A straight wire carrying a current of $$14 \mathrm{~A}$$ is bent into a semi-circular arc of radius $$2.2 \mathrm{~cm}$$ as shown in the figure. The magnetic field produced by the current at the centre $$(\mathrm{O})$$ of the arc. is ____________ $$\times ~10^{-4} \mathrm{~T}$$

The ratio of magnetic field at the centre of a current carrying coil of radius $$r$$ to the magnetic field at distance $$r$$ from the centre of coil on its axis is $$\sqrt{x}: 1$$. The value of $$x$$ is __________

A proton with a kinetic energy of $$2.0 ~\mathrm{eV}$$ moves into a region of uniform magnetic field of magnitude $$\frac{\pi}{2} \times 10^{-3} \mathrm{~T}$$. The angle between the direction of magnetic field and velocity of proton is $$60^{\circ}$$. The pitch of the helical path taken by the proton is __________ $$\mathrm{cm}$$. (Take, mass of proton $$=1.6 \times 10^{-27} \mathrm{~kg}$$ and Charge on proton $$=1.6 \times 10^{-19} \mathrm{C}$$ ).

Two identical circular wires of radius $$20 \mathrm{~cm}$$ and carrying current $$\sqrt{2} \mathrm{~A}$$ are placed in perpendicular planes as shown in figure. The net magnetic field at the centre of the circular wires is __________ $$\times 10^{-8} \mathrm{~T}$$.

(Take $$\pi=3.14$$)