Question

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 $r(>>$ 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 $\frac{\mu_{0}}{2 \pi} \frac{ m }{ r ^{3}}$, 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 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

• A. $m / r ^{3}$
• B. $m ^{2} / r ^{2}$
• C. $m / r ^{2}$
• D. $m ^{2} / r$

Answer 1

Answer: (A)

$m / r ^{3}$

Answer 2

A

$m / r ^{3}$