Explain why eddy currents are induced in the iron core of a solenoid that is connected to an AC supply.
If we sketch out a picture of the circuit described here, we know we have an AC power supply and then a solenoid in the circuit. Not only that, but the windings of the solenoid have an iron core in them. This solid cylinder of iron positioned within the windings of our solenoid has the effect of increasing its overall inductance. But in this question, we want to figure out why it is that eddy currents are induced to form in this core.
Recall that eddy currents are current loops that form in a bulk material. If we had a big chunk of conducting material for example, any eddy currents that would form would be small loops of current within and across this material. The question when it comes to our particular circuit is why is it that eddy currents would form in this iron core. Remember that we’re given an AC power supply, which means that the current that runs through the circuit and therefore through the solenoid is varying in time.
We know that if the current that was moving through the solenoid was constant in time, that is it didn’t change, it came from a DC power supply, then even that current would induce a magnetic field to be formed within the windings of this coil. And because we have an alternating current source, that means the current in the windings is changing and therefore the induced magnetic field within the windings of the coil is changing as well.
Imagine that we were to look at this solenoid end on so that one of the loops might look like this. With the change in current running through the solenoid, we would have a changing magnetic field in this loop. We have a changing magnetic field then over some cross-sectional area. That is this area is experiencing a change in magnetic flux. And we realize that this change in magnetic flux happens through every single one of the turns of our solenoid. And these turns we recall are filled with our iron core.
All this to say the iron core itself is experiencing a change in magnetic flux. When the iron core experiences a changing magnetic flux, that has an effect on the core. Across and throughout our iron core, an emf is induced. We could think of this as potential differences separated by small distances in the core. And we know that when a potential difference is established, that creates an electric field which tends to drive current. It’s that electromotive force which induces the flow of small loops of current, eddy currents, in our iron core.
We can say then that the reason these eddy currents form is due to the variation in the magnetic flux that intercepts this iron core. This is the reason behind the formation of eddy currents.