An $\alpha$-particle and a proton travel with the same velocity in a magnetic field perpendicular to the direction of their velocities. Find the ratio of the radii of their circular paths.

$A$ proton moving with a constant velocity passes through a region of space without any change in its velocity. If $E$ and $B$ represent the electric and magnetic fields respectively,this region may have:

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 enters a magnetic field whose direction is perpendicular to the velocity of the electron. Then

The following figure shows the path of an electron that passes through two regions containing uniform magnetic fields of magnitudes $B_1$ and $B_2$. Its path in each region is a half-circle. Choose the correct option.

$A$ charged particle enters a uniform magnetic field with a velocity vector making an angle of $30^o$ with the magnetic field. The particle describes a helical trajectory of pitch $x$. The radius of the helix is