Who hasn’t attended a cheesy magic show? Chances are we all have, probably in an elementary school assembly or the birthday of some family or friend. Remember that really impressive trick—no, not the rabbit coming out of a hat—but the other one…the really impressive one where the magician uses his powers of telekinesis to make a ring jump up from some kind of rod ?

Now, about this telekinesis…sitting down?...it’s a fake. And no, great-great-great Aunt Gertrude didn’t come back to haunt this world from beyond the grave either. The magician was probably a poor physicist unable to pay back his student loans and unemployed due to the harsh economy of the US. Just kidding, there are plenty of jobs for physicists out there. The real “magic” trick at work is actually a physics concept explained by Faraday’s Law.

Don’t worry, we’ll get back to the magician in the cape later.

Since we’ve all been (at least) partially awake while reading our physics modules, we’ll remember that electric and magnetic fields originate from electric charges that are either moving or stationary. This points to the fact that electricity and magnetism are strongly related since their phenomena influence each other.

Caption: Faraday the heart-throb.
Source

Now, picture this: an time with no Internet, no cars, no iPhones…no we are not referring to the Dark Ages but to the year 1831. A guy, let’s call him Faraday for good measure, has just been dumped by his girlfriend and has nothing to do but play around with magnets and wires while his soul lingers in the depths of romantic despair. We’ve all been there. But what does he do as he thinks of ways to win back her heart? He experiments, of course. He experiments with magnets and wires.

Faraday realizes that if he brings a magnet near a loop of wire, a current flows in the wire. As soon as he stops moving the magnet, the current no longer flows. If he moves the loop of wire and holds the magnet still, then once again, an induced current flows. See a pattern here? Apart from the fact that this wasn’t actually motivated by a broken relationship?

Yes, that’s right: it’s the relative motion between the wire and the magnet that creates the induced current in the wire. Faraday discovered a new phenomenon: electromagnetic induction, which says that electrical currents arise from changing magnetic fields.

Wait. What?

Let’s take a step back.

One more.

We happen to know that if we place an amount of charge at one end of a conductor, the charge will redistribute itself throughout the entire conductor until electrostatic equilibrium is reached. Nature is pretty boring; it prefers things to be quiet, calm, and non-eventful and in equilibrium (yawn). After the charge redistributes itself along a conductor, there’s no electric field within the conductor.

Something could force charge to stay on one end, such as a battery, or, in impressive, multisyllabic words, the electromotive force, or EMF, ε, and in that way keep the charge flowing through the conductor.

An EMF has a positive and negative terminal (like a battery), maintains a potential difference in the circuit, and all of that ensures that charge flows continuously in the circuit from positive to negative. Oh, and technically, the EMF isn’t a force but an electric potential difference, V, just for the record.

Faraday getting a current induced in a circuit implies that an EMF, ε, was induced, and this ε is equal to the change of magnetic flux through the circuit. This concept is known as Faraday’s law. Faraday casually pointed out that the whole “magnetism” thing is somehow connected to the whole “electricity” thing, and the world has never been the same again.

The magnetic flux Φ_B is simply the number of magnetic field lines that pass through some defined area. Mathematically, we say that Φ_B = BA cos θ. Don’t forget about this expression all together; we’ll scrutinize it later on, but for now, we can set it aside.

Faraday’s Law means the EMF induced in a circuit is given in terms of time by ,also known as Lenz’s Law, where Φ_B is the magnetic flux through a surface bound by that circuit. And by “surface bound by that circuit,” we mean a loop of wire that forms a circle, for instance, or any closed shape.

What’s up with the negative sign? Glad you asked. We just read that if we move a magnet through a loop of wire, we induce a current, but we also know that a current induces a magnetic field. No, this isn’t a bad GRE logic problem or chicken or egg conundrum. It’s a more like what we call the “couch potato problem” from inertia. If we happily vegetate on the couch, we won’t be inclined to move and we’ll resist any sort of change.

So, what we’re saying here is that if we go back to the right-hand rule of currents, which we’re familiar with by now, we’ll deduce that the direction of the induced current and EMF is such that the newborn magnetic field opposes the change in flux. That’s why there’s a negative sign in Lenz’s Law.

Going back to the magician (one with or without a PhD in physics), we know how he secretly made use of electromagnetism to fool his gaped-jaw audience. A solenoid coil of wire wrapped around an iron core, cleverly disguised as an innocent-looking non-physics object, is plugged into a source of alternating EMF, creating a magnetic field. The flux is zero before he connects the circuit, but as the alternating current flows in the coil a flux appears, and the changing magnetic field from the solenoid induces a current in the ring above it. That current flows in such a direction that its magnetic field opposes the new flux, and the two now-magnets repel each other and the one on top rockets up, up, and away.

Physics is so cool we all want to become physicists with awesome demos. The social lives of nerds, lots of magnets and wires to play with, and flourishing careers on stage as magicians.

Brain Snack

In reality, Faraday was a pull-himself-up-by-the-bootstraps kinda guy. He only managed to break into the elite world of aristocratic scientists with time and money on their hands by working as an assistant to one of them first. Way to work the system, Faraday.