An $\alpha$-particle of mass $m$ moves on a circular path of radius $r$ in a plane inside and normal to a uniform magnetic field $B$. The time taken by this particle to complete one revolution is . . . . . . .

If an electron and a proton having same momenta enter perpendicular to a magnetic field,then

$A$ particle having charge of $1 \, C$,mass $1 \, kg$ and speed $1 \, m/s$ enters a uniform magnetic field,having magnetic induction of $1 \, T$,at an angle $\theta = 30^\circ$ between the velocity vector and the magnetic induction. The pitch of its helical path is (in meters):

An electron,a proton,a deuteron,and an $\alpha -$ particle enter a uniform magnetic field normally with the same velocity. Which particle will have the maximum rotational frequency?

$A$ monoenergetic $(18 \;keV)$ electron beam initially in the horizontal direction is subjected to a horizontal magnetic field of $0.04 \;G$ normal to the initial direction. Estimate the up or down deflection of the beam over a distance of $30 \;cm$ $(m_{e} = 9.11 \times 10^{-31} \;kg)$.

The figure shows the face of a cathode-ray oscilloscope tube,as viewed from the front. The electron beam is coming out normally from the plane of the paper. The electron beam passes through a region where there are electric and magnetic fields directed as shown. The deflections of the spot from the center of the screen produced by the electric field $E$ and the magnetic field $B$ separately are equal in magnitude. Which one of the diagrams below shows a possible position of the spot on the screen when both fields are operating?