A sample of paramagnetic salt contains $2 \times 10^{24}$ atomic dipoles each of dipole moment $15 \times 10^{-23} \mathrm{JT}^{-1}$. The sample is placed under homogeneous magnetic field of 0.6 T and cooled to a temperature 4.2 K . The degree of magnetic saturation achived is $20 \%$. Then total dipole moment of the sample for a magnetic field of 0.9 T and a temperature of 2.8 K is

The work done in rotating a bar magnet which is initially in the direction of a uniform magnetic field through $45^{\circ}$ is $W$. The additional work to be done to rotate the magnet further through $15^{\circ}$ is

A short bar magnet of magnetic moment $10^4 \mathrm{JT}^{-1}$ is free to rotate in a horizontal plane. The work done in rotating the magnet slowly from the direction parallel to a horizontal magnetic field of $4 \times 10^{-5} \mathrm{~T}$ to a direction $60^{\circ}$ to the direction of the field is