$A$ uniform magnetic field $B$ is acting from south to north and is of magnitude $1.5 \ Wb/m^2$. If a proton having mass $m = 1.7 \times 10^{-27} \ kg$ and charge $q = 1.6 \times 10^{-19} \ C$ moves in this field vertically downwards with energy $5 \ MeV$,then the force acting on it will be

$A$ metallic block carrying current $I$ is subjected to a uniform magnetic induction $\overrightarrow{B}$ as shown in the figure. The moving charges experience a force $\overrightarrow{F}$ given by ........... which results in the lowering of the potential of the face ........ Assume the speed of the carriers to be $v$.

$A$ proton is moving with a uniform velocity of $10^{6} \ m/s$ along the $Y$-axis, under the joint action of a magnetic field along the $Z$-axis and an electric field of magnitude $2 \times 10^{4} \ V/m$ along the negative $X$-axis. If the electric field is switched off, the proton starts moving in a circle. The radius of the circle is nearly: (Given: $\frac{e}{m}$ ratio for proton $= 10^{8} \ C/kg$) (in $m$)

$A$ particle of mass $m$ and charge $q$,moving with velocity $V$,enters region $II$ normal to the boundary as shown in the figure. Region $II$ has a uniform magnetic field $B$ perpendicular to the plane of the paper. The length of the region $II$ is $l$. Choose the incorrect option.

$A$ particle of charge $q$ and mass $m$ starts moving from the origin under the action of an electric field $\vec E = E\hat i$ and a magnetic field $\vec B = B\hat i$ with an initial velocity $\vec v = v_0\hat j$. The speed of the particle will become $2v_0$ after a time:

$H^+$,$He^+$,and $O^{++}$ are projected in a uniform transverse magnetic field with equal accelerating potential. If their masses are $1 \, a.m.u.$,$4 \, a.m.u.$,and $16 \, a.m.u.$ respectively,find the ratio of their radii.