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.
