An electric motor uses the attraction and repulsion of electromagnets and permanent magnets to produce rotary motion. The following is a diagram of a permanent magnet DC motor. It works by sending a current through a coil of wire, making that coil an electromagnet. That coil will then be attracted or repelled by permanent magnets. The coil is on an axle so that it will rotate. The magnetic forces will cause it to rotate one way or the other, depending on the polarity of the applied voltage.

A permanent magnet DC motor

The rotating part of the motor, that includes the armature and commutator is called the rotor. The armature is the rotating coil. The commutator is a split ring that rotates with the armature. The stationary part, including the field magnets, brushes and housing is called the stator.

The rotor from a simple permanent magnet DC motor. You can see the split in the commutator on the left side of the shaft.

The brushes, often made of carbon, contact the commutator to provide power to the armature.

Carbon motor brushes

The field magnets are the permanent magnets or electromagnets that provide a magnetic field for the armature to interact with.

As the commutator rotates the brushes stay in contact with it continuing to supply power. The commutator also acts as a switch. With each half-turn of the armature, the commutator changes which direction the current flows through the coil. During one half-turn the armature is magnetized in one direction and during the other half-turn it is magnetized in the other. When the armature lines up with the field magnets the commutator reverses the polarity of the armature so that the magnetic fields push then pull the armature another half turn to line them up again. This repeats over and over as the motor turns.

The current through the armature causes the magnetic field to be oriented as shown. The north pole of the armature is attracted to the south pole of the left magnet. Likewise, the south pole of the armature is attracted to the north pole or the right magnet.
This magnetic interaction causes the armature to rotate counter clockwise. The poles of the armature try to line up with the poles of the field magnets.
Momentum carries the armature past the magnets as the commutator swaps the battery connection.
The commutator has switched the poles of the armature. Now the north pole of the armature is repelled from the north pole of the right magnet and vice versa. The armature continues to rotate.
Now the armature has made ½ turn. The former north pole is now the south pole and vice versa. The next half cycle begins like the first.

How do you know which end of the armature will be north and which will be south. Make a fist with your right hand with the thumb pointing out. Your fingers curl in the direction of conventional current and you thumb points to the north pole. This is called the right hand rule. For electron flow use your left hand.

Generators

A DC generator is exactly the same as a DC motor. If you spin the armature of a DC motor it will produce DC voltage (and current if there is a circuit between the terminals). You can demonstrate this by putting a voltmeter or current meter across a motor and spinning the armature. You may even get enough current to run a small light bulb or LED. Before nuclear submarines, many diesel submarines used motors to run the propellers from batteries when submerged. When surfaced, diesel engines turned the propellers. Since the electric motors were on the propeller shafts they were also turned by the engines. Therefore, while surfaced the motors were used as generators to charge the batteries.¹ Often electric vehicles use the traction motors (the motors that turn the wheels of the vehicle) as generators. While braking they put some charge back into the battery.

If you short the terminals on a motor the motor will self-brake. This is because turning the armature generates current. This current creates a magnetic field that tries to turn the motor in the opposite direction to which it is rotating. You can demonstrate this by spinning the armature of a small electric motor. It should spin freely. Next use a clip lead to short the terminals together and spin the armature again. You will see that the armature quickly stops. Electric trains, from light rail to heavy diesel-electric locomotives often use this effect to help slow or stop the vehicle. This called dynamic braking.

A slight change in design creates an AC generator or alternator. Instead of a commutator (a single split slip ring) an alternator has two complete slip rings with a brush on each. A commutator will cause the generator to produce DC. It acts as a switch to cause the current to flow in only one direction.

A generator with slip rings instead of a commutator produces alternating current and is called an alternator.

A commutator causes the generator to produce direct current (this is identical to a DC motor).

Although this design with slip rings will produce AC, this is not how working alternators are designed. In  typical alternators the armature is fed DC through the slip rings making the armature an electromagnet.  The armature rotates inside the stator which is lined with coils. Alternating current is produced in the stator coils as the armature's magnetic field spins past them. Alternators will be covered in more detail in the volume on AC circuits.

Here is an interactive simulation of an alternator and generator:



Small DC motors are usually made with permanent magnets. Before the development of rare earth magnets permanent magnets were not powerful enough for large motors. Large motors are usually made with electromagnets for the field magnets. The permanent magnets are replaced with coils of wire called field coils as shown below. There are two ways to make electromagnet motors: series wound and shunt wound.

Series wound electromagnet DC motor

Shunt wound electromagnet DC moror

Series wound motors have the field coils connected in series with the armature. Shunt wound motors have the field coils connected in parallel with the armature (i.e. a shunt or bypass). A shunt wound motor typically runs at a fairly constant speed regardless of the load² when operated within its design parameters. This is because the strength of the magnetic field from the field winding is relatively unaffected by the current through the armature winding.

As mentioned above, a DC motor is also a generator. When a motor is spinning it produces current that opposes the current that is driving the motor. This is called back EMF just as is the the current produced by self induction. When a motor is slowed by a heavy load it produces less back EMF. Therefore more current flows into the motor and it produces more torque. This is a convenient negative feedback system. When a motor is lightly loaded it needs and has less torque but when heavily loaded it needs and has more torque. This effect is much more pronounced in a series wound motor. With the field coils in series with the armature you get more current in the field coils as well as the armature when the motor is slowed by a heavy load. A series wound motor should never be operated with no load. It will turn at such a high speed that centrifugal force could damage it. For example, a series motor would not be used to drive a belt because if the belt slips the motor could spin fast enough to damage itself.

Some small DC motors are made with a two coil armature similar to the diagrams above. However, they are usually made with three or more coils in the armature.

A rotor from a permanent magnet DC motor with a three-coil armature. Like most motors, the armature has a core made of laminated soft iron.

Wiring of a three coil armature and commutator.

Each coil has its own contact on the commutator so most commutators have more than the two splits shown in the diagrams. Having multiple coils in the armature increases efficiency. Only the coils near the field magnets are energized leaving the others dormant while they are far from the magnets.

1	Many submarines were also designed more like a diesel-electric locomotive. The diesel engines ran generators that both charged the batteries and ran the motors on the propeller shafts. On these designs there was no mechanical connection between the diesel engines and the propellers.
2	In this case the load is how much whatever the motor is turning resists that turning force. In other words, how hard the motor is working.