As shown in the figure, a long straight conductor with semicircular arc of radius $$\frac{\pi}{10}$$m is carrying current $$\mathrm{I=3A}$$. The magnitude of the magnetic field, at the center O of the arc is :

(The permeability of the vacuum $$=4\pi\times10^{-7}~\mathrm{NA}^{-2}$$)

Find the magnetic field at the point $$\mathrm{P}$$ in figure. The curved portion is a semicircle connected to two long straight wires.

A long conducting wire having a current I flowing through it, is bent into a circular coil of $\mathrm{N}$ turns. Then it is bent into a circular coil of $\mathrm{n}$ turns. The magnetic field is calculated at the centre of coils in both the cases. The ratio of the magnetic field in first case to that of second case 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 $$\mu_{0}=4 \pi \times 10^{-7} \mathrm{NA}^{-2}$$)