$A$ particle of charge $2 \ C$ is moving with a velocity of $(3 \hat{i} + 4 \hat{j}) \ ms^{-1}$ in the presence of magnetic and electric fields. If the magnetic field is $(\hat{i} + 2 \hat{j} + 3 \hat{k}) \ T$ and the electric field is $(-2 \hat{k}) \ NC^{-1}$,then the Lorentz force on the particle is: (in $N$)

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 Lorentz force? Write an expression for it.

$A$ particle of mass $m$ and charge $q$ is in an electric and magnetic field given by $\vec E = 2\hat i + 3\hat j$ and $\vec B = 4\hat j + 6\hat k$. The charged particle is shifted from the origin $(0, 0, 0)$ to the point $P(1, 1, 0)$ along a straight path. The magnitude of the total work done is: (in $q$)

$A$ 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:

$A$ collimated beam of charged and uncharged particles is directed towards a hole marked $P$ on a screen as shown below. If the electric and magnetic fields as indicated below are turned $ON$,which of the following statements is correct?