9.3.B - Motor Effect

An electric motor is an electromechanical device that uses a turning force (torque) to convert electrical energy into mechanical energy. Most electric motors operate through the interaction of magnetic fields and current-carrying conductors to generate force. The reverse process, producing electrical energy from mechanical energy, is done by generators such as an alternator or a dynamo.

Electric motors are found in applications as diverse as industrial fans, blowers and pumps, machine tools, household appliances, power tools, and disk drives. They may be powered by direct current or by alternating current from a central electrical distribution grid.

Motors may be classified by the source of electric power (AC or DC), by their internal construction or by the type of motion they provide.

In this topic students:

  • Use equations to describe torque in situations where a force is applied at a distance from a pivot and in loops of wire carrying a current
  • Describe the main features of a DC electric motor in terms of structure and function
  • Explain the application of the motor effect in a galvanometer and a loudspeaker


A force is applied to a spanner to produce
torque on the nut from the spanner.

Calculating torque when F and d are not

Torque, also called moment or moment of force, is the tendency of a force to rotate an object about an axis, fulcrum or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist.

Loosely speaking, torque is a measure of the turning force on an object such as a bolt or a flywheel. For example, pushing or pulling the handle of a wrench connected to a nut or bolt produces a torque (turning force) that loosens or tightens the nut or bolt. The length of the lever arm is particularly important; choosing this length appropriately lies behind the operation of levers, pulleys, gears and most other simple machines involving a mechanical advantage.

Examples of this turning effect occur when you turn on a tap, turn the steering wheel of a car, turn the handlebars of a bicycle or loosen a nut using a spanner, as shown in the diagram below. It is easier to rotate an object if the force, F, is applied at a greater distance, d, from the pivot axis. It is also easier to rotate the object if the force is at right angles to a line joining the pivot axis to its point of application.

The torque, τ, increases when the force, F, is applied at a greater distance, d, from the pivot axis. It is greatest when the force is applied at right angles to a line joining the point of application of the force and the pivot axis.

If the force is perpendicular to the line joining the point of application of the force and the pivot point, the following formula can be used:

The SI unit for torque is the newton metre (Nm).

If the force is not perpendicular to the line joining the point of application of the force and the pivot point, the component of the force that is perpendicular to the line can be used. The magnitude of the torque can then be calculated using the following formula.

Equation - Torque





distance between force and pivot

angle between line joining pivot and force

newton metres (Nm)

metres (m)

degrees (°)

You should use this equation when calculating the magnitude of the torque or turning force around a pivot or centre.

Torque on Electrical Coils

A highly simplified DC motor showing just
one single loop of the armataure that is
responsible for producing the torque.

The example on the right shows a simplified section of an electric motor (one loop). The coil will rotate clockwise because of the forces produced due to a current carrying conductor in a magnetic field. Side a-b will experience an upwards force and side c-d will experience a downwards force. Since these sides (a-b and c-d) are always and right angles to the field lines, the force will always be maximum (from F=BIlsinθ where θ=90°) as the coil turns.

You should note that for the diagram in the position shown, the torque is a maximum because the angle between the plane of coil and the magnetic field is zero (cosθ=1). When the coil rotates through 90°, the torque will be zero for an instant (but inertia will keep it rotating). The torque is zero in this position because the only force acting on the wires are directly upwards and directly downwards. The combination of these two forces will provide no turning force.

When the coil has rotated 90° and the torque is zero, the direction of current will change to keep the torque acting in the same direction. This will cause the force on the sides a-b and c-d to reverse direction so that the coil will keep rotating in the same direction. This current reversal is achieved through the use of a split ring commutator.

Equation - Electrical Torque








number of turns in coil

magnetic field strength


coil area

angle between plane of coil and magnetic field lines

newton metres (Nm)


teslas (T)

amps (A)

metres squared (m2)

degrees (°)

You should use this equation when calculating the magnitude of the torque or turning force on a rotating loop or coil of wire in a magnetic field.

DC Motors

A simplest of DC electric motors consists of a coil of wire placed in a magnetic field. When current flows through the coil, the combination of two forces on either side of the coil produce a torque which turns the coil. Since the coil is connected to an axle, useful mechanical energy in the form of a turning force can be produced. The brushes and commutator conduct the current from the supply into and away from the coil. The part of the motor that moves is called the rotor and the stationary, non-moving part is called the stator.

The basic structure of a DC electric motor showing
one loop.

The simplest of DC motors are constructed as shown in the diagram on the right. At the position shown, the force on side X is downwards and on side Y it is upwards. This results in an anticlockwise torque and the coil rotates anticlockwise. When the plane of the coil is vertical (rotated anticlockwise 45° from the position shown in the diagram), the torque is zero. This is because the force on Y is directly upwards and the force on X is directly downwards. At this point, the current is zero because the split ring commutator is aligned with the gap against the brushes. At this instant the current in the armature is reversing the the force is also reversing. The momentum of the armature will keep it moving past the vertical position, establishing contact between the brushes and the other half of the commutator. The current is now reversed and the force on side Y is now downwards and side X is upwards. This keeps the torque in the anticlockwise direction for a complete revolution.

