State Faraday’s law of electromagnetic induction.
This law of Michael Faraday’s is based on an experiment that he performed. This experiment involved a coil of conducting wire arranged in a series of loops and connected to an ammeter to measure current as well as a permanent bar magnet that could be moved around. Here’s what Faraday tried. Knowing that the permanent magnet created a magnetic field around itself, which can be represented using these dashed magnetic field lines, Faraday wondered what would happen to his simple circuit if he moved a magnet, and therefore the magnetic field lines, into the loops of this coil.
When he did, when the magnet moved through the loops of the coil, Faraday noticed that the ammeter went off of a zero reading. It measured a nonzero current. But then, something interesting happened. Faraday held the magnet in place, stationary in the loops of the coil. And the ammeter reading returned to zero. Then, moving the magnet back out of the coils to its original position, current was once more induced in the ammeter, but this time in the opposite direction. And then, just like before, as soon as the magnet was stationary and this time outside of the coils, the current measured returned to zero.
Faraday continued to experiment, changing things like the number of turns in this coil. He found that the more turns in the coil, the more current was measured for a given movement of the magnet. And he also found that the faster he moved the magnet in and out of the coils, the more current again was measured. Faraday thought of it this way. He thought of the magnetic field lines, the magnetic flux that were moving through the coils of this wire. He realized that because the magnet was in motion, that meant that the flux through these coils was changing with time. And the faster the magnet was moved, the more that flux changed in time. Based on his recorded readings of the ammeter, he saw that the faster the flux changed through these loops, the more current was induced.
Now, Faraday realized something. Even though he was measuring current in his circuit, he realized that in order for any current to flow through the circuit, there must be an electromotive force driving it. So rather than claiming that a change in magnetic flux, Δ𝜙 sub 𝑚, per unit time led directly to an induced current in this loop, Faraday saw that actually this change in magnetic flux over time led to an emf, an electromotive force, which then led to a current flowing through the loop. It’s this connection, that the change in magnetic flux per unit time induces an electromotive force, which came to be known as Faraday’s law of electromagnetic induction.
Based on his careful analysis of how the change in magnetic flux over time led to a particular change in emf, we can state this law this way. We can say that the magnitude of the induced electromotive force, that’s the emf here, is proportional to the rate by which the conductor, the conductor being our wire arranged in loops, cuts the lines of the magnetic flux coming from the bar magnet linked with it. This is a way of stating in words this law of electromagnetic induction, often written as an equation.