If ' N ' is the number of turns in a circular coil, the value of its self-inductance varies as

Step-by-step solution

The magnetic field at the centre of a circular coil of radius R having N turns carrying current I is given by B = ₀ N I 2R The magnetic flux linked with a single turn of the coil is ₁ = B A = ( ₀ N I 2R ) ( R^2) = ₀ N I R 2 The total magnetic flux linked with the entire coil of N turns is = N ₁ = N ( ₀ N I R 2 ) = ₀ N^2 I R 2 The self-inductance L of the coil is defined by = L I . Therefore, L = I = ₀ N^2 R 2 From this expression, it is clear that the self-inductance L is directly proportional to the square of the