Match List I with List II for a circular current-carrying coil of radius R , where x is the distance from the centre on its axis and B_c is the magnetic field at the centre. List I (Distance x ) List II (Magnetic Field B ) (A) x = 0 (I) B_c 8 (B) x = R (II) B_c (C) x = 3 R (III) B_c 27 (D) x = 2 2 R (IV) B_c 2 2 Choose the correct answer from the options given below:

Step-by-step solution

The magnetic field on the axis of a circular coil of radius R at a distance x from the centre is given by: B = ₀ I R^2 2(R^2 + x^2)^ 3/2 The magnetic field at the centre ( x = 0 ) is B_c = ₀ I 2R . Thus, the ratio is B B_c = ( R^2 R^2 + x^2 )^ 3/2 . (A) For x = 0 : B = B_c (B) For x = R : B B_c = ( R^2 2R^2 )^ 3/2 = 1 2 2 B = B_c 2 2 (C) For x = 3 R : B B_c = ( R^2 R^2 + 3R^2 )^ 3/2 = ( 1 4 )^ 3/2 = 1 8 B = B_c 8 (D) For x = 2 2 R : B B_c = ( R^2 R^2 + 8R^2 )^ 3/2 = ( 1 9 )^ 3/2 = 1 27 B = B_c 27 Therefore, the cor