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

A bar magnet of magnetic moment $M$ is placed at right angles to a magnetic induction $B.$ If a force $F$ is experienced by each pole of the magnet, the length of the magnet will be

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 straight magnetic strip has a magnetic moment of $44 \mathrm{Am}^2$. If the strip is bent in a semicircular shape, its magnetic moment will be .. . . . . . .$\mathrm{Am}^2$ $\left(\right.$ Given $\left.\pi=\frac{22}{7}\right)$

A long magnetic needle of length $2\,L$, magnetic moment $ M$  and pole strength $m$ units is broken into two pieces at the middle. The magnetic moment and pole strength of each piece will be