Magnetic field intensity is defined as

The magnetic potential at a point on the axial line of a bar magnet of dipole moment $M$ is $V$. What is the magnetic potential due to a bar magnet of dipole moment $\frac{M}{4}$ at the same point

Points $A$ and $B$ are situated perpendicular to the axis of a $2\,cm$  long bar magnet at large distances $X$ and $3X$  from its centre on opposite sides. The ratio of the magnetic fields at $ A$ and $B$  will be approximately equal to

A bar magnet having centre $O$ has a length of $4 $ $cm. $ Point $P_1$ is in the broad side-on and $P_2 $ is in the end side-on position with $OP_1 = OP_2 = 10$ metres. The ratio of magnetic intensities $H$ at $P_1$ and $P_2$ 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;

Two points $A$ and $B$ are situated at a distance $x$ and $2x$ respectively from the nearer pole of a magnet $2\,cm$ long. The ratio of magnetic field at $A$ and $B$ is