A charged particle is released from rest in a region of steady uniform electric and magnetic fields which are parallel to each other the particle will move in a

Two parallel wires in the plane of the paper are distance $X _0$ apart. A point charge is moving with speed $u$ between the wires in the same plane at a distance $X_1$ from one of the wires. When the wires carry current of magnitude $I$ in the same direction, the radius of curvature of the path of the point charge is $R_1$. In contrast, if the currents $I$ in the two wires have direction opposite to each other, the radius of curvature of the path is $R_2$.

If $\frac{x_0}{x_1}=3$, the value of $\frac{R_1}{R_2}$ is.

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 $I$

Derived force on moving charge in uniform magnetic field with velocity $\overrightarrow {{v_d}} $.

Proton, deuteron and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively $r_p, r_d$ and $r_{\alpha}$ Which one of the following relation is correct?

In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an electric potential $V$ and then made to describe semicircular paths of radius $R$ using a magnetic field $B$. If $V$ and $B$ are kept constant, the ratio $\left( {\frac{{{\text{charge on the ion}}}}{{{\text{mass of the ion}}}}} \right)$ will be proportional to