Toroidy

A straight solenoid bent in the form of a doughnut-shaped coil is called a toroid.

A toroid can be assumed as an aggregate of circular loops perpendicular to its axis. The magnetic field lines are circular and concentric to the toroid axis.

If the fingers of the right hand curl in the current direction, the thumb points to the magnetic field direction.

Consider a circular Amperian loop inside the toroid. The magnetic field along this loop has constant magnitude and is tangential to the path.

Now, applying Ampere's Law, the line integral of the magnetic field equals the product of the magnetic field and the circumference of the loop.

The net enclosed current in the loop equals the total number of turns times the current.

Thus, the obtained magnetic field inside a toroid varies inversely with the distance from its axis.

The magnetic field inside the hollow circle is zero since it does not enclose any current.

Outside the toroid, the currents flowing in opposite directions cancel each other out. Hence, the magnetic field is zero.