$A$ uniform magnetic field $\vec{B} = B_0 \hat{j}$ exists in space. $A$ particle of mass $m$ and charge $q$ is projected towards the negative $x$-axis with speed $v$ from the point $(d, 0, 0)$. The maximum value of $v$ for which the particle does not hit the $y-z$ plane is

$A$ particle of specific charge $q / m = \pi \text{ C kg}^{-1}$ is projected from the origin towards the positive $X$-axis with a velocity $10 \text{ ms}^{-1}$ in a uniform magnetic field $\vec{B} = -2 \hat{k} \text{ T}$. The velocity $\vec{v}$ of the particle after time $t = \frac{1}{12} \text{ s}$ will be (in $\text{ ms}^{-1}$):

$A$ 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 ........ $keV$.

Electrons move at right angles to a magnetic field of $1.5 \times 10^{-2} \text{ T}$ with a speed of $6 \times 10^7 \text{ m/s}$. If the specific charge of the electron is $1.7 \times 10^{11} \text{ C/kg}$,the radius of the circular path will be...... $\text{cm}$.

An electron is moving on a circular path of radius $r$ with speed $v$ in a transverse magnetic field $B$. The $e/m$ ratio for it will be:

$A$ particle of charge $16 \times 10^{-16} \, C$ moving with velocity $10 \, ms^{-1}$ along the $x$-axis enters a region where a magnetic field of induction $\vec{B}$ is along the $y$-axis and an electric field of magnitude $10^4 \, Vm^{-1}$ is along the negative $z$-axis. If the charged particle continues moving along the $x$-axis,the magnitude of $\vec{B}$ is: