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A special metal ๐ conducts electricity without any resistance. A closed wire loop, made of ๐, 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 ๐, with its center at the origin. A magnetic dipole of moment ๐ 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 $$\frac{\mu_0}{2 \pi} \frac{m}{r^3}$$, where $$\mu_0$$ is the permeability of free space. The magnitude of the force between two magnetic dipoles with moments, ๐1 and ๐2, separated by a distance ๐ on the common axis, with their north poles facing each other, is $$\frac{k m_1 m_2}{r^4}$$, where k is a constant of appropriate dimensions. The direction of this force is along the line joining the two dipoles.

Question 33