Two identical thin bar magnets each of length $l $ and pole strength $m$  are placed at right angle to each other with north pole of one touching south pole of the other. 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;

The current is flowing through solenoid, then solenoid acting as what ?

Two short bar magnets of magnetic moments ' $M$ ' each are arranged at the opposite corners of a square of side ' $d$ ', such that their centres coincide with the corners and their axes are parallel to one side of the square. If the like poles are in the same direction, the magnetic induction at any of the other corners of the square is

Magnetic intensity for an axial point due to a short bar magnet of magnetic moment $M$ is given by