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A changing magnetic field makes the electric field curl around. So if you move a magnet through a loop of wire, the electric field will push electrons around the wire — and you'll get an electric current! The third Maxwell equation makes this precise.

This effect was discovered by Faraday in 1831, so one version of Maxwell's third equation is also called 'Faraday's law of induction'. This was an amazing discovery: the first big clue that electricity and magnetism are connected. Now we know they're two aspects of the same thing, just like space and time: if you move rapidly through an electric field you'll see a magnetic field, and vice versa. But it took Einstein to dig down that deep, and he got there by thinking hard about light, and Maxwell's equations.

It took 40 years from Faraday's discovery until Maxwell formalized the mathematical concept of 'curl' in 1871, based on ideas involving quaternions. In fact Maxwell chose the word 'curl' after discarding 'whirl', 'twirl' and 'twist'. Good choice!

Let me show you a modern version of Faraday's experiment, and then his original experimental apparatus.

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