Imagine that an electron is travelling with velocity +v inside a uniform sphere of charge at potential +V.(adsbygoogle = window.adsbygoogle || []).push({});

In the rest frame of the electron the charged sphere has velocity -v.

Thus in the rest frame of the electron, inside the charged sphere, there is a vector potential A given by

A = - V/c^2 v.

Now imagine that one applies a force to accelerate the electron to dv/dt.

In the electron's instantaneous rest frame there will be an induced electric field E given by

E = - dA / dt

E = V/c^2 dv/dt

The electron will feel an induced retarding force given by

F = -e E

F = -eV/c^2 dv/dt

Thus the charged sphere induces a kind of electromagnetic inertia on the electron.

Is this reasoning correct?

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# Electromagnetic inertia induced by surrounding charges?

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