$A$ 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 $q$)

If the magnetic field is parallel to the positive $y$-axis and the charged particle is moving along the positive $x$-axis (Figure),which way would the Lorentz force be for
$(a)$ an electron (negative charge),
$(b)$ a proton (positive charge).

$A$ 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 enters an electric field with intensity $\vec{E} = 3\hat{i} + 6\hat{j} + 2\hat{k} \text{ V m}^{-1}$ and a magnetic field with induction $\vec{B} = 2\hat{i} + 3\hat{j} \text{ T}$ with a velocity $\vec{v} = 2\hat{i} + 3\hat{j} \text{ m s}^{-1}$. The magnitude of the force acting on the electron is (Given, $e = -1.6 \times 10^{-19} \text{ C}$)

Write the formula for the magnetic force acting on a moving charge $q$ in a magnetic field $B$.

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: