The torque on a bar magnet due to the earth's magnetic field is maximum when the axis of the magnet is

$A$ sample of a ferromagnetic iron in the shape of a cube of side $1.0 \mu m$ contains $8.7 \times 10^{28}$ atoms per cubic metre and the magnetic dipole moment of each iron atom is $9.3 \times 10^{-24} A m^2$. Then the maximum possible magnetic dipole moment (in $A m^2$) of the sample is nearly

Verify Ampere's law for the magnetic field of a point dipole with dipole moment $\vec{M} = M\hat{k}$. Take $C$ as the closed curve running clockwise along the $x$-axis from $x = R$ to $x = a$,then along a circular arc of radius $r$ in the $xz$-plane from $\theta = 0$ to $\theta = \pi$,and finally back to the starting point.

The resultant magnetic moment of a neon atom will be

Three identical bar magnets are riveted together at the centre in the same plane as shown in the figure. This system is placed at rest in a slowly varying magnetic field. It is found that the system of magnets does not show any motion. The north-south poles of one magnet are shown in the figure. Determine the poles of the remaining two.

If two identical bar magnets,each of length $l$,pole strength $m$ and magnetic moment $M$ are placed perpendicular to each other with their unlike poles in contact,the magnetic moment of the combination is