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 positive charge $'q'$ of mass $'m'$ is moving along the $+ x$ axis. We wish to apply a uniform magnetic field $B$ for time $\Delta t$ so that the charge reverses its direction crossing the $y$ axis at a distance $d.$ Then

Two charged particle $A$ and $B$ each of charge $+e$ and masses $12$ $amu$ and $13$ $amu$ respectively follow a circular trajectory in chamber $X$ after the velocity selector as shown in the figure. Both particles enter the velocity selector with speed $1.5 \times 10^6 \,ms^{-1}.$ A uniform magnetic field of strength $1.0$ $T$ is maintained within the chamber $X$ and in the velocity selector.

An electron and a proton enter region of uniform magnetic field in a direction at right angles to the field with the same kinetic energy. They describe circular paths of radius ${r_e}$ and ${r_p}$ respectively. Then

A charged particle of mass $m$ and charge $q$ describes circular motion of radius $r$ in a uniform magnetic field of strength $B$. The frequency of revolution is

A beam of electrons is moving with constant velocity in a region having electric and magnetic fields of strength $20\;V{m^{ - 1}}$ and $0.5 T$ at right angles to the direction of motion of the electrons. What is the velocity of the electrons............ $m{s^{ - 1}}$