• # question_answer Write the expression for Lorentz magnetic force on a particle of charge 'q' moving with velocity v in a magnetic field B. Show that no work is done by this force on the charged particle.

Lorentz magnetic force,    ${{F}_{m}}=q(v\times B)$ Work done by Lorentz magnetic force is $dW={{F}_{m}}\cdot s={{F}_{m}}\cdot v\,dt$ $W=\int{{{F}_{m}}\cdot v\,\,dt=\int{q(v\times B)}\cdot v\,\,dt}$ W = 0 $[\because (v\times B)\bot v,$ and $(v\times B)\cdot v=0]$ Therefore, no work is done by this force on the charged particle.