Electromagnetic induction.

Step 1 of 6

The change is what counts

A current makes a magnetic field. Can a magnetic field make a current? Michael Faraday looked for it for years, and in 1831 found that it can, but only on one condition.

On the board is a coil of $200$⁠ turns, connected to a centre-zero voltmeter and a small bulb. A bar magnet is pushed in and out once a second, and the needle swings one way as the magnet goes in and the other way as it comes out. Predict what will happen when the magnet stops.

Step 2 of 6

Faraday’s law

To say how much voltage appears, you need a new quantity: the magnetic flux through a turn, $\Phi = B A$⁠ when the field is at right angles to the turn, that is, how much field passes through its area. Flux is measured in webers (Wb = T·m²).

When the flux through the turns changes, an induced voltage appears across the ends of the coil, the electromotive force (EMF) $\mathcal{E}$⁠, and its size is given by Faraday’s law:

$\mathcal{E} = -N\,\frac{\Delta\Phi}{\Delta t}$$\mathcal{E} =$$-N\,\frac{\Delta\Phi}{\Delta t}$⁠

$N$⁠ is the number of turns, because each turn makes the same voltage and they are joined one after another, and $\dfrac{\Delta\Phi}{\Delta t}$⁠ is the rate at which the flux changes. The minus sign comes in a moment.

Step 3 of 6

Faster, and with more turns

In the Scene, with $200$⁠ turns and one push a second, the voltage peaks at 0.5 V. Now there are $400$⁠ turns, and the magnet is pushed three times a second with the same stroke.

Step 4 of 6

Reach a peak

Now you set Speed and Turns of wire. Once the peak is high enough, the bulb lights too.

Step 5 of 6

The coil pushes back

While the bulb is lit, energy leaves the circuit as light and heat. Where does it come from? The induced current turns the coil itself into an electromagnet, and its poles always oppose the change that made them. This is Lenz’s law, and it is what the minus sign in Faraday’s law says.

Show field and current is On: the magnet’s field lines pass through the coil, the arrows show the current in the wire, and the poles the coil takes on while the magnet moves appear at its ends.

Step 6 of 6

Spinning: an alternating voltage

Spin is chosen under Motion: now the magnet turns twice a second beside the end of an iron core inside the coil, as in a bicycle dynamo. Its north and south poles face the core in turn, the flux rises and falls as a sine wave, and so does the voltage: an alternating voltage. Every generator in a power station works this way.

An alternating voltage is at its peak only for an instant. To say what it is “worth”, you use the effective voltage: the steady voltage that would heat the same bulb just as much. For a sine wave with peak $V_0$⁠:

$V_{\text{eff}} = \frac{V_0}{\sqrt 2}$$V_{\text{eff}} =$$\frac{V_0}{\sqrt 2}$⁠