If I move a point charge on some trajectory, then it will produce an electric field as well as a magnetic field. As the charge is moving, and as a point charge can not produce a steady current, then due to a varying current, an electromagnetic field will be induced. It will again produce another electric field, and also the magnetic field will induce electric field.

Now I am getting confused, how many electric field and magnetic are here. One electric field due to its own charge, on magnetic field due to its motion and another electric field due to the varying current.

Is the first electric field will also be occured even in magnetostatics? (due to motion of charge)

Do those two electric field follow principal of superposition? I mean do they superpose to form a ultimate resultant field?


When there are time varying fields we can write $E$ in terms of the vector potential $B=\nabla\times A.$ $$E=-\nabla V - \frac{\partial}{\partial t}A.$$ If we go to the Coulomb gauge, the term $E_{Coulomb}=-\nabla V$ is just due to the Coulomb potential of the charge as in ordinary electrostatics. And the second term $E_{induction}=-\partial A/\partial t$ is needed to satisfy Faraday's law so in that sense it is the field due to the changing magnetic field.

So yes the full $E$ field is the superposition of these two fields, but that is not a particularly useful way to think about it, because we still need to calculate $A$. It is not as easy to calculate $A$ as it is to calculate $V$ because the $B$ field depends on the changing $E$ field too (not just the current).

An easier way to figure out the $E$ and $B$ fields is to consider a point charge at rest, put the $E$ field ($B=0$ in this frame) into the electromagnetic tensor and boost with a Lorentz transformation to a moving frame.

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