A particle of charge $q$ and mass $m$ moving with a velocity $v$ along the $x$-axis enters the region $x > 0$ with uniform magnetic field $B$ along the $\hat k$ direction. The particle will penetrate in this region in the $x$-direction upto a distance $d$ equal to

A mass spectrometer is a device which select particle of equal mass. An iron with electric charge $q > 0$ and mass $m$ starts at rest from a source $S$ and is accelerated through a potential difference $V$. It passes $\rho$ through a hole into a region of constant magnetic field $\vec B\,$ perpendicular to the plane of the paper as shown in the figure. The particle is deflected by the magnetic field and emerges through the bottom hole at a distance $d$ from the top hole. The mass of the particle is 

An electron is travelling along the $x$-direction. It encounters a magnetic field in the $y$-direction. Its subsequent motion will be

The time period of a charged particle undergoing a circular motion in a uniform magnetic field is independent of its

A particle of charge $q$ and mass $m$ is moving along the $x$ -axis with a velocity $v$ and enters a region of electric field $E$ and magnetic field $B$ as shown in figure below for which figure the net force on the charge may be zero