Two parallel wires in the plane of the paper are distance $X _0$ apart. A point charge is moving with speed $u$ between the wires in the same plane at a distance $X_1$ from one of the wires. When the wires carry current of magnitude $I$ in the same direction, the radius of curvature of the path of the point charge is $R_1$. In contrast, if the currents $I$ in the two wires have direction opposite to each other, the radius of curvature of the path is $R_2$.

If $\frac{x_0}{x_1}=3$, the value of $\frac{R_1}{R_2}$ is.

An electron beam passes through a magnetic field of $2 \times 10^{-3}\,Wb/m^2$ and an electric field of $1.0 \times 10^4\,V/m$ both acting simultaneously. The path of electron remains undeviated. The speed of electron if the electric field is removed, and the radius of electron path will be respectively

A proton with a kinetic energy of $2.0\,eV$ moves into a region of uniform magnetic field of magnitude $\frac{\pi}{2} \times 10^{-3}\,T$. 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 $..........cm$ (Take, mass of proton $=1.6 \times 10^{-27}\,kg$ and Charge on proton $=1.6 \times 10^{-19}\,kg)$

If $\alpha $ and $\beta  - $ particles are moving with equal velocity perpendicular to the flux density $B$, then the radii of their paths will be

A particle of charge $16\times10^{-16}\, C$ moving with velocity $10\, ms^{-1}$ along $x-$ axis enters a region where magnetic field of induction $\vec B$ is along the $y-$ axis and an electric field of magnitude $10^4\, Vm^{-1}$ is along the negative $z-$ axis. If the charged particle continues moving along $x-$ axis, the magnitude of $\vec B$ is

A singly ionized magnesium atom $(A=24)$ ion is accelerated to kinetic energy $5\,keV$ and is projected perpendicularly into a magnetic field $B$ of the magnitude $0.5\,T$. The radius of path formed will be___________ $cm$