The magnetic moment of a magnet of length $10\, cm$  and pole strength $ 4.0\, Am$  will be......$A{m^2}$

Force between two identical bar magnets whose centres are $r $ metre apart is $ 4.8\, N$ , when their axes are in the same line. If separation is increased to $2r,$ the force between them is reduced to.....$N$

Figure shows a small magnetised needle $P$ placed at a point $O$. The arrow shows the direction of its magnetic moment. The other arrows show different positions (and orientations of the magnetic moment) of another identical magnetised needle $Q$.

$(a)$ In which configuration the system is not in equilibrium?

$(b)$ In which configuration is the system in $(i)$ stable, and $(ii)$ unstable equilibrium?

$(c)$ Which configuration corresponds to the lowest potential energy among all the configurations shown?

Some equipotential surfaces of the magnetic scalar potential are shown in the figure. Magnetic field at a point in the region is

Three identical bar magnets each of magnetic moment $M$ are placed in the form of an equilateral triangle as shown. The net magnetic moment of the system is

Assume the dipole model for earth’s magnetic field $\mathrm{B}$ which is given by

${{\rm{B}}_{\rm{v}}} = $ vertical component of magnetic field

$ = \frac{{{\mu _0}}}{{4\pi }}\frac{{2m\,\cos \theta }}{{{r^3}}}$

${{\rm{B}}_H} = $ Horizontal component of magnetic field

${{\rm{B}}_H} = \frac{{{\mu _0}}}{{4\pi }}\frac{{m\,\sin \theta }}{{{r^3}}}$

$\theta $ $= 90^{°}$ -latitude as measured from magnetic equator.

$(a)$ Find loci of points for which : $\left| {{\rm{\vec B}}} \right|$ is minimum;