, m/r 3 m/r 5

, m 2 /r 2 m 2 /r 5

and m/r 2 m 2 /r 6

. ONLY ONE of these four options is the correct answer. • For each question, choose the option corresponding to the correct answer. • Answer to each question will be evaluated according to the following marking scheme: Full Mark +3 If ONLY the correct option is chosen; Zero Marks 0 If none of the options is chosen (i.e. the question is unanswered); Negative Marks -1 In all other cases. Paragraph A special metal S conducts electricity without any resistance. A closed wire loop, made of S, does not allow any change in flux through itself by inducing a suitable current to generate a compensating flux. The induced current in the loop cannot decay due to its zero resistance. This current gives rise to a magnetic moment which in turn repels the source of magnetic field or flux. Consider such a loop, of radius a, with its centre at the origin. A magnetic dipole of moment m is brought along the axis of this loop from infinity to a point at distance r(r>>a) from the centre of the loop with its north pole always facing the loop, as shown in the figure below. The magnitude of magnetic field of a dipole m, at a point on its axis at distance r, is , where is the permeability of free space. The magnitude of the force between two magnetic dipoles with moments, m 1 and m 2 , separated by a distance r on the common axis, with their north poles facing each other, is , where k is a constant of appropriate dimensions. The direction of this force is along the line joining the two dipoles. (i) When the dipole m is placed at a distance r from the center of the loop (as shown in the figure), the current induced in the loop will be proportional to m 2 /r (ii) The work done in bringing the dipole from infinity to a distance r from the center of the loop by the given process is proportional to m 2 /r 7