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Question Video: Identifying the Direction of Rotation of a Coil in a DC Motor Physics

Would the direct current motor shown in the following figure rotate clockwise or counterclockwise?

04:01

Video Transcript

Would the direct current motor shown in the following figure rotate clockwise or counterclockwise?

The diagram we’ve been given shows a simple DC motor. It consists of two poles of a permanent magnet and a coil of wire which is connected to a split-ring commutator.

To begin, let’s recall that the rotation of a DC motor is caused by forces acting on the current-carrying coil due to the magnetic field between the two magnet poles. The direction of these forces depends on both the direction of the current in the coil and the direction of the magnetic field that the coil is in. Now, we can find the directions of the forces acting on the coil using Fleming’s left-hand rule. To use Fleming’s left-hand rule here, we first have to determine the direction of the magnetic field and of the current in the coil.

The magnetic field is created by a permanent magnet, whose north and south poles have been shown in our diagram. We should remember that by convention, the magnetic field always points from north to south. That means that the magnetic field here, which we’ll call B, points from left to right. Now, let’s think about the current in the coil. We can recall that by convention, current goes from positive to negative. So, here, the conventional current, which we’ll call 𝐼, goes from the positive terminal on the left, all the way around the coil, and out towards the negative terminal on the right.

Finally, we need to remember that a current in a magnetic field will experience a force, but only if it’s at an angle to the field. This means that the front and back sides of the coil don’t experience any force, as the current at these points is parallel to the magnetic field, not at an angle. So here, we’re only interested in the current in the left and right sides of the coil, which carry current perpendicular to the magnetic field.

So, let’s recap how to use Fleming’s left-hand rule to find the direction of the force acting on a current-carrying wire in a magnetic field. To begin, we point our first finger of our left hand in the direction of the magnetic field. Then, we point our second finger at 90 degrees to the first, in the direction of the current. Finally, if we point our thumb so that it’s at 90 degrees to both fingers, it will point in the direction of the force acting on the wire. We can apply this rule to either the left or the right sides of the coil.

It’s good to note here that the current points in opposite directions on each side of the coil. So the forces on each side will also point in opposite directions. Now this results in an overall rotational force, or torque, acting on the wire coil. This means that, in practice, we actually only need to work out the direction of the force acting on one side of the coil.

So, let’s apply Fleming’s left-hand rule to the right-hand side of this coil. On this side, the current is pointing out of the screen. Following the steps outlined, we point the first finger of our left hand in the direction of the magnetic field, which in this case is to the right. Then, we point our second finger in the direction of the current on this side of the coil, which is out of the screen towards us. Finally, with our thumb perpendicular to both fingers, we can see that it points upwards. This, therefore, is the direction of the force acting on this side of the coil. We’ve labeled this force 𝐹 on our diagram. We can see that a force acting upward on the right side of the coil like this would cause the coil to rotate counterclockwise.

As we mentioned earlier, we don’t actually need to apply the left-hand rule on both sides of the coil. However, if we did apply the left-hand rule to the left side of the coil as well, we’d find that a downward force is produced at this point. So, overall, a counterclockwise torque is produced. Therefore, we know that for this direct current motor, the direction of rotation would be counterclockwise. This is our final answer.

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