The magnetic potential due to a magnetic dipole at a point on its axis situated at a distance of $20 \mathrm{~cm}$ from its center is $1.5 \times 10^{-5} \  \mathrm{Tm}$. The magnetic moment of the dipole is___________ $\mathrm{Am}^2$. (Given : $\frac{\mu_0}{4 \pi}=10^{-7} \  \mathrm{TmA}^{-1}$ )

Two short magnets of equal dipole moments $M $ are fastened perpendicularly at their centre (figure). The magnitude of the magnetic field at a distance $d $ from the centre on the bisector of the right angle is

The distance between the poles of a horse shoe magnet is $0.1\, m$ and its pole strength is $0.01\, amp-m$. The induction of magnetic field at a point midway between the poles will be

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

A small bar magnet has a magnetic moment $1.2 \,A-m^2$. The magnetic field at a distance $ 0.1\, m $ on its axis will be : ($\mu_0 = 4\pi \times 10^{-7} \,T-m/A$)

A short bar magnet of magnetic movement $5.25 \times 10^{-2} \;J\, T ^{-1}$ is placed with its axis perpendicular to the earth's field direction. At what distance from the centre of the magnet, the resultant field is inclined at $45^{\circ}$ with earth's field on

$(a)$ its normal bisector and

$(b)$ its axis.

Magnitude of the earth's field at the place is given to be $0.42 \;G$. Ignore the length of the magnet in comparison to the distances involved.