$A$ metal sample carrying a current along the $x-$ axis with current density $J$ is subjected to a magnetic field $B$ (along the $z-$ axis). The electric field $E$ developed along the $y-$ axis is directly proportional to $J$ as well as $B$. The constant of proportionality has the $SI$ unit:

$A$ proton moves with a velocity of $5 \times 10^6 \hat{j} \text{ ms}^{-1}$ through a uniform electric field $\vec{E} = 4 \times 10^6 [2 \hat{i} + 0.2 \hat{j} + 0.1 \hat{k}] \text{ Vm}^{-1}$ and a uniform magnetic field $\vec{B} = 0.2 [\hat{i} + 0.2 \hat{j} + \hat{k}] \text{ T}$. The approximate net force acting on the proton is

$A$ charge $q$ moves with velocity $\vec{V}$ through an electric field $\vec{E}$ as well as a magnetic field $\vec{B}$. Then the force acting on it is:

An electron is moving with a velocity $\vec{v} = (2 \hat{i} + 3 \hat{j}) \text{ m/s}$ in an electric field $\vec{E} = (3 \hat{i} + 6 \hat{j} + 2 \hat{k}) \text{ V/m}$ and a magnetic field $\vec{B} = (2 \hat{j} + 3 \hat{k}) \text{ T}$. Calculate the magnitude and direction (with $x$-axis) of the Lorentz force acting on the electron.

If $E$ and $B$ are the magnitudes of electric and magnetic fields respectively in some region of space,then the possibilities for which a charged particle may move in that space with a uniform velocity of magnitude $v$ are

$A$ charge moves with velocity $\overrightarrow{V}$ through an electric field $\overrightarrow{E}$ as well as a magnetic field $\overrightarrow{B}$. Then the force acting on it is: