An electron moving with a uniform velocity along the positive $x$-direction enters a magnetic field directed along the positive $y$-direction. The force on the electron is directed along

Two identical charged particles enter a uniform magnetic field with the same speed but at angles $30^{\circ}$ and $60^{\circ}$ with the field. Let $a, b,$ and $c$ be the ratios of their time periods,radii,and pitches of the helical paths,respectively. Then:

$A$ $2 \, MeV$ proton is moving perpendicular to a uniform magnetic field of $2.5 \, T$. The force on the proton is

$A$ nucleus at rest undergoes $\alpha -$ decay according to the equation ${}_{92}^{226}X \to Y + \alpha$. At $t=0$,the emitted $\alpha -$ particle enters a region of space where a uniform magnetic field $\vec{B} = B_0 \hat{i}$ and an electric field $\vec{E} = E_0 \hat{i}$ exist. The $\alpha -$ particle enters the region with velocity $\vec{v} = v_0 \hat{j}$ at $x = 0$. After a time $t = \left( \sqrt{3} \times 10^7 \frac{m_{\alpha}}{q_{\alpha} E_0} \right)$,the particle is found to have twice its initial speed. The initial speed $v_0$ of the $\alpha -$ particle is:

$A$ tightly wound long solenoid has $n$ turns per unit length,a radius $r$ and carries a current $I$. $A$ particle having charge $q$ and mass $m$ is projected from a point on the axis in a direction perpendicular to the axis. The maximum speed of the particle for which the particle does not strike the solenoid is

An electron and a proton enter a magnetic field perpendicularly. Both have the same kinetic energy. Which of the following is true?