The north pole of a bar magnet is moved toward a conducting loop. The current induced in the loop creates a magnetic field that:

Watch out

Lenz’s law says induced effects oppose the change in flux, not the flux itself. When flux is decreasing, the induced current flows to reinforce the field and slow the drop — opposing the change means sometimes aiding the existing field.

Checkpoint

Lenz’s law — that an induced current opposes the change producing it — is a direct consequence of the conservation of:

On the exam

To get an induced-current direction: (1) decide whether flux is increasing or decreasing, (2) the induced field opposes that change, (3) use the right-hand rule to find the current direction that makes that field. Then sanity-check with energy conservation — the loop should resist the motion.

Answer the 2 checkpoints as you read.