${H^ + },\,H{e^ + }$ and ${O^{ + + }}$ ions having same kinetic energy pass through a region of space filled with uniform magnetic field $B$ directed perpendicular to the velocity of ions. The masses of the ions ${H^ + },\,H{e^ + }$and ${O^{ + + }}$ are respectively in the ratio $1:4:16$. As a result

If a proton enters perpendicularly a magnetic field with velocity $v$, then time period of revolution is $T$. If proton enters with velocity $2 v$, then time period will be

A negatively charged particle projected towards east is deflected towards north by a magnetic field. The field may be

A proton (mass $m$ ) accelerated by a potential difference $V$  flies through a uniform transverse magnetic field $B.$ The field occupies a region of space by width $'d'$. If $\alpha $ be the angle of deviation of proton from initial direction of motion (see figure), the value of $sin\,\alpha $ will be

In a certain region static electric and magnetic fields exist. The magnetic field is given by $\vec B = {B_0}\left( {\hat i + 2\hat j – 4\hat k} \right)$. If a test charge moving with a velocity $\vec v = {v_0}\left( {3\hat i – \hat j + 2\hat k} \right)$ experiences no force in that region, then the electric field in the region, in $SI\, units$, is