A particle of mass $m$ and charge $\mathrm{q}$, moving with velocity $\mathrm{V}$ enters Region $II$ normal to the boundary as shown in the figure. Region $II$ has a uniform magnetic field B perpendicular to the plane of the paper. The length of the Region $II$ is $\ell$. Choose the correct choice$(s)$.

Figure: $Image$

$(A)$ The particle enters Region $III$ only if its velocity $V>\frac{q / B}{m}$

$(B)$ The particle enters Region $III$ only if its velocity $\mathrm{V}<\frac{\mathrm{q} / \mathrm{B}}{\mathrm{m}}$

$(C)$ Path length of the particle in Region $II$ is maximum when velocity $V=\frac{q / B}{m}$

$(D)$ Time spent in Region $II$ is same for any velocity $V$ as long as the particle returns to Region $I$

An electron is travelling horizontally towards east. A magnetic field in vertically downward direction exerts a force on the electron along

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

A particle is projected with a velocity ( $10\ m/s$ ) along $y-$ axis from point $(2, 3)$ . Magnetic field of $\left( {3\hat i + 4\hat j} \right)$ Tesla exist uniformly in the space. Its speed when particle passes through $y-$ axis for the third time is : (neglect gravity)

A charge $q$ moves in a region where electric field and magnetic field both exist, then force on it is