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 rod with circular cross-section area $$2 \mathrm{~cm}^{2}$$ and length $$40 \mathrm{~cm}$$ is wound uniformly with 400 turns of an insulated wire. If a current of $$0.4 \mathrm{~A}$$ flows in the wire windings, the total magnetic flux produced inside windings is $$4 \pi \times 10^{-6} \mathrm{~Wb}$$. The relative permeability of the rod is

(Given : Permeability of vacuum $$\mu_{0}=4 \pi \times 10^{-7} \mathrm{NA}^{-2}$$)

As shown in the figure, a current of $2 \mathrm{~A}$ flowing in an equilateral triangle of side $4 \sqrt{3} \mathrm{~cm}$. The magnetic field at the centroid $\mathrm{O}$ of the triangle is

(Neglect the effect of earth's magnetic field)