The split ring commutator in this motor reverses the current every half cycle to reverese the direction of the force on each side of the loop and hence keep the torque in the same direction throughout each revolution. The brushes maintain electrical contact between the stator and the rotor without the wires becoming entangled as the motor turns. The armature is the moving part of the motor that carries the current and is represented by only one loop in the diagram above.

Comparison of force and torque for a single
rotating loop in a magnetic field.

You should be clear in your mind about how the force is distinct from the torque in a rotating coil or loop. These are two different quantities and must not be treated as though they were the same.

In the diagram on the right, the force on side AB is downwards in the position shown in the diagram. Side AB will experience the same force regardless of its position in its rotation between 270° - 90° (shown at 0°). At 90° (vertical) the commutator changes the direction of the current and the force so that the force is now downwards on side AB between 90° - 270°. The opposite would be true for the other side of the loop. The force would be upwards to begin with and then change to downwards after the rotation through 90° from the starting position shown.

Reversing the current and the force every half cycle keeps the torque direction the constant. However, the magnitude of the torque changes because the angle between the plane of the loop and the magnetic field lines is changing. Note that we are now talking about the angle between the plane of the loop and the magnetic field lines which is the same as the angle of rotation used in the previous paragraph. Because of the relationship between torque and θ in the equation τ=nBIAcosθ, the graph of torque v angle of rotation will be a cos curve that is always positive because of the effect of the split ring commutator in reversing the current direction.

If a radial magnetic field is used instead of the perpendicular field shown in the diagram above, the torque is kept at a higher magnitude for a larger proprtional of the loop's rotation. The radial field provides an orientation with respect to the conductor such that the force is always at right angles to the line joining the axis and the point of application of the force. This keeps the torque at maximum for a greater portion of a revolution. Thinking about it another way, the radial magnetic field has the effect of keeping the field lines parallel to the plane of the loop for a greater part of the loop's rotation and this also keeps the torque more consistent.

The blue line shows the effect on the torque of using a radial magnetic field in a DC motor.

A more modern version of a DC
motor with two windings.

Most modern motors typically have two or three windings each of which acts as an electromagnet. The rotating armature, in the form of an electromagnet, has a north and a south pole. The commutator reverses the direction of the current twice every cycle, to flow through the armature so that the poles of the electromagnet push and pull against the permanent magnets on the outside of the motor. As the poles of the armature electromagnet pass the poles of the permanent magnets, the commutator reverses the polarity of the armature electromagnet. During that instant of switching polarity, inertia keeps the classical motor going in the proper direction.

In the motor in the diagram on the right there are two electromagnets, one shown purple and the other shown pink. Let's consider the purple electromagnet first. The current is flowing in such a direction as to produce a north pole above the windings as shown. The repulsion from the north pole of the permanent magnet (also purple) and the attraction to the south pole (pink) creates a clockwise torque. The pink winding at the bottom has a south pole which also causes a clockwise torque for the same reasons. The split ring commutator reverses the current every half cycle so that the poles of the electromagnets reverse and keep the motor spinning in the same direction. The windings are wound around a piece of soft iron to concentrate the lines of flux between the north and south poles of the radial magnetic field.

There are a number of limitations to the classic design of the DC motor, many due to the need for brushes to rub against the commutator. The rubbing creates friction, and the higher the speed, the harder the brushes have to press to maintain good contact. Not only does this friction make the motor noisy, but it also creates an upper limit on the speed and causes the brushes eventually to wear out and to require replacement. The imperfect electric contact also causes electrical noise in the attached circuit. These problems ultimately result in a loss of energy so that not all of the electrical energy supplied to the motor is converted to mechanical energy.



Loudspeaker Cone

The operation of the motor effect in a loudspeaker cone.

The louspeakers of your radio and other sound producing systems change electrical signlas into sound waves by utilising the motor effect. The electrical signals pass through a coil wound around the neck of a paper cone as shown in the diagram.

This coil acts as an electromagnetic which is located near a permanent magnet. When current flows one way, magnetic force pushes the electromagnet away from the permanent magnet, pushing the cone outwards. When current flows the other way, the cone is pushed inwards. Vibrations in the electric signal then cause the cone to vibrate. Vibrations of the cone produce sound waves in air.


A moving coil galvanometer.

Galvanometer is the historical name given to a moving coil electric current detector. When a current is passed through a coil in a magnetic field, the coil experiences a turning force proportional to the current. If the coil's movement is opposed by a coil spring, then the amount of deflection of a needle attached to the coil may be proportional to the current passing through the coil. Such “meter movements” were at the heart of the moving coil meters such as voltmeters and ammeters until they were largely replaced with solid state meters.