The mid points of two small magnetic dipoles of length $d$ in end-on positions, are separated by a distance $x, (x > > d)$. The force between them is proportional to $x^{-n}$ where $n$ 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;

A current loop placed in a magnetic field behaves like a

A bar magnet of length $10 \,cm$  and having the pole strength equal to $10^{-3}$ weber is kept in a magnetic field having magnetic induction $ (B)$  equal to $4\pi \times {10^{ - 3}}$ Tesla. It makes an angle of $30°$  with the direction of magnetic induction. The value of the torque acting on the magnet is

Magnetic moments of two bar magnets may be compared with the help of

The dipole moment of a short bar magnet is $1.25\, A-m^2$. The magnetic field on its axis at a distance of $0.5$ metre from the centre of the magnet is