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

Two identical dipoles each of magnetic moment $1.0\, A-m^2$ are placed at a separation of $2\,m$ with their axes perpendicular to each other. What is the magnetic field at a point midway between the dipoles ?

Two identical short bar magnets, each having magnetic moment $M,$ are placed a distance of $2d $ apart with axes perpendicular to each other in a horizontal plane. The magnetic induction at a point midway between them is

Write difference between electrostatic and magnetics :

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;