A toroid is a long coil of wire ( N turns) wound over a circular core. The coefficient of self-induction of the toroid is [The magnetic field in it is uniform and R>>r , where r= radius of wire, R= radius of coil] ( ₀= permeability of free space )

Step-by-step solution

We know relation between the flux and the induction is: L= I Flux through the given area A with magnetic field B is given by, =N A B The field at the center of the toroid is given by B= ₀ n I , where aligned & n= N 2 R & =N ( r^2 ) [ ₀ ( N 2 R ) I ] & = ₀ N^2 r^2 I 2 R aligned Using the definition of self-induction: L= I = ₀ N^2 r^2 2 R