$A$ bar magnet of magnetic moment $10^4\,J/T$ is free to rotate in a horizontal plane. The work done in rotating the magnet slowly from a direction parallel to a horizontal magnetic field of $4 \times 10^{-5}\,T$ to a direction $60^\circ$ from the field will be... $J$.

$A$ bar magnet having a magnetic moment of $2.0 \times 10^{5} \; J T^{-1}$ is placed along the direction of a uniform magnetic field of magnitude $B = 14 \times 10^{-5} \; T$. The work done in rotating the magnet slowly through $60^{\circ}$ from the direction of the field is .............. $J$.

Two short bar magnets $A$ and $B$ (having magnetic moments $M_{1}$ and $M_{2}$ respectively) are kept one above the other with their magnetic axes perpendicular to each other. If their resultant magnetic field at a point on the axis of magnet $A$ is inclined at $45^{\circ}$ with the axis of magnet $A$,then the ratio of magnetic moments $\frac{M_{2}}{M_{1}}$ is $[\tan 45^{\circ} = 1]$.

Points $A$ and $B$ are situated perpendicular to the axis of a small 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

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:

The figure shows a bar magnet and a long straight wire $W$,carrying current into the plane of the paper. Point $P$ is the point of intersection of the axis of the magnet and the line of shortest distance between the magnet and the wire. If $P$ is the midpoint of the magnet,then which of the following statements is correct?