Video Transcript
In this video, our topic is direct-current motors. We’re going to learn how these motors work and really they follow an ingenious design. And we’ll also see how to figure out which way this motor will tend to turn, given a certain orientation of this wire here.
Let’s begin by building up a direct-current motor starting with the battery. These motors are called direct current because they run off of a source that always sends current in the same direction. In a motor like this, the battery is connected by wire to two crescent-shaped objects here. These are called brushes, and these brushes help to maintain electrical contact with the part of the motor that goes here, which is called a commutator. Commutators often look like a solid ring or a circle that’s been split into two electrically separate halves. A commutator is made of metal, and so it conducts electricity. And each one of its halves is electrically connected to one end of a loop of wire. Right now, this loop is oriented in a horizontal plane, but it’s capable of rotating along with the commutator about an axis through its center.
This loop is sometimes referred to as an armature or also called a coil. This is the part of the direct-current or DC motor that moves as the motor operates. Now, around the armature goes a permanent magnet, which is sometimes referred to as the stator of the motor. This is to emphasize that it remains stationary in contrast to the rotating armature. These are the essential components of a DC motor. And the basic physical principle that makes such a motor work is that electric charge when it moves in a magnetic field experiences a force. For individual charges, whose charge is represented by 𝑞, the magnitude of that force is equal to the charge times the speed with which it’s moving times the strength of the magnetic field it’s moving through.
Alternatively, if we’re working, instead, with a wire with a certain length carrying a certain current, then that force is given by this relationship. It’s equal to the magnetic field’s strength times the current in the wire times the wire’s length. If we go back over to our motor, because of this DC supply, we know that positive charge will move clockwise through this circuit. But then, when the charge moves from the brush onto the commutator, it enters the wire loop and starts to move through it. It’s only after moving all around this wire loop that the charge enters back into the commutator, this time on the other side. And then because the commutator is electrically connected to the brush, the charge then moves through this part of the circuit and travels on to the battery’s negative terminal.
So, this is how charge moves through this overall circuit. And it shows us that, indeed, there is current in this wire loop. And because this loop is in a magnetic field, that means that the loop will experience a force, sometimes called the Lorentz force. What we’re going to do now is learn a technique for figuring out the direction in which that force acts. To do this, let’s focus just on the direction of conventional current in these parts of our loop. So in the instance over here on the left side, the current is moving away from us, we could say. And over on the right, it’s coming toward us. We can learn the direction in which the Lorentz or magnetic force acts on these sides of the coil by using what’s called a right-hand rule. This rule gets its name from the fact that we use a right hand to figure out this direction.
Referring to this force equation right here, the first thing we do is figure out, for the length of wire of interest, what is the direction of the current 𝐼? So, over on our sketch of the motor, say that we focus on this length of the wire here, we can see that the current in that section of wire is pointed away from us, we could say into the screen. So what we do then is take the four fingers on our right hand and point them in that same direction as the current. The fingers are hard to see here because we have them directed into the screen. But that is the way they’re pointing. And what we do next is figure out which way the magnetic field points in which this current-carrying wire exists.
Now, over on our sketch, we have the north pole of a magnet here and the south pole here. Magnetic field lines always point from north to south. So in the region of space in which our coil exists, the magnetic field is pointed left to right. And this is the second direction in which we’ll point our fingers using this right-hand rule. We’ll take our fingers, which are pointed into the screen, and we’ll curl them so they point to the right. So now, though they’re a bit hidden by our view of our wrist, our four fingers are pointed to the right. And it’s at this point that we can look at the direction in which our thumb points.
Now as a side note, in order to apply this right-hand rule, it’s important that the direction of the current be perpendicular to the direction of the magnetic field. And then perpendicular to both of these is the direction of the force on the wire. And that’s what the direction of our thumb indicates. It’s the way that the magnetic force pushes on this stretch of wire. And we can draw this force in on our sketch. On this side of our wire loop then, the force acts downward. And now, let’s consider the direction of the force on the current in the right side of the wire.
Once again, we’ll use this right-hand rule. On this side of the wire, we can see that current moves toward us. We could say that it points out of the screen, which means we’ll take the four fingers on our right hand and point them in that same direction, pointing out at us. And then, just like before, the direction of the magnetic field this wire is in is pointed to the right. And so, we curl our right-hand fingers to point that way, like this. And our thumb, pointed perpendicular to both the direction of the current and the direction of the magnetic field, shows us that the force acting on this section of wire points up.
Now, assuming the lengths of wire on the right and left sides of our loop are the same, we know the current magnitude is the same in each one as is the magnetic field’s strength they experience. So the magnitude of these forces that each side will experience are also the same. From our sketch though, we can see that they act in opposite directions. And this tends to create a torque that acts on this wire loop. So long as this torque is in effect, the loop will tend to rotate like this, counterclockwise. Now, we said that these forces on either arm of the wire create a torque. And let’s be clear why that is. We can see the axis around which our loop of wire will rotate. And we also see that these forces acting on our loop of wire are not along that axis. Rather, the forces are separated from that axis by these distances here. And so, a lever arm exists; and therefore, a torque is created.
Now, before we go further, the question may come up. We’ve only considered two of the four sides of this coil of wire. What about the other two, that is, the front and the back? Well, it turns out that for both of these sides of the wire, because the current in these sides points either parallel or antiparallel to the magnetic field direction, the magnetic force on those parts of the wire is zero. So, the sides we’ve considered, the left and the right, are the only sides that experience a force. And therefore, they’re the only contributors to a torque on this coil, and the reason that it rotates. So, say that our coil of wire does start to rotate. Imagine that it goes through a rotation of 45 degrees.
