Two ions having same mass have charges in the ratio $1: 2$. They are projected normally in a uniform magnetic field with their speeds in the ratio $2: 3$. The ratio of the radii of their circular trajectories is -

$A$ charged particle is moving in a magnetic field of strength $B$ perpendicular to the direction of the field. If $q$ and $m$ denote the charge and mass of the particle respectively,then the frequency of rotation of the particle is

An electron and a proton enter a magnetic field perpendicularly. Both have the same kinetic energy. Which of the following is true?

An electron moving with a speed $u$ along the positive $x$-axis at $y = 0$ enters a region of uniform magnetic field $\overrightarrow B = -B_0 \hat k$ which exists to the right of the $y$-axis. The electron exits from the region after some time with the speed $v$ at coordinate $y$,then

$A$ particle with charge $+Q$ and mass $m$ enters a magnetic field of magnitude $B,$ existing only to the right of the boundary $YZ.$ The direction of the motion of the particle is perpendicular to the direction of $B.$ Let $T = 2\pi\frac{m}{QB}.$ The time spent by the particle in the field will be:

An electron is moving along the positive $X$-axis. You want to apply a magnetic field for a short time so that the electron may reverse its direction and move parallel to the negative $X$-axis. This can be done by applying the magnetic field along