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Electromagnetic induction is one of the fundamental building blocks of today's world—it's the secret behind everything from generators to sparkplugs to transformers (yes, normal transformers as well as the Cybertron kind). Essentially, the idea of electromagnetic induction is that changing magnetic fields create electric fields. When there's a coil of wire present in a changing magnetic field, that electric field manifests itself as a voltage that can drive current around the wire. The stronger the magnetic field or the bigger the coil's loops or the faster the field changes, the bigger the voltage that appears.
To capture this, we need to look at magnetic flux. Magnetic flux is just like electric flux—the number of field lines from a magnetic field B passing through a given area A. We can find the magnetic flux (ΦB) of a field through a loop of wire perpendicular to the field lines by saying:
ΦB = BA
This is measured in T⋅m2, otherwise known as a weber (Wb).
When magnetic flux changes, electromagnetic induction takes place. In equation form, Faraday's Law describes electromagnetic induction for a coil of wire in a magnetic field:
Here, N is the number of loops of wire in the coil, and is the electromotive force, or emf (say "ee-em-eff"), created when the magnetic flux changes.
"Electromotive force" sounds like something Optimus Prime must harness in his robot war against the Decepticons, but an emf is really just a fancy name for the voltage that appears on the wire. It's not even a force at all—voltage, recall, is a measure of energy per unit of charge—but since it is the electromotive force that's responsible for electron motion in a circuit, you can see where some nineteenth-century physicist got a little fast and loose with the language.
Faraday's Law is related to changes, hence the deltas in the equation. When we talk about electromagnetic induction, we can't look at a snapshot in time. Instead, we have to look at what happens over a short period of time, Δt. In that time, if the magnetic flux through our wire changes, then—and only then—do we get an emf. This can happen in a whole bunch of different ways, such as changing B, the field strength, or A, the area of the loop in the field.
For example, moving a magnet into a coil of wire would change ΦB, but so would cranking up the dial on your magnetic field, or even spinning a loop of wire near a magnet. In the end, we're just looking at ΔΦB, or the difference between the flux through our loop at time t = 0 and t = Δt. Remember, there has to be some change of flux—moving a loop of wire at constant speed in a constant magnetic field won't cut it since the net change in B and the net change in A are both just zero.
The negative sign in Faraday's Law comes from another pretty smart guy named Lenz. Lenz's Law states that the emf that appears in a coil will always oppose the change in the magnetic field. Nature doesn't like change when it comes to magnetic fields, and will always try to keep things the way they were. This means changing magnetic fields create voltages that in turn create currents in the direction that will oppose the change in magnetic field.
Lenz's Law is straightforward to understand, but can be tricky to apply. Make sure your right hand rule is right.
Copper is a nonmagnetic material. But when you drop a magnet through a hollow copper cylinder, the changing magnetic field induces a current in the copper—which in turn creates a magnetic field exactly opposing the falling magnet. This slows the magnet down really eerily.