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When a charge particle experiences a time varying magnetic field which induces a non-conservative electric field, can we use the Lorentz force formula to calculate the force on the charge?

I think we can't because both electric and magnetic fields are varying continuously. So is there any other formulae regarding electromagnetic force? Or is the force the charge experiences in this case actually due to electromagnetic waves?

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Maxwell's equations together with the Lorentz force law form the foundation stone of classical electrodynamics and is successful in explaining any time-varying electromagnetic phenomenon including electromagnetic waves, where the fields are oscillating.

The Maxwell's equations are well consistent with time varying fields and hence you can use the Lorentz force equation

$$\vec{F}=q(\vec{E}+\vec{v}\times\vec{B})$$

with $\vec{E}$ and $\vec{B}$ showing time dependence: $\vec{E}=\vec{E}(t)$ and $\vec{B}=\vec{B}(t)$, consistent with the Maxwell's equations.

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