The magnetic field due to current carrying a circular loop of radius 5 ~cm at a point on the axis at a distance of 12 ~cm from the centre is 250 T . The magnetic field at the centre of the loop is

Step-by-step solution

Given, R=5 ~cm =0.05 ~m aligned r & =12 ~cm =0.12 ~m B & =250 T & =250 10⁻⁶ ~T aligned The magnetic field due to a current carrying circular loop at its axial line is B= 1 2 ₀ n I R^2 (R^2+r^2 )^ 3 / 2 Here, n=1 , B= 1 2 ₀ I R^2 (R^2+r^2 )^ 3 / 2 The magnetic field at the centre of loop is B₀= 1 2 ₀ I R Dividing Eq. (ii) by Eq. (i), we get aligned B₀ B & = ₀ I 2 R 2 (R^2+r^2 )^ 3 / 2 ₀ I R^2 & = (R^2+r^2 )^ 3 / 2 R^3 B₀ & =B (R^2+r^2 )^ 3 / 2 R^3 aligned aligned & =250 10⁻⁶ [(0.05)^2+(0.12)^2 ]^ 3 / 2 (0.05)^3 & =2