A circular coil having 200 turns, $$2.5 \times 10^{-4} \mathrm{~m}^2$$ area and carrying $$100 \mu \mathrm{A}$$ current is placed in a uniform magnetic field of $$1 \mathrm{~T}$$. Initially the magnetic dipole moment $$(\vec{M})$$ was directed along $$\vec{B}$$. Amount of work, required to rotate the coil through $$90^{\circ}$$ from its initial orientation such that $$\vec{M}$$ becomes perpendicular to $$\vec{B}$$, is ________ $$\mu$$J.

A solenoid of length $$0.5 \mathrm{~m}$$ has a radius of $$1 \mathrm{~cm}$$ and is made up of '$$\mathrm{m}$$' number of turns. It carries a current of $$5 \mathrm{~A}$$. If the magnitude of the magnetic field inside the solenoid is $$6.28 \times 10^{-3} \mathrm{~T}$$ then the value of $$\mathrm{m}$$ is __________.

A 2A current carrying straight metal wire of resistance $$1 \Omega$$, resistivity $$2 \times 10^{-6} \Omega \mathrm{m}$$, area of cross-section $$10 \mathrm{~mm}^2$$ and mass $$500 \mathrm{~g}$$ is suspended horizontally in mid air by applying a uniform magnetic field $$\vec{B}$$. The magnitude of B is ________ $$\times 10^{-1} \mathrm{~T}$$ (given, $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$).

Two parallel long current carrying wire separated by a distance $$2 r$$ are shown in the figure. The ratio of magnetic field at $$A$$ to the magnetic field produced at $$C$$ is $$\frac{x}{7}$$. The value of $$x$$ is __________.