Two circular coils X (smaller) and Y (bigger), each having a single turn, carry equal currents in the same direction and subtend the same angle at point 'O' along the axis of the coil. The distances of the centers of coil to point 'O' are d and ( d 2 ) for coil Y and X respectively. The radii of coils Y and X are (2r) and (r) respectively. The magnetic induction due to the bigger coil at point 'O' is B_y and that due

Step-by-step solution

The magnetic field on the axis of a circular coil of radius R at a distance x from its center is given by: B = ₀ I R^2 2(R^2 + x^2)^ 3/2 For coil Y (bigger coil): Radius R_y = 2r , distance x_y = d . B_y = ₀ I (2r)^2 2((2r)^2 + d^2)^ 3/2 = 4 ₀ I r^2 2(4r^2 + d^2)^ 3/2 = 2 ₀ I r^2 (4r^2 + d^2)^ 3/2 For coil X (smaller coil): Radius R_x = r , distance x_x = d 2 . B_x = ₀ I r^2 2 (r^2 + ( d 2 )^2 )^ 3/2 = ₀ I r^2 2 ( 4r^2 + d^2 4 )^ 3/2 = 8 ₀ I r^2 2(4r^2 + d^2)^ 3/2 = 4 ₀ I r^2 (4r^2 + d^2)^ 3/2 Comparing the express