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

At some location on earth, the horizontal component of earth’s magnetic field is 18 × 10^–6 T. At this location, magnetic needle of length 0.12 m and pole strength 1.8 Am is suspended from its mid-point using a thread, it makes 45^o angle with horizontal in equilibrium. To keep this needle horizontal, the vertical force that should be applied at one of its ends is -