A particle of charge $q$ and mass $m$ starts moving from the origin under the action of an electric field $\vec E = {E_0}\hat i$ and $\vec B = {B_0}\hat i$ with velocity ${\rm{\vec v}} = {{\rm{v}}_0}\hat j$. The speed of the particle will become $2v_0$ after a time
$t = \frac{{2m{{\rm{v}}_0}}}{{qE}}$
$t = \frac{{2Bq}}{{m{{\rm{v}}_0}}}$
$t =\frac{{\sqrt 3 \,Bq}}{{m{{\rm{v}}_0}}}$
$t =\frac{{\sqrt 3 \,m{{\rm{v}}_0}}}{{qE}}$
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
charged particle with charge $q$ enters a region of constant, uniform and mutually orthogonal fields $\vec E$ and $\vec B$ with a velocity $\vec v$ perpendicular to both $\vec E$ and $\vec B$ , and comes out without any change in magnitude or direction of $\vec v$ . Then
Two ions have equal masses but one is singly ionized and second is doubly ionized. They are projected from the same place in a uniform transverse magnetic field with same velocity then:
$(a)$ Both ions will go along circles of equal radii
$(b)$ The radius of circle described by the single ionized charge is double of radius of circle described by doubly ionized charge
$(c)$ Both circle do not touches to each other
$(d)$ Both circle touches to each other
Under the influence of a uniform magnetic field a charged particle is moving in a circle of radius $R$ with constant speed $v$. The time period of the motion
A proton, a deuteron and an $\alpha-$particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is