A simple motor works on the basis of torques on current loops.
We will apply the fundamental rules of magnetic fields and current loops to understand how a simple electric motor works.
We saw that a segment of a current-carrying wire feels a force from a magnetic field.
Here, the current is to the right, the B field is into the page and the force is upward.
Here we have a current loop immersed in a magnetic field.
The forces cancel on this current loop because the magnetic field is perpendicular to the plane of the loop.
Here, the plane of our current loop is no longer perpendicular to the magnetic field.
The forces on the sides of the loop always cancel. Torque on the upper segment pulls upward
while torque on the lower segment pulls downward, tending to rotate the loop in the magnetic field.
We have defined the moment arm d in terms of the current segment l. Recalling that μ = IA, this allows us
to write the torque as the cross product of the magnetic moment and the ambient magnetic field.
This sequence of diagrams illustrates how a simple motor works.
The magnetic field exerts a force on a current loop, at right angles to the direction of the field and to the direction of the current.
This torques the loop and causes it to rotate.
As the current loop turns, the magnetic field continues to exert a force on it.
When the loop turns far enough, the force would work to stop turning it,
In a motor, the polarity of the current is switched to run the other way.
This makes the force on the loop such that it continues to turn.
This is the basic mechanism of an electric motor.
Check out this website
for a cool animation of a simple motor.
Find more detail on how a motor works here.