Electromagnetic induction and Lenz's law

A magnet moves towards a coil with no battery, and the meter detects current. Stop the magnet, keeping it nearby: the reading disappears. Why is a strong field not enough, and why does a change matter?

Imagine a surface stretched across a wire ring, like a film across a hoop. We need to describe not just the field at one point, but how it passes through this whole surface. For this we introduce magnetic flux Φ. It depends on magnetic flux density, area and surface orientation. Here, ‘flux’ does not mean that a magnetic substance flows through the ring: it is a quantity combining the field with the geometry.

For a uniform field perpendicular to the ring's plane, the flux magnitude is Φ = BS. Double the area at the same B and the flux doubles; halve B and the flux halves. B in T and S in m² give webers: 1 Вб = 1 Тл·м². Rotating the ring changes this relationship: if the field lies along its plane, the flux through it is zero. Thus Φ = BS requires the stated orientation.

Flux can be increased in different ways: bring a magnet closer, increase the current in a neighbouring coil, change the ring's area or rotate it. In each case, compare the field through the chosen surface before and after. Now move the whole ring within an unchanged uniform field, keeping its area and orientation fixed. The flux stays the same. This shows why ‘motion means induction’ is not a sufficient rule.

A change in magnetic flux produces an induced emf. Although emf stands for ‘electromotive force’, it is not a force measured in newtons: it is measured in volts and describes the work done by the induced electrical action per unit charge around the loop. An induced current can flow if the path is conducting and closed. A break stops sustained current, but need not remove the voltage between the ends: a path and a cause of motion are separate conditions.

Stop the magnet relative to the stationary coil. If all other conditions stay fixed, the flux no longer changes, so this change no longer produces an induced emf. A large constant field cannot replace a small changing one. In an ordinary resistive circuit, the earlier current dies away after a transient. A steady zero reading therefore does not mean that there is no magnetic field near the coil.

Which way does the current flow? It creates its own magnetic field. Lenz's law says this field opposes the change in external flux that caused the current. If external flux grows, the induced field opposes the growth; if it falls, the induced field tends to maintain it. It need not always point against the external field. First identify the change, then the required opposing action, and only then the current direction.

Bring a north pole N towards a closed coil: the external flux grows. The near end becomes N and repels the magnet, opposing its approach. Now withdraw the same pole: the flux falls, the near end becomes S and attracts the departing N. In both experiments, the action opposes the change that caused the current. ‘The coil always repels the magnet’ would pass the first test and fail the second.

Where does the energy that heats the coil come from if there is no battery? An external body does work by moving the magnet against the induced action. This energy is transferred to the circuit and can be released as heat. If the induced current reinforced the motion that caused it without any energy input, the system could continuously create energy from nothing. Lenz's opposing action is therefore consistent with energy conservation; a permanent magnet alone is not an unlimited energy source.

A north pole is withdrawn from a closed coil. What pole forms at its near end?

As the north pole moves away, the flux it produces through the coil decreases. By Lenz's law, the current's own field must oppose this decrease.

The coil must attract the departing N. Its near end therefore becomes a south pole S; like poles would produce the opposite effect.

If the magnet stops and nothing else changes, the external flux stops changing. In an ordinary coil, the current then dies away after the transient.

The near end becomes a south pole. Attraction opposes withdrawal, so external work is needed to keep the magnet moving away.

Induction depends on a change in flux through the loop, not merely the presence of a magnet or just any motion.

An emf and voltage can arise across a break, but sustained induced current needs a closed conducting path.

Lenz's law gives an action opposing the flux change and helps trace the source of the energy obtained.

A generator keeps changing flux by rotation. Next we will trace the energy's path to the consumer.