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.

An electron is moving in a circular path under the influence of a transverse magnetic field of $3.57 \times 10^{-2}\, T $. If the value of $e/m$ is  $1.76 \times 10^{11}\, C/kg $, the frequency of revolution of the electron is

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

A particle of mass $m$ and charge $q$ is in an electric and magnetic field given by

$\vec E = 2\hat i + 3\hat j ;\, B = 4\hat j + 6\hat k$

The charged particle is shifted from the origin to the point $P(x = 1 ;\, y = 1)$ along a straight path. The magnitude of the total work done is

Two particles $x$ and $y$ have equal charges and possessing equal kinetic energy enter in a uniform magnetic field and describe circular path of radius of curvature $r_1$ and $r_2$ respectively. The ratio of their masses is