10 min readConcept sheet1-mark assertion-reason, 2-mark 'find the direction' questions and 3-mark explanations

Lenz's law and conservation of energy

The induced current flows in a direction that opposes the change in flux that produced it. This is the law of conservation of energy at work.

Lenz's law (1834)The induced emf tends to produce a current that opposes the change in magnetic flux that produced it

Minus signThe − in ε = −N dΦ/dt expresses Lenz's law

EnergyWork done against the opposing force becomes electrical energy, then heat

Clock ruleAnticlockwise current seen from a face makes it a north pole; clockwise makes it a south pole

Statement of Lenz's law

In 1834 Heinrich Lenz gave a rule for the direction of the induced current. Lenz's law: the polarity of the induced emf is such that it tends to produce a current that opposes the change in magnetic flux that produced it. Note the word change. The induced current does not oppose the flux itself. If the flux is rising, the induced current tries to reduce it. If the flux is falling, the induced current tries to keep it up. The minus sign in ε = −N dΦ/dt stands for this rule.

Finding the direction: north pole approaching a coil

1
The north pole of a magnet moves towards a closed coil. The flux through the coil, pointing away from the magnet, increases.
2
To oppose this increase, the coil must repel the magnet.
3
So the face of the coil nearer the magnet becomes a north pole.
4
A face acts as a north pole when the current in it looks anticlockwise to an observer facing it.
5★
So, seen from the magnet's side, the induced current flows anticlockwise.

★ key step

Direction of the induced current in four cases (seen from the magnet's side)

Motion of the magnet	Flux through coil	Near face becomes	Current seen from magnet	Force on magnet
N pole moves towards coil	Increases	North pole	Anticlockwise	Repulsion
N pole moves away	Decreases	South pole	Clockwise	Attraction
S pole moves towards coil	Increases	South pole	Clockwise	Repulsion
S pole moves away	Decreases	North pole	Anticlockwise	Attraction

Lenz's law and conservation of energy

If the current aided the changeSuppose the near face became a south pole as the N pole approached. It would attract the magnet and speed it up. The flux would change faster, giving a larger current and a stronger pull. Electrical and kinetic energy would grow from nothing: a perpetual motion machine, which is impossible.

Since the current opposes the changeThe coil repels the approaching magnet, so we must do work to push it in. This mechanical work becomes the electrical energy of the induced current, which then appears as heat in the coil. Energy is conserved.

So Lenz's law is the law of conservation of energy applied to electromagnetic induction.

Quick checks examiners like

In an open coil, or a ring with a cut, an emf is induced but no current flows, so there is no opposing force.
A magnet dropped through a long vertical coil with its ends joined falls with an acceleration less than g. With the ends open, it falls freely with acceleration g.
A light aluminium ring near a solenoid jumps away when the current is switched on, because the rising flux is opposed.
Use the clock rule: anticlockwise current, seen from a face, makes that face a north pole; clockwise makes it a south pole.

In real life

Regenerative braking in Indian metro trains and electric scooters uses Lenz's law. The motor runs as a generator, the induced current opposes the motion and slows the vehicle, and the energy goes back to the supply or the battery.

Exam angle

2 marks: “The north pole of a bar magnet is moved away from a closed coil. Find the direction of the induced current as seen from the magnet's side. Give a reason.” Clockwise. The flux falls, so the coil tries to keep it by attracting the magnet; its near face becomes a south pole, which needs a clockwise current seen from that side.

3 marks: “State Lenz's law. Show that it is a consequence of the law of conservation of energy.” Statement; a magnet approaching a coil is repelled, so work must be done, and this work becomes electrical energy and heat; if the current aided the change, energy would be created from nothing, which is impossible.

1 marks: “A magnet falls through a long copper coil whose ends are joined. Is its acceleration equal to, less than or more than g?” Less than g, because the induced current opposes its motion.

Remember it

Lenz says 'Not so fast!': the coil always fights the change, so you pay with work and get electrical energy.