Q.Obtain an expression for magnetic induction of a toroid of 'N' turns about an axis passing through its centre and perpendicular to its plane.

A toroid is a solenoid of finite length bent around and closed into a hollow, ring- or tube-shaped structure, with no open ends. Its field lines form concentric circles running around its own central circular axis, entirely confined within the winding (unlike a solenoid, which leaks some field near its open ends). Applying Ampere's law to a circular Amperian loop of radius R running along this central axis, threading through all N turns of the winding, gives $B(2\pi R)=\mu_0(iN)$, so $B=\dfrac{\mu_0iN}{2\pi R}$. …