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 $$\pi=3.14$$)

A charge particle of $$2 ~\mu \mathrm{C}$$ accelerated by a potential difference of $$100 \mathrm{~V}$$ enters a region of uniform magnetic field of magnitude $$4 ~\mathrm{mT}$$ at right angle to the direction of field. The charge particle completes semicircle of radius $$3 \mathrm{~cm}$$ inside magnetic field. The mass of the charge particle is __________ $$\times 10^{-18} \mathrm{~kg}$$

Two long parallel wires carrying currents 8A and 15A in opposite directions are placed at a distance of 7 cm from each other. A point P is at equidistant from both the wires such that the lines joining the point P to the wires are perpendicular to each other. The magnitude of magnetic field at P is _____________ $$\times~10^{-6}$$ T.

(Given : $$\sqrt2=1.4$$)