A long conducting wire having a current I flowing through it, is bent into a circular coil of N turns. Then it is bent into a circular coil of n turns. The magnetic field is calculated at the centre of coils in both the cases. The ratio of the magnetic field in first case to that of second case is:

Step-by-step solution

As in both cases, length of the wire will remain the same, therefore l = 2 π R N = 2 π r n ⇒ R r = n N Now magnetic field due to single circular coil is given by, B = μ 0 I 2 r . Therefore, required ratio of total magnetic field wil be, B 1 B 2 = N μ 0 I 2 R n μ 0 I 2 r = N 2 n 2