The figure shows a magnet falling towards a coil. Which of the choices in the table is correct? Note that each row is a choice.
Let’s start out by taking a look at the figure which we see shows us a permanent bar magnet with the north pole down falling into the loops of a coil. This coil is part of a loop of wire that includes a galvanometer, a device for measuring current. We see marked out in our figure the locations marked one and two as well as A and B. Looking at that table, we see that it gives us four options for our answer, marked out a), b), c), and d).
The first factor we’ll look at to see which answer option is correct is the direction of the current through the galvanometer. We see in our answer options that the current can either be flowing from point one to point two, like this, or from point two to point one in that direction. And, next, we’ll want to figure out what type of magnetic pole, whether a north pole or a south pole, is formed at point A in our figure. So let’s get started figuring out the answers to these questions. And we’ll start by considering this magnet as it falls.
A magnet, we know, creates a magnetic field around itself. We can represent this field using magnetic field lines. We’ve only drawn in two field lines in this case, just for simplicity. But we know that the magnetic field created by the bar magnet extends beyond what we’ve drawn. And in addition, notice the direction of the field lines. They always move from the north pole towards the south pole of a magnet. This magnet, as we see, is falling. It’s falling through the loops of this coiled wire. Because the magnet creates magnetic field lines and that these field lines are moving through loops of wire, that means that as it descends, the magnet creates a magnetic flux that changes through the coil. And that change in magnetic flux increases in the direction the magnet falls, downward.
We can symbolize this change in magnetic flux as Δ𝛷 sub m. And we saw that this change is due to the effects of the falling magnet. Knowing this, we can recall what happens when the magnetic flux through a coil of wire changes over time. According to Faraday’s law of electromagnetic induction, a change in magnetic flux over a a change in time induces an emf. And an emf, an electromotive force, we know is what’s responsible for creating the flow of current in a circuit. All this is pretty amazing because it means that just by dropping a bar magnet through the loops of this coil, we can actually make current flow in the coil, when otherwise it wouldn’t have.
And that brings us to our first question. What is the direction of the current as it runs through the galvanometer in a circuit? Now we know that the current in this circuit can flow in one of two directions. It can either flow from point one to point two in this section of the circuit, what we’ll call clockwise, or in the opposite direction, from two to one. To solve for that direction, we can return to Faraday’s law and reconsider the form of this equation. In particular, notice the minus sign in the equation. This means that the emf which is induced by this change in magnetic flux creates current such as to oppose that change in magnetic flux, what we’ve called Δ𝛷 sub m. This could raise the question, just how would current induced in a circuit oppose a change in magnetic flux?
It could do it by creating a magnetic field in our coil opposite the direction of the change caused by the falling magnet. In other words, there is an induced magnetic field in the coil caused by the current running through it, which points opposite the direction of the change in magnetic flux Δ𝛷 sub m. This is the implication of the minus sign in Faraday’s law, that the induced current will create a field which opposes the changing field due to the falling magnet in this case. So then, what kind of current, in particular what direction of current, would produce an upward-pointing magnetic field in these loops?
To figure that out, we can refer to a rule known as the right-hand screw rule. This rule tells us that if we take a right-handed screw and point the end of the screw in the direction of the magnetic field, then the direction that the screw would naturally turn is the direction of the current that would create that magnetic field. So let’s apply this idea. Let’s take a right-handed screw point it upward, since that’s the direction of the magnetic field created by our loops. And we see then that this would imply a screw rotation in this direction for a right-handed screw like we have. If we map that direction over to the loops of this coil, we see that the current would have to run in this direction we marked out with arrows in order to create the magnetic field we’ve drawn. If we follow this current direction as it moves through the rest of the circuit, we see it passes point two then goes through the galvanometer and on to point one.
So this settles the first question of the direction of the current as it goes through the galvanometer. The direction is from point two to point one. And when we look at our answer options a), b), c), and d), we see that this eliminates options a) and b) from contention. They have the current moving in the opposite direction. Now that that’s settled, let’s look at the second question.
What kind of pole, north or south, is formed at point A in our figure? In figuring this out, the important point to remember is that a magnetic field which points up, from the bottom towards the top of the coil, is created in the coil in response to the falling magnet. And as we said, this magnetic field is responding that way in order to oppose the change caused by the magnet. That’s why since the magnet’s overall magnetic field direction with respect to the coil is downward, we have an induced magnetic field pointing upward. With the two magnetic fields at loggerheads pointing in opposite directions, that tells us that our coil has essentially become itself a magnet, with the opposite polarity of the falling magnet.
That means that within the coil, the north pole of this induced magnet is at the top, and the south pole of the induced magnet is at the bottom. We know this polar orientation because of the direction of the magnetic field within the loops. It points up. This means the magnetic pole formed at point A is a south magnetic pole. That corresponds to our last answer option, which is answer option d). So to recap, the current direction through the galvanometer is from point two to point one. And the magnetic pole formed at point A is a south magnetic pole.