29.13 : Toroids

A toroid is a closely wound donut-shaped coil constructed using a single conducting wire. In general, it is assumed that a toriod consists of multiple circular loops perpendicular to its axis.

When connected to a supply, the magnetic field generated in the toroid has field lines circular and concentric to its axis. Conventionally, the direction of this magnetic field is expressed using the right-hand rule. If the fingers of the right hand curl in the current direction, the thumb points in the magnetic field direction. The magnetic field inside a toroid varies inversely with the distance from its axis. The magnetic field inside the hollow circle is zero as it does not enclose any current, while outside the toroid, the currents flowing in opposite directions cancel each other out. Hence, the magnetic field is zero.

If a toroid with an inner radius of 10 cm and an outer radius of 15 cm carries a current of 2 A, how many turns does it require to produce a magnetic field of 1 mT 12 cm away from its center? Assume that the turns are equally spaced.

Here, the known quantities are the inner radius, outer radius, current, magnetic field, and distance from the center of the toroid. The number of turns need to be estimated using these known quantities.

The expression for the magnetic field inside a toroid is given as follows:

Substituting the values of the known quantities, the number of turns required to produce a magnetic field inside the toroid at a distance of 12 cm from its center is estimated to be 1,500.