The magnetic field at the centre of a current carrying circular loop of radius R is 16 ~T . The magnetic field at a distance x= 3 R on its axis from the centre is _ _ _ _ T .

Step-by-step solution

The magnetic field at the center of a circular loop is B_ center = ₀ I 2R = 16 T. On the axis at distance x from center: B(x) = ₀ I R^2 2(R^2 + x^2)^ 3/2 . At x = 3 R : B( 3 R) = ₀ I R^2 2(R^2 + 3R^2)^ 3/2 = ₀ I R^2 2(4R^2)^ 3/2 = ₀ I 16R . The ratio: B( 3 R) B_ center = 1/16R 1/2R = 1 8 . Therefore: B( 3 R) = 1 8 16 = 2 T.