Why Lenz must be true

A magnet swings toward a closed coil. What does the induced current's magnetic effect do to the swing?

You can now predict the induced current's direction: it always opposes the change. But why does the current always oppose? Why does nature never pick the other direction?

In earlier grades you saw that energy cannot be created or destroyed. That law decides it.

Suppose you push a magnet into a closed coil. The induced current opposes the push, so pushing takes work.

The work you feel yourself doing as you push is what becomes the electrical energy of the induced current.

The energy ledger balances: energy comes in from your hand and goes out as the current's electrical energy.

Now suppose the opposite happened: suppose the induced current aided the change.

The coil would pull the magnet in. The magnet would speed up, inducing a larger current, which would pull it in harder still.

Opposition keeps the energy ledger balanced. An aiding current would create energy from nothing.

In that world, if the induced current aided the change instead of opposing it, the motion would speed itself up and create energy from nothing. Energy cannot be created. So the aiding direction is impossible, and the opposing direction is the only one left.

A magnet is pushed into a closed coil at a steady speed. Where does the electrical energy of the induced current come from?

The induced current opposes the push, so the hand must do work to keep the magnet moving.

Energy cannot be created or destroyed, so that work must go somewhere.

The work the hand does against the opposition becomes the electrical energy of the induced current.

A magnet falls more slowly through a closed coil than it does through a plastic tube of the same size. Where does the energy of the induced current come from?

The induced current opposes the fall, so the magnet gains less kinetic energy than it would in the tube.

Energy cannot be created or destroyed.

The kinetic energy the magnet does not gain becomes the electrical energy of the induced current.

A magnet is pulled out of a closed coil against the current's opposition. What does the work become?

Why must an induced current oppose the change producing it, never aid it?

A bike's light runs from a magnet spinning past a coil. Pedaling feels harder with the light on. What does the extra work become?

Your turn

If an induced current aided a magnet's approach instead of opposing it, what would happen?

Lenz's law follows from a conservation law. Which one?

Pushing a magnet into a closed coil feels harder than pushing it into a cardboard tube of the same size. What is the correct reason?