An electron enters a region where magnetic $(B)$ and electric $(E)$ fields are mutually perpendicular to one another,then

The electrostatic force $(\vec{F}_1)$ and magnetic force $(\vec{F}_2)$ acting on a charge $q$ moving with velocity $\vec{v}$ can be written as:

$A$ 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

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

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.

What is the behavior of a charged particle moving in a region where the electric field $\vec{E}$ and magnetic field $\vec{B}$ are perpendicular to each other?