The magnetic force $F = q(v \times B)$ is

Lorentz magnetic force is acting on a particle of charge $q$ moving with velocity $\vec{V}$ in magnetic field $\vec{B}$. The work done by this force on the charged particle is

In the case of the Hall effect for a strip having charge $Q$ and area of cross-section $A$,the Lorentz force 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.

$A$ 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 $q$)

$A$ particle of charge $q$ and velocity $v$ passes undeflected through a space with non-zero electric field $E$ and magnetic field $B$. The undeflected condition will hold if: