This lesson about the magnetic fields produced by electric currents is gonna show us what these fields look like when they’re produced by different current arrangements. We’ll see how to draw the magnetic fields. And we’ll also learn how they’re made stronger.
We can start out by thinking about this, a single electric charge. We know this charge creates an electric field around itself. And we also know that if we put it in motion, it will create a magnetic field. Charge in motion, when we’re talking about lots of charges moving together, is a really good description of electric current. All this moving charge creates a magnetic field around the wire that it travels along. To get a sense for what that looks like, we can take an end-on view of this wire. From this perspective, the wire will look like this, with the negative electric charge flowing toward us. At this angle, it looks like it’s coming out of the screen.
We might guess that the magnetic field around the wire looks something like the electric field created by a single charge. That is, maybe we think it would look something like this, pointing radially out from the wire. But actually, the magnetic field looks very different. It actually looks like this, like a bunch of circles centered on the conducting wire. We’ve only drawn three of these circles here. But really, the magnetic field extends out infinitely far away from the wire. So we could’ve drawn more. We just drew three to give a sense for what the field looks like.
Notice a couple of things about this magnetic field. For one thing, it has a direction. Each magnetic field line has an arrow, which shows which way it points. Another thing to see is if we look at the direction of the flow of electric charge along this axis right through the conductor, we see that the direction the charge moves is always perpendicular to the direction of the magnetic field. And that’s actually always the case. The magnetic field produced by a moving charge always points perpendicular to that motion. Anyway, like we said, the magnetic field will look like this, if we look at the conductor end on.
From the side on perspective, those field lines would look something like this. The fact that these magnetic field lines have a particular direction to them brings us to the first important rule we want to learn. This rule is called the right hand rule because we use our right hand in it. And its purpose is to show the magnetic field direction. Here’s how this rule works when we have a straight current-carrying conductor.
First, we take our right hand and we put it up to this line of current. Then, we point our thumb in the direction that conventional current travels in this wire. And it’s important to make sure we’re pointing in that direction, in the direction of positive charge flow through the wire. Then, what we do is we curl our fingers around the wire. It’s that direction that our fingers curl that shows which way the magnetic field points along the wire. Once we know that, we can start drawing in more magnetic field lines. This is how the right hand rule works when we have a line of current.
Let’s try this rule out up here. First, we can extend our conductor a bit. Then we take our right hand, put it up to the wire, and point our thumb in the direction of conventional current flow. Notice that, in this wire, we have negative charge flowing to the right. So that means we have positive charge effectively flowing to the left. That’s the direction of conventional current. So that’s the way we point our thumb. Then, what we do is we curl our fingers around the wire. And the direction our fingers curl is the direction the magnetic field will take around this wire. So we see that the way we’ve drawn in these magnetic field lines agrees with this right hand rule.
Now, this particular version of the right hand rule applies only to the case where current is moving in a straight line. But we can think of other ways that current can flow. Say that, instead of current flowing in a line like this, we took the ends of this conductor when we join them together. Doing that would give us a loop of current like this. The question then becomes what does the magnetic field created by this loop look like.
One way to think of it will be to divide up this loop into very many, very tiny segments. Each of these segments is so small we could think of them as being a straight line and then apply our right hand rule from earlier. That method would work. But if we’re only interested in the magnetic field at the center of this current-carrying loop, then there’s another way to do it. This other way involves what we could call version two of the right hand rule.
In this version, we figure out the direction of the magnetic field created through the center point of a current-carrying wire. The process goes like this. Step one, draw an axis that goes perpendicularly through the center of this current-carrying loop. Step two, take our right hand and put it up to this imaginary axis, in such a way that our fingers can curl around the axis in the same direction that the current travels through the loop.
When we’ve done that and curled our fingers around this imaginary axis, then our thumb points in the direction of the magnetic field that goes through the center of this loop. If we applied this right hand rule to our loop here, as our first step, we’ll draw an axis that runs perpendicular to the plane of this current-carrying loop. And it goes through the center of the loop. From this perspective, the axis would just look like this. It goes into and out of the screen.
Then, we take our right hand, in this case, it takes a bit of twisting, and put it up to that imaginary axis, in such a way that our fingers can curl around the axis in the same direction that current flows through our loop. Then, when we actually do curl our fingers, our thumb, that’s this bit right here, points in the direction of the magnetic field. Our thumb here is pointing into the screen. So that means the magnetic field created by this loop points into the screen at the center of the loop.
This is a quick way, a shortcut of finding the direction of the magnetic field as it goes to the center of a current-carrying loop. If we had tried out our earlier idea of dividing up this loop into very small linear segments, then what we might do is go segment by segment. So we start here. And considering this linear segment, it runs along a line that looks something like this. Of course, most of this line that we’ve drawn isn’t real. The only part that really does exist is the actual part in the circle.
And then, knowing that conventional current travels along this line in this direction, we could take our right hand, put it up to this line, with our thumb pointing in the direction of current flow, and then curl our fingers around this line. That direction of curl shows us the direction of the magnetic field that would be created by this very small linear segment of wire. We can see that, according to this direction, if we follow that direction at the center of the loop, that would imply a magnetic field which goes into the screen. Of course, this is only the magnetic field created by one very very small segment of this circular loop.
But if we did the same thing with another segment, say this one over here, then we would draw a line representing what that segment, if we extended it out, would look like as a line of current. Then once again, put our right hand on that line so our thumb can point in the direction of current flow. And then once more, we curl our fingers around that line.
Notice that, for this line segment too, if we follow that direction of curl through the center of this loop, it also implies the magnetic field that goes into the screen. What we’re seeing here is that if we did go around this loop, very small segment at a time, and used our version one, right hand rule, when we added up the results of all of those, we would find what we found using our shortcut of version two. And that is that the magnetic field at the center of this loop points into the screen, given this direction of current. This shortcut that we’ve just learned, version two of the right hand rule, becomes especially useful when we’re working not just with one loop of current, but with many.
Say that we have not just one current-carrying loop. But we have a whole stack of them arranged in a row. Stacking all these loops together like this, with current running in the same direction through all of them, we’ve come pretty close to creating a component that shows up in electrical circuits. The way to create what that component actually looks like is to connect all these loops one to another. So let’s say we do that. Let’s say we take this first loop. We open it up. And then, we connect it to the second loop. And then same thing with the second loop, we connect it to the third and the third to the fourth and so forth and so on, all the way down the line. By joining these loops, we’ve created a coil of wire, where current runs continuously from one end out through the other.
When we find this particular structure in an electrical circuit, it’s called a solenoid. And as we’ve seen, a solenoid is essentially many current-carrying loops joined in a row. And because it’s made that way, we can get a sense for what the magnetic field of a solenoid looks like, using our right hand rule. Let’s start out by focusing on this very first loop of current in the solenoid.
If we look at that loop from this perspective, putting our eye at this angle to it, then that loop would look like this. Basically, the right side of this loop corresponds to this part of the first loop in our solenoid. That part of the loop is closest to us when we’re looking at it from this direction. And then, the left part of the loop corresponds to this part of the loop in our solenoid, which is further away from our eye.
To figure out the magnetic field created by this individual loop, just at the center of the loop, we’ll use our second version of the right hand rule. This version tells us to start by making a perpendicular axis through the center of the loop. That would point this way into and out of the page. Then, we take our right hand. And we put it up to this axis so that our fingers can curl around the axis in the same way that current flows through the loop. Then curling our fingers in that direction, our thumb now points in the way the magnetic field points at the center of this loop. We can see that’s into the screen or into the page.
Now, we want to draw this magnetic field line on our diagram of the solenoid. To do that, we’ll find the point at the center of this first loop. That point is just about there. Then, since the right side of the loop from this perspective corresponds to this side of it from our side on view, that means the magnetic field in the solenoid points from left to right. It would look like this, going behind the front edge of the loop and going in front of the back edge. Now, this is good. But remember, we’ve only found the magnetic field for one of the many loops in our solenoid. So then, we move on to the second loop.
