Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The magnetic field at a distance x = R on the axis of a circular current-carrying coil of radius R is 1 2 2 times the magnetic field at its centre. Reason (R): The magnetic field on the axis of a circular coil varies inversely as the cube of the distance from the centre ( B 1 x^3 ) for distances mu

Step-by-step solution

Assertion: The magnetic field on the axis of a circular coil is B = ₀ I R^2 2(R^2 + x^2)^ 3/2 . At x = R , B = ₀ I R^2 2(2R^2)^ 3/2 = ₀ I 2R 1 2 2 = B_c 2 2 . Thus, the Assertion is correct. Reason: For x R , the term R^2 can be neglected in the denominator. B ₀ I R^2 2(x^2)^ 3/2 = ₀ I R^2 2x^3 . So, B 1 x^3 . Thus, the Reason is correct. However, the Reason describes a far-field approximation ( x R ) which cannot be used to derive the exact magnetic field at a near-field point ( x = R ). The exact formula must be