One proton beam enters a magnetic field of ${10^{ - 4}}$ $T$ normally, Specific charge = ${10^{11}}\,C/kg.$ velocity = ${10^7}\,m/s$. What is the radius of the circle described by it....$m$

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?

A very long straight wire carries a current $I$. At the instant when a charge $ + Q$ at point $P$ has velocity $\overrightarrow V $, as shown, the force on the charge is

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

Which law is useful to determine relation between current and magnetic fields due to it.

A charged particle enters a magnetic field $H$ with its initial velocity making an angle of $45^\circ $ with $H$. The path of the particle will be