JEE Advanced 2021 Paper 2

Paragraph for next 2 questions 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 center at the origin. A magnetic dipole of moment $m$ is brought along the axis of this loop from infinity to a point at distance $r(\gg>a)$ from the center 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 $\;\frac{\mu_{0} m}{2 \pi r^{3}}$, where $\mu_{0}$ 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 $\;\frac{km_{1} m_{2}}{r^{4}}$, where $k$ is a constant of appropriate dimensions. The direction of this force is along the line joining the two dipoles.