When a charged particle moving with velocity $\vec{v}$ is subjected to a magnetic field of induction $\vec{B}$,the force on it is non-zero. This implies that

$A$ deuteron of kinetic energy $50 \, keV$ is describing a circular orbit of radius $0.5 \, m$ in a plane perpendicular to a magnetic field $\vec{B}$. The kinetic energy of a proton that describes a circular orbit of radius $0.5 \, m$ in the same plane with the same $\vec{B}$ is ........ $keV$.

Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and magnetic fields $\vec{E}=E_0 \hat{j}$ and $\vec{B}=B_0 \hat{j}$. At time $t=0$,this charge has velocity $\vec{v}$ in the $x-y$ plane,making an angle $\theta$ with the $x$-axis. Which of the following option$(s)$ is(are) correct for time $t>0$?
$(A)$ If $\theta=0^{\circ}$,the charge moves in a circular path in the $x-z$ plane.
$(B)$ If $\theta=0^{\circ}$,the charge undergoes helical motion with constant pitch along the $y$-axis.
$(C)$ If $\theta=10^{\circ}$,the charge undergoes helical motion with its pitch increasing with time,along the $y$-axis.
$(D)$ If $\theta=90^{\circ}$,the charge undergoes linear but accelerated motion along the $y$-axis.

If the velocity of an electron is $(2 \hat{i} + 3 \hat{j}) \text{ m s}^{-1}$ and it enters a magnetic field of $4 \hat{k} \text{ T}$,then . . . . . . .

Two particles $X$ and $Y$ having equal charges,after being accelerated through the same potential difference,enter a region of uniform magnetic field and describe circular paths of radii $R_1$ and $R_2$ respectively. The ratio of the mass of $X$ to that of $Y$ is

If a proton is projected in a direction perpendicular to a uniform magnetic field with velocity $v$ and an electron is projected along the lines of force,what will happen to the proton and electron?