Video Transcript
When the coil of a direct current motor is aligned normally to the plane of the
magnetic field of the motor, the torque on the coil is zero. Which of the following most correctly states how a direct current motor can produce
uniform circular motion despite there being two positions of the motor coil that
occur during one complete revolution for which the force on the coil is zero? (A) When the coil is at a position where it is aligned normally to the plane of the
magnetic field of the motor, the current supplied to the coil is slightly
increased. (B) When the coil is at a position where it is aligned normally to the plane of the
magnetic field of the motor, the direction of the current supplied to the coil is
reversed. (C) When the coil is at a position where it is aligned normally to the plane of the
magnetic field of the motor, the position of the magnets in the motor is slightly
adjusted. (D) Before the coil can move to a position where it is aligned normally to the plane
of the magnetic field of the motor, it must acquire sufficient angular velocity to
allow the coil to continue to turn past the position where the force acting on it is
zero.
In this question, we are asked to think about the motion of a coil in a direct
current motor. We are told that the coil undergoes uniform circular motion even though there is zero
torque on the coil when it is aligned normally to the plane of the magnetic field of
the motor. We need to work out how this can be the case. Let’s remind ourselves of what a direct current motor is and how they function before
we look at the options to figure this out.
A direct current motor consists of a wire coil placed in a magnetic field. A direct current power source is connected to the coil, producing a current. The power source is connected to the coil using a commutator and brushes so that the
coil can rotate. The coil’s axis of rotation is shown by this dashed line here. Recall that the coil rotates because when a current-carrying wire is within a
magnetic field, it will experience a force.
In order to find the direction of this force, we can use Fleming’s left-hand
rule. To use the left-hand rule, we hold out the thumb, forefinger, and middle finger of
our left hand to form three perpendicular axes like this. Now if we point our index finger in the direction of the magnetic field and our
middle finger in the direction of the current, our thumb will be pointed in the
direction of the force exerted on the wire. Let’s use this left-hand rule and try to find the direction of the force exerted on
the coil when it’s in this position, parallel to the plane of the magnetic
field.
Let’s think about the length of wire on the right-hand side of the coil. Here, the current is directed out of the screen, and the magnetic field is directed
from north to south, left to right across the screen. If we position our left hand so that our middle finger points out of the screen and
our index finger points from left to right, we find that our thumb points
upwards. So, here, the force on this length of the wire is pointing upwards. We can repeat this process for the length of wire on the left-hand side of the
coil. Here, the current is into the screen, so we need our middle finger to point into the
screen. The magnetic field is still directed from north to south, so our index finger should
still point from left to right. We then find that our thumb points downwards. This is the direction of the force on this length of the wire.
Together, these forces produce a torque on the coil that causes it to rotate in this
direction. There is a torque on the coil because the forces on each length of the wire are
acting at a distance from the coil’s axis of rotation. The magnitude of the torque produced by the forces is proportional to this
distance.
Now let’s think about the torque on the coil a short time later, when it has rotated
through one-quarter turn. Here, the coil is aligned normally to the plane of the magnetic field of the
motor. When the coil is in this position, any forces on the coil will act through the axis
of rotation. In other words, the distance between the forces and the axis of rotation is zero. Hence, the torque on the coil is also zero. So, when the coil is in this position, there is no net torque on the coil and no net
force acting on the coil.
To answer this question, we need to work out how the coil can keep rotating uniformly
even though the coil passes through points where it experiences zero net force. Clearing some space on screen, let’s look at each of the options we’ve been given and
see which one makes the most sense.
Option (A) states that when the coil is at a position where it is aligned normally to
the plane of the magnetic field of the motor, the current supplied to the coil is
slightly increased. We know that the motor is powered by a direct current source. A direct current source produces a current of constant magnitude. So, this answer cannot be correct.
Option (B) states that when the coil is at a position where it is aligned normally to
the plane of the magnetic field of the motor, the direction of the current supplied
to the coil is reversed. Again, we know that this can’t be true because the motor is powered by a direct
current source. This means that the current supplied by the power source is always in the same
direction.
Option (C) states that when the coil is at a position where it is aligned normally to
the plane of the magnetic field of the motor, the position of the magnets in the
motor is slightly adjusted. We know that the magnets in a direct current motor are stationary and cannot
move. So this option is also incorrect.
The final option states that before the coil is aligned normally to the magnetic
field, it must acquire sufficient angular velocity to allow the coil to continue to
turn past the position where the force acting on it is zero. This option is the correct answer. The coil is already rotating by the time it reaches this position. So, because there is nothing to stop the coil from rotating, it’ll keep going. The coil is able to move through this position even though the net force and the
torque on the coil are momentarily zero. So, option (D) is the correct answer to this question.