Now, if we take a look at our commutator, this split metal ring that rotates with our coil, we can see that the two sides of the commutator, its two halves, are still in electrical contact with the same brushes on the same sides that they were contacting earlier. This means that electrical charge, as it moves through the coil, will move in the same direction as it did before. This means that, once again, current in the left arm of our coil points into the screen and current in the right arm points out of it, toward us. Now, since these current directions are the same as earlier and the magnetic field direction the current experiences hasn’t changed, that means the force directions on these two sides of the coil will also be the same as before.
On the left, that force will be directed downward. And on the right, it will point up. And once again, these forces don’t act on a line through the center of rotation of our coil, which means that they will tend to create a torque. But, and this is an important point, the magnitude of this torque will not be as great as before because these forces are being exerted closer to the axis of rotation than before. Now, if we let this coil continue to rotate, as it will because of this torque, then this issue of the torque getting smaller and smaller as the coil approaches a vertical orientation will really reach its limit when the coil is in fact vertical.
Notice that when it’s arranged this way, even if there was an upward- or a downward-acting force on the left and right sides of the coil — right now though, we could call them the top and bottom sides instead — those forces will act in a line with the axis of rotation of the coil. And because of this, they won’t generate any torque. So, when it’s in a vertical plane pointed straight up and down, there’s no net torque on the coil. For a motor with just one coil like we have here, the only thing that keeps the coil turning at this point is its inertia. It was already moving counterclockwise, and so it will continue to do so unless it’s resisted.
Now, at this orientation, something important is going on with our commutator. Up until now, this side of our commutator has always been in electrical contact with this brush. And likewise, this other side of the commutator has been in touch with this brush. But as the commutator continues to turn, that’s about to change. Soon enough, this side of the commutator will be in contact electrically with this brush, and this side will be in contact with this one. Now, that does nothing to change the direction of the current as it moves in this blue part of our circuit here. But what it will do is reverse the direction of the current as it travels through our rotating coil. This is a very deliberate part of the design of a direct-current motor.
Let’s let the coil rotate another 45 degrees. Once it’s in this position, we might think that the current in the coil will travel the same direction as it did before. If this were so, then the current in what is now the left side of the coil would be moving out of the screen at us while the current on the right side would be moving into the screen. But if we quickly apply our right-hand rule to both these sides of the loop, we can see that this would create a problem. That’s because by our right-hand rule, the force on this left side of our loop would be pointed upward while the force on the right side would point the opposite direction, downward. And we can see that this would then create a torque that’s clockwise about our axis of rotation. In other words, it would resist the direction that the coil had been moving previously.
If this was the way our motor really worked, we can imagine it rotating first one way, then back in the opposite direction, then in the first direction again, then back again, and so on. It would just oscillate back and forth about a vertical orientation. But that’s not helpful when we want to actually create a motor. And so, this is the whole reason that this split ring, the commutator, is part of our direct-current motor. As the commutator turns, every half revolution, it comes in contact with a different brush in our DC circuit. And this means that the current direction in our loop switches so that, now, in what was previously the right side of our loop, now the left side, current points into the screen. And then on the opposite side and what is now the right side of our loop, it points out of the screen.
Under these conditions then, if we look once more at the left and the right sides of this loop and apply the right-hand rule, we’ll see that the magnetic force acting on what is now the left side, once again, points downward while the force acting on what is now the right side points in the opposite direction, up. This means the torque on the coil is in the same direction as it was previously, counterclockwise, and so the coil will continue to rotate this way. And so, under this influence, the coil will continue to rotate until it reaches once more a horizontal orientation. And then, with the current on the left side of the coil still directed into the screen and the current on the right side directed out of it, the coil continues to experience a counterclockwise torque.
By the way, the reason this device is called a motor is because a bar is typically put along the rotation axis of the coil. So, as the coil turns, the bar turns as well. And this is capable of causing, say, a wheel or gear or other mechanical object to rotate. And this rotating object can do mechanical work. In a DC motor then, energy is converted from electrical energy within this circuit to mechanical energy output to this rotating shaft.
Let’s now summarize what we’ve learned about direct-current motors. In this lesson, we saw that a direct-current or DC motor converts electrical energy to mechanical energy. We saw that this happens by means of a current-carrying loop of wire, which, when positioned between the poles of a permanent magnet, will rotate about an axis through its center. Even though our coil has four sides to it, only the left and the right side will experience a magnetic force. And the direction of that force is given by a right-hand rule.
To use this rule, we first figure out the direction of the current in the section of wire we’re considering. Say that in that part of the coil, the current is directed into the screen. So then, taking our right hand, we point our four fingers in that same direction. Then, we discern the direction of the magnetic field that that part of the coil is in. Say that that field points left to right. With our right hand then, we curl are four fingers so they point in the direction of that field. Once we’ve done that, if we then point our thumb perpendicular to both the direction of the current and the magnetic field, then our thumb points in the direction of the force experienced by this section of wire.
And we saw that no matter what the orientation of this coil, so long as we knew the direction of current in a stretch of wire and the way the magnetic field experienced by that wire points, we can always use the right-hand rule to figure out the resulting force direction. Except in cases where the coil is oriented vertically, that force creates a torque and causes the coil to rotate.
