Rotating coil

As shown in the diagram above, imagine a coil inside a magnetic field. The current is initially flowing clockwise through the coil. Using what we learnt from the previous section, force on a current-carrying conductor, we know that the sides AB and CD will experience a force by the magnetic field whilst the sides BC and DA do not (since they are parallel to the magnetic field).

Using the right hand palm rule, side AB will experience a force downwards whilst side CD will experience a force upwards. This causes the coil to rotate anti-clockwise and it will continue rotating until the coil is vertical. At its vertical position, all the sides are perpendicular to the magnetic field and so the direction of force is outwards. Obviously due to the inertia of the coil, it will continue past the vertical position. Now imagine at the instant the coil is vertical, the direction of the current is reversed. So, side CD will experience a force downwards and AB will experience a force upwards. This allows the coil to continue rotating clockwise

Motor

The explanation of a rotating coil given above forms the basis of DC motors. Below is a simple diagram of a DC motor:

A DC motors works because of the following:

• A coil is placed between 2 magnets; a north pole and south pole facing each other

• Current is supplied through the split ring commutator (SRC) and a carbon brush. The purpose of the SRC is to change the direction of the current every half rotation of the coil (hence allowing the coil to continue rotating in one direction). The purpose of the carbon brush is to prevent the wire from being tangled as the coil rotates

• Interaction of the current carrying coil with the magnetic field produced by the magnets, results in a magnetic force which in effect produces torque (i.e. rotation)

Torque of motor

We know that the force on a current-carrying conductor is given by F = nIlB and that the magnitude of torque is given by τ = rF, so the torque due to one side is given by rnIlB. Since there are two sides, the torque equation becomes 2rnIlB. If we would like to calculate the total maximum torque, then this would only occur when the coil is horizontal. If we take the width of the coil to be, w, then in our torque equation 2rnIlB, r corresponds to w/2 and so 2 w/2 l represents the area of the coil. Therefore, total maximum torque can be found by

The torque of a motor with a singular coil will fluctuate from maximum to minimum and hence be jerky because the force fluctuates as the coil rotates (and so torque would too). To prevent this, multiple coils are placed at different angles. This is called armature winding. This is helpful because when one coil experiences zero torque, other coils experience some amount of torque, and so the resultant torque will be a smooth torque. The diagram below represents this visually.

*diagram*

Strength of motor

The strength of a DC motor can be increased in a number of ways by increasing the:

• Number of turns, hence increasing the value of n

• Magnetic field strength

• Current inside the coil

• Length and width of the coil

• Inserting a soft iron core inside the coil