In the figure shown,a charge $q$ of mass $m$ moving with a velocity $v$ along the $x$-axis enters a region of uniform magnetic field $B$ directed into the page. If the particle is able to enter the region $x > b$,then the velocity $v$ must be greater than:

Two charged particles $A$ and $B$ of masses $m$ and $2m$, charges $2q$ and $3q$ respectively, moving with the same velocity, enter a uniform magnetic field such that both particles make the same angle $( < 90^{\circ} )$ with the direction of the magnetic field. Then the ratio of the pitches of the helical paths of the particles $A$ and $B$ is

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

$A$ particle having a charge of $10\,\mu C$ and $1\,\mu g$ mass moves along a circular path of $10\, cm$ radius in the presence of a uniform magnetic field of $0.1\, T$. When the charge is at point $P$,a uniform electric field is applied in the region such that the charge moves tangentially with a constant speed. The value of the electric field is......$V/m$

An electron and a proton having same momenta enter perpendicular into a magnetic field then