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.

Answer:

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.