# 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

## 1 Answer

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 $dW = \vec{F}.\vec{dr} = 0$.

• This is incorrect, as explained in my answer to the question that this question duplicates. – Ben Crowell Aug 12 '13 at 18:47
• @ Ben Crowell: Your answer to that question is not correct. Magnetic dipoles are also constituted of moving charges. Hence there can be no work done irrespective of what the illusion may be. – CIA Aug 13 '13 at 8:02
• Magnetic dipoles are also constituted of moving charges. Hence there can be no work done irrespective of what the illusion may be. Do you claim that this applies to electrons, for example? What moving charges do you claim are inside an electron? Preons? – Ben Crowell Aug 13 '13 at 19:13