A sample of a ferromagnetic iron in the shape of a cube of side $1.0 \mu \mathrm{~m}$ contains $8.7 \times 10^{28}$ atoms per cubic metre and the magnetic dipole moment of each iron atom is $93 \times 10^{-24} \mathrm{Am}^2$. Then, the maximum possible magnetic dipole moment (in $\mathrm{Am}^2$ ) of the sample is nearly

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

A short bar magnet has a magnetic moment of $0.48 \mathrm{JT}^{-1}$. The magnitude of magnetic field at a point at 10 cm distance from the centre of the magnet on its axis is

A short bar magnet is placed in a uniform magnetic field of 2 T such that the axis of the magnet makes an angle of $45^{\circ}$ with the direction of the magnetic field. If the torque acting on the magnet is $0.36 \sqrt{2} \mathrm{~N}-\mathrm{m}$, then the moment of the magnet is

Two short magnets of equal dipole moments $$M$$ are fastened perpendicularly at their centres. The magnitude of the magnetic field at a distance $$d$$ from the centre on the bisector of the right angle is($$\mu_0=$$ Permeability of free space)

A steel wire of length $$l$$ and magnetic moment $$M$$ is bent into a semicircular arc of radius $$R$$. The new magnetic moment is

A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down at $$30^{\circ}$$ with the horizontal. The horizontal component of the earth's magnetic field at the place is 0.3 G . Then the magnitude of the earth's magnetic field at the location is

A compass needle oscillates 20 times per minute at a place where the dip is $$45^{\circ}$$ and the magnetic field is $$B_1$$. The same needle oscillates 30 times per minute at a place where the dip is $$30^{\circ}$$ and magnetic field is $$B_2$$. Then, $$B_1: B_2$$ is

A paramagnetic sample showing a net magnetisation of $$0.8 \mathrm{~A} \mathrm{~m}^{-1}$$, when placed in an external magnetic field of strength $$0.8 \mathrm{~T}$$, at a temperature $$5 \mathrm{~K}$$. If the temperature is raised to $$20 \mathrm{~K}$$, then the magnetisation becomes

The plane of a dip circle is set in the geographic meridian and the apparent dip is $$\delta_1$$. It is then set in a vertical plane perpendicular to the geographic meridian. The apparent dip angle is $$\delta_2$$. The declination $$\theta$$ at the place is