But notice something. The current running through this second loop is the same as the current direction running through the first one. That means our diagram up here and our application of the right hand rule still applies now that we’re talking about the second loop in our solenoid. And that means that the net magnetic field created at the center of this loop also points left to right.
To show the difference between these two field lines, we’ll draw them in in different colours. So we’ll find the center of this second loop. That looks to be right about there. And then, we’ll draw in this field line in pink. Next, we move on to the third loop in our solenoid. Current flows through this loop in the same direction as it did through the first two. So the magnetic field also points the same way. We draw that field line in in green.
We can see that as we go down the line of our solenoid, through all the loops, we’ll get the same direction magnetic field through their centers. What happens then is that all these individual magnetic fields add up to a net or overall magnetic field within the coil. Combining the fields through the center of each of these loops, that net field line would look like this, through the core of the solenoid. In this field line, by the way, we continue on along this axis even outside of the solenoid. Now at this point, we found the direction of the magnetic field through the exact geometric center of this solenoid. But there’s more space across these loops than just their center.
If we were to draw a few other field lines that go through the solenoid core, they might look like this. These are actually closed loops like we were used to seeing magnetic field lines form. At this point, the field of this solenoid may start to look familiar. Say that we had a permanent magnet like this bar magnet right here. The magnetic field for this bar magnet would look something like this. Seeing the similarity between this field and the one created by our solenoid, we can say that, up here, with our solenoid, we have essentially created a magnet, but using electric current to do it. That is, the magnetic field created by this electric current is essentially indistinguishable from the magnetic field created by a magnet.
There’s a particular name given to devices of this type. This device is an electromagnet. We can see how this name makes sense, electro because we’re using an electric current to create a magnet, that is, a magnetic field that’s essentially the same as that created by a magnet. Now, when it comes to designing an electromagnet, making one for some application, often we’re interested in increasing the electromagnet’s strength, in other words making this magnetic field here, in the core of our solenoid, as powerful as possible.
One way to do that is to add in what’s called a magnetizable material. A magnetizable material is one which isn’t itself a magnet. But if you put it in an external magnetic field, it becomes one. Here, we’ve taken a magnetizable material, iron. And we’ve filled the core of our solenoid with it. When we do this, we focus and strengthen the magnetic field, sometimes five, ten, or even hundreds of times as strong as it was before.
This topic of materials to strengthen electromagnets brings up another point. When we think about what materials we might use to do this, they generally fall into two different classes. In the first class of material, if we apply an external magnetic field to it, then this material, though is magnetizable, takes a long time to show it. The external field needs to be active for quite some time before this material would generate its own internal magnetic field. That process happens quite slowly. But if we then turn off the external field, then the internally generated field persists for a long time too. These materials, which take a long time to gain as well as lose an induced magnetic field, are called hard magnetic materials.
On the other hand, if we apply an external field to this second material class, it very quickly responds with its own induced field. But then, when that external field goes away, the material is also quick to respond with dissipating its internal field. This second material class is made up of what are called soft magnetic materials. This means the internal or induced field of the material responds very quickly to an external field.
Note that these descriptions hard and soft don’t have to do with the relative hardness or softness of the materials themselves. In fact, it’s not unusual to describe the iron core of an electromagnet as a soft iron core. What these terms really refer to is the material’s responsiveness to an external field. Based on their differences, there are different uses for both types. Hard magnetic materials make great permanent magnets while soft magnetic materials are outstanding as cores for things like transformers.
Let’s now summarize what we’ve learned about magnetic fields produced by electric currents. In this lesson, we saw that electric currents create magnetic fields. We looked at three different current configurations, one current running in a straight line, then current running through a circular loop. And finally, considering joining many loops together, we saw what’s called a solenoid. We then learned how to find the direction of the magnetic fields formed around these currents, using something called the right hand rule, which has two different versions.
We also learned what an electromagnet is. It’s a magnet that’s created by electric current. And finally, we learned about hard and soft magnetic materials. We saw that hard magnetic materials are ones which respond slowly to external fields. And soft magnetic materials respond quickly.