Question

Write the expression for Lorentz magnetic force on a particle of charge $q$ moving with velocity $v$ in a magnetic field $B$. Shown that two no work is done by this force on the charged particle.

Answer 1

Lorentz force = magnetic force + electric force

F = [ qvb sin$\theta$ + qe ]

$\overrightarrow{F}=q(\overrightarrow{V}\times \overrightarrow{B})$

(1) $\overrightarrow{F}$ is perpendicular to both $\overrightarrow{V}$ and $\overrightarrow{B}$.

if $\overrightarrow{ds}$ is the instantaneous displacement of the change

$\overrightarrow{ds}$ is also perpendicular to $\overrightarrow{F}$

$W=\overrightarrow{F}.\overrightarrow{ds}$

= Fs $cos{90}^0$

but $cos{90}^0$ = 0

W = 0

Hence increase in kinetic energy is zero