Equivalence principle: electric charge and coil

The near-range magnetic field $vec{B}$ of a point charge $q$ at distance $vec{r}$, moving at a non-relativistic velocity $vec{v}$, is given by

$$vec{B}=frac{q}{4piepsilon_0c^2}frac{vec{v}timeshat{r}}{r^2}.$$

Faraday’s law of induction for the induced EMF $V_c$ in a coil, with area $A$ and turns $N$, due to a changing magnetic field strength $dB/dt$ through its center is given by

$$V_c=-NAfrac{dB}{dt}.$$

In scenario $A$ the charge $q$ is falling downwards due to the gravitational force $mg$ and the coil is fixed at a distance $r$ so that the induced voltage $V_c$ measured by the coil is

$$V_c = – frac{1}{4piepsilon_0c^2}frac{N A q g}{r^2}.$$

But according to the equivalence principle this is exactly the same as scenario $B$ in which the charge $q$ is fixed and the coil at distance $r$ is accelerating upwards with acceleration $g$.

In scenario $B$ is there still an induced voltage $V_c$ across the moving coil?

I think one could actually do an experiment like this but one would replace the charge with a parallel plate capacitor.

Further comments

In scenario $A$ I assume the charge is freely accelerating downwards due to the force of gravity whereas the coil is fixed to the Earth/observer (Newtonian viewpoint).

In scenario $B$ I assume the charge is at a rest whereas the coil (and the Earth/observer) is accelerating upwards (Einsteinian equivalent viewpoint).

Therefore I assume there is always a relative acceleration between them.

I think you get a voltage in the coil in both scenarios but as I understand it standard EM theory says you only get a voltage if the charge itself is accelerating.

One could argue that a falling object is not really accelerating as it does not experience proper acceleration. But it certainly looks to the observer on Earth that it is accelerating! This common sense Newtonian view is backed up by the modern weak-field description of gravity as a standard force, acting in flat spacetime, mediated by gravitons.

A better version of the argument?

One could imagine a Newtonian scenario where the charge is at a fixed position in the gravitational field and the coil is accelerating downwards under the force of gravity.

In the equivalent Einsteinian point of view the charge is experiencing an upwards proper acceleration to keep it at a fixed position whereas the coil feels no forces in an inertial frame. According to standard EM theory the accelerating charge should induce a voltage in the coil.

Therefore in the equivalent Newtonian point of view there should also be a voltage across the coil.

Possible explanation of reciprocal effect using virtual photons

I think Newton’s third law of equal and opposite action and reaction applies in the case of electromagnetic interactions between charged particles, and does obey special relativity, by the following mechanism:

Charged particle A emits positive energy virtual photons forwards in time that impart energy-momentum to particle B. Simultaneously particle B emits negative energy virtual photons backwards in time that impart an equal amount of opposite energy-momentum back to particle A.