# Work done by magnetic field [duplicate]

I know Lorentz force don't do any work. but I want to know whether any type of magnetic field do a work or not.

• The Lorentz force is the only force on a charged particle, and the magnetic component, as you know, is always at right angles to the velocity, so there is no work done "directly" by a magnetic field. However, it could be misleading to say that the magnetic field cannot do work at all - a time varying magnetic field always begets an electric field which does do work on a charge - alternatively one can store energy in the magnetic field - it has energy density $\frac{|\mathbf{B}|^2}{2\mu_0}$ and the electric field arising from the time varying magnetic field is how that stored work is retrieved. – WetSavannaAnimal Aug 12 '13 at 9:41
• – Ben Crowell Aug 12 '13 at 14:19

Magnetic forces do not do any work as per $\vec{F} = q\vec{v} \times \vec{B}$, irrespective of the nature of the magnetic field. This is because the magnetic force is always perpendicular to the direction of displacement so $dW = \vec{F}.\vec{dr} = 0$.