An electron gun is placed inside a long solenoid of radius $\mathrm{R}$ on its axis. The solenoid has $\mathrm{n}$ turns/length and carries a current $I$. The electron gun shoots an electron along the radius of the solenoid with speed $v$. If the electron does not hit the surface of the solenoid, maximum possible value of ${v}$ is (all symbols have their standard meaning)

Two particles $\mathrm{X}$ and $\mathrm{Y}$ having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describes circular paths of radii $R_1$ and $R_2$ respectively. The mass ratio of $\mathrm{X}$ and $\mathrm{Y}$ is :

Motion of a moving electron is not affected by

If an electron is going in the direction of magnetic field $\overrightarrow B $ with the velocity of $\overrightarrow {v\,} $ then the force on electron is

A particle of mass $m$ and charge $q$ is thrown from origin at $t = 0$ with velocity $2\hat{i}$ + $3\hat{j}$ + $4\hat{k}$ units in a region with uniform magnetic field $\vec B$ = $2\hat{i}$ units. After time $t =\frac{{\pi m}}{{qB}}$ , an electric field  is switched on such that particle moves on a straight line with constant speed. $\vec E$ may be