Lorenz magnetic force is acting on a particle of charge q moving with velocity V in a magnetic field B . The work done by this force on the charged particle is

Step-by-step solution

The Lorentz magnetic force acting on a particle of charge q moving with velocity V in a magnetic field B is given by F = q( V B ) . By definition of the cross product, the force F is perpendicular to both V and B . The work done by a force F through displacement d r is dW = F d r . Since d r = V dt , this becomes dW = ( F V ) dt . As F is perpendicular to V , their dot product vanishes: F V = 0 . Consequently, W = dW = 0 dt = 0 . The magnetic force does no work and therefore cannot change the particle's kinetic ene