Consider a rectangular loop of wire carrying a current through a magnetic field. If you apply the right-hand rule to each of the four sides of the loop, you will find that the force is always oriented away from the center (figure below). In this situation the loop of current does not move, it is in equilibrium.
Now we consider a new situation in which the loop is oriented with its plane parallel to the field (figure below)
The top and the bottom wires are now, respectively, parallel and anti-parallel to the field, so there is no force on them (right-hand rule). The vertical wires have equal forces in opposite directions (right-hand rule). The result is a torque and the loop will rotate. It will pass the equilibrium position (first figure), at which point the direction of the torque will reverse and so on. The loop will oscillate around its equilibrium position until friction brings it to rest there.
This movement of the loop suggests that the Lorentz force can be used to convert electric energy into mechanical energy.
The electric motor
An electric motor is a device that uses the Lorentz force to convert electric energy into mechanical energy. The figure in the textbook (on page 278) shows how such a motor works.
A magnetic field produced by a magnet exerts a torque on a coil of current.
If the current always flows in the same direction the coil doesn’t rotate
continuously. As described before the coil turns into its equilibrium position,
with its plane perpendicular to the magnetic field. When it overshoots this
position the torque reverses and brings it back. The coil will oscillate around
the equilibrium position until it comes to rest there.
The loop can be made to turn continuously by feeding the current to it through a
"split-ring commutator". This is a ring divided in half. The ends of
the loop are connected to the two halves of the commutator which turns with the
loop. The Current flows into the loop through a pair of fixed brushes that
scrapes on the commutator as it turns. When the loop reaches its equilibrium
position, each brush passes the split and makes contact with the other half of
the commutator, thereby the current starts to flow into the loop in the opposite
direction. As a result the torque doesn’t reverse when the loop overshoots the
equilibrium position, but always insists in the same direction, and the loop
turns continuously. (A good simulation about the electric motor can be found at: http://www.sciencejoywagon.com/physicszone/lesson/otherpub/wfendt/electricmotor.htm
In a real motor, the magnet is usually not a permanent magnet, but a pair of coils that form the magnetic field. Also the rotating armature is not a single coil but a large number of coil in order to amplify the effect. next...