A magnetic compass needle oscillates 30 times per minute at a place where the dip is 45^o, and 40 times per minute where the dip is 30^o. If B₁ and B₂ are respectively the total magnetic field due to the earth at the two places, then the ratio $${{{B_1}} \over {{B_2}}}$$ is best given by :

Two magnetic dipoles X and Y are placed at a separation d, with their axes perpendicular to each other. The dipole moment of Y is twice that of X. A particle of charge q is passing, through their midpoint P, at angle q = 45° with the horizontal line, as shown in figure. What would be the magnitude of force on the particle at that instant ?
(d is much larger than the dimensions of the dipole)

A paramagnetic material has 10²⁸ atoms/m³. Its magnetic susceptibility at temperature 350 K is 2.8 $$ \times $$ 10^–4. Its susceptibility at 300 K is :

A paramagnetic substance in the form of a cube with sides 1 cm has a magnetic dipole moment of 20 $$ \times $$ 10^–6 J/ T when a magnetic intensity of 60 $$ \times $$ 10³ A/m is applied. Its magnetic susceptibility is