A proton of energy $8\, eV$ is moving in a circular path in a uniform magnetic field. The energy of an alpha particle moving in the same magnetic field and along the same path will be…..$eV$

Two charged particles of mass $m$ and charge $q$ each are projected from origin simultaneously with same speed $V$ in transverse magnetic field. If ${\vec r_1}$ and ${\vec r_2}$ are the position vectors of particles (with respect to origin) at $t = \frac{{\pi m}}{{qB}}$ then the value of  ${\vec r_1}.{\vec r_2}$ at that time is

A charge $q$ is released in presence of electric $(E)$ and magnetic field $(B)$ then after some time its velocity is $v$ then

An electron is projected with velocity $\vec v$ in a uniform magnetic field $\vec B$ . The angle $\theta$  between $\vec v$ and $\vec B$  lines between $0^o$ and $\frac{\pi}{2}$ . It velocity $\vec v$ vector returns to its initial  value in time interval of 

A rectangular region of dimensions ( $\omega \times l(\omega) \ll l$ ) has a constant magnetic field into the plane of the paper as shown in the figure below. On one side, the region is bounded by a screen. On the other side, positive ions of mass $m$ and charge $q$ are accelerated from rest and towards the screen by a parallel plate capacitor at constant potential difference $V < 0$ and come out through a small hole in the upper plate. Which one of the following statements is correct regarding the charge on the ions that hit the screen?