Consider a long solenoid of length l and radius r . If n is the number of turns per unit length and ₀ is the permeability of free space, the inductance of the solenoid is :

Step-by-step solution

The magnetic field inside a long solenoid is given by B = ₀ n I , where n is the number of turns per unit length and I is the current. The magnetic flux through a single turn of the solenoid is = B A = ( ₀ n I)( r^2) . The total number of turns in the solenoid of length l is N = n l . The total magnetic flux linkage is = N = (n l)( ₀ n I r^2) = ₀ n^2 r^2 l I . The self-inductance L is defined by the relation = L I . Substituting the value of , we get L = ₀ n^2 r^2 l . Answer: ₀ n^2r^2l