A bar magnet with a magnetic moment $$5.0 \mathrm{Am}^{2}$$ is placed in parallel position relative to a magnetic field of $$0.4 \mathrm{~T}$$. The amount of required work done in turning the magnet from parallel to antiparallel position relative to the field direction is _____________.

A solenoid of 1200 turns is wound uniformly in a single layer on a glass tube 2 m long and 0.2 m in diameter. The magnetic intensity at the center of the solenoid when a current of 2 A flows through it is :

The vertical component of the earth's magnetic field is $$6 \times 10^{-5} \mathrm{~T}$$ at any place where the angle of dip is $$37^{\circ}$$. The earth's resultant magnetic field at that place will be $$\left(\right.$$Given $$\left.\tan 37^{\circ}=\frac{3}{4}\right)$$

A compass needle of oscillation magnetometer oscillates 20 times per minute at a place $$\mathrm{P}$$ of $$\operatorname{dip} 30^{\circ}$$. The number of oscillations per minute become 10 at another place $$\mathrm{Q}$$ of $$60^{\circ}$$ dip. The ratio of the total magnetic field at the two places $$\left(B_{Q}: B_{P}\right)$$ is :