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Efficient motors How do electric motors work?
The motor effect

There are different ways of thinking about how electric motors work:

  • a rotating electromagnet
  • two parallel forces producing a torque

Interactive graphic of motor Interactive graphic of motor Interactive graphic of motor
Interactive graphic of motor
Picture 3.4 A simple model d.c. motor.
See The electric motor - what makes it turn? to find out more.
Rotating electromagnet

When the rotor coil is connected to a battery, a current flows through it. This turns it into an electromagnet. In picture 3.4, the top of the coil becomes a north pole, so the top is attracted to the south pole of the permanent magnet on the left. Hence the rotor starts to turn anticlockwise.

When the rotor is vertical, the turning effect stops (the rotor electromagnet is lined up with the permanent magnets). Therefore, at this point the current is reversed (by the commutator) and the rotor has to turn round by 180 ° to line up again.

The current is reversed every 180 ° to keep the rotor turning.

However, the force on the rotor is quite weak as it approaches the swap over point. Let's see why by looking at it a different way.

Interactive graphic of motor
Picture 3.5 The torque gets less because the parallel forces get closer to each other.
Parallel forces
The current I flows along the sides of the coil.

Each side is of length .

As it flows across the magnetic field of flux density B, it experiences a force, F.

The size of this force is:


The current and magnetic field are at right angles to each other. The force will be at right angles to both of them.

We can use Fleming's left hand motor rule to see that the force on the right is upwards and the force on the left is downwards.

Two equal, anti-parallel forces like this are called a couple. They produce a turning effect, or torque, on the coil. The size of the torque is

T = F d

where d is the perpendicular distance between the forces.

See The electric motor effect for more about Fleming's Left Hand Motor Rule).

The biggest torque
The torque can be increased by:
  • increasing the magnetic field strength
  • increasing the current
  • increasing the length,
  • increasing the number of turns on the coil

Also, the torque is a maximum when the perpendicular distance between the forces is biggest. This is when the coil is in the horizontal position.

Interactive graphic of motor
Picture 3.6 The torque gets less because the parallel forces get closer to each other.
Coil in different positions
As the coil rotates, the perpendicular distance between the forces gets less. Therefore, the moment of the couple decreases.

When the coil has turned through 90 °, the moment is zero because the forces are acting along the same line (i.e. the perpendicular distance between them is zero). This is one reason why practical motors do not have a single rotor coil like this.

A single coil drives the rotor round for 180 ° before the contacts are swapped. The torque is reduced considerably once the plane of the coil is more than 30 ° to the magnetic field. To avoid this loss of torque, most motors use more than one coil.

For example, the motor in a toy car or train will usually have three coils. Instead of driving the rotor for 180 °, each coil drives it for just 60 ° (30 ° each side of horizontal). In this way, the coil in use is always feeling nearly its maximum torque.

Photo of coils and armature
Picture 3.7 The rotor from a typical small motor. It has three coils to maintain close to the maximum torque all through a cycle.
Question 9
a) The force on a current-carrying conductor varies with the current, the magnetic field strength and the length of the conductor. How does force vary with:

i. current?

ii. magnetic field strength?

iii. length of the conductor in the magnetic field?

b) The torque on a rotor varies with the angle of the plane of the rotor coil to the magnetic field. At what angle is the torque

i. a maximum?

ii. zero?

c) Given your answer to part b, what trig function of the angle might describe the way that torque varies with that angle?

d) Calculate the force on a wire of length 5 m carrying a current of 4 A at 90 ° to a magnetic field of flux density 2 ×10-3 T.

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