A charged particle of specific charge $\alpha$ is released from origin at time $t = 0$ with velocity $\vec V = {V_o}\hat i + {V_o}\hat j$ in magnetic field $\vec B = {B_o}\hat i$ . The coordinates of the particle at time $t = \frac{\pi }{{{B_o}\alpha }}$ are (specific charge $\alpha = \,q/m$)
$\left( {\frac{{{V_o}}}{{2{B_o}\alpha }},\frac{{\sqrt 2 {V_o}}}{{\alpha {B_o}}},\frac{{ - {V_o}}}{{{B_o}\alpha }}} \right)$
$\left( {\frac{{ - {V_o}}}{{2{B_o}\alpha }},\,0,\,0} \right)$
$\left( {0,\,\frac{{2{V_o}}}{{{B_o}\alpha }},\frac{{{V_o}\pi }}{{2{B_o}\alpha }}} \right)$
$\left( {\frac{{{V_o}\pi }}{{{B_o}\alpha }},\,0,\, - \frac{{2{V_o}}}{{{B_o}\alpha }},} \right)$
An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement$(s)$ is/are true?
$(A)$ They will never come out of the magnetic field region.
$(B)$ They will come out travelling along parallel paths.
$(C)$ They will come out at the same time.
$(D)$ They will come out at different times.
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
${H^ + },\,H{e^ + }$ and ${O^{ + + }}$ ions having same kinetic energy pass through a region of space filled with uniform magnetic field $B$ directed perpendicular to the velocity of ions. The masses of the ions ${H^ + },\,H{e^ + }$and ${O^{ + + }}$ are respectively in the ratio $1:4:16$. As a result
An electron is moving along positive $x$-axis.Auniform electric field exists towards negative $y$-axis. What should be the direction of magnetic field of suitable magnitude so that net force of electron is zero
An electron enters a region where magnetic $(B)$ and electric $(E)$ fields are mutually perpendicular to one another, then