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