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Povel

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- Assuming that a charged spherical shell is moving inertially, would an accelerated observer (test charge) inside of it detect an electric field?

The electric field inside a charged spherical shell moving inertially is, per Gauss's law, zero.

If the spherical shell is accelerated, the field inside is not zero anymore, but it gains a non-null component along the direction of the acceleration, as mentioned, for example, in this paper.

The following picture from the above paper shows the field lines in the xy-plane in the instantaneous rest frame. The shell is undergoing rigid hyperbolic motion along the x-axis (toward the right)

The question I have is the following:

This question is also equivalent to asking the following ones:

I read in a couple of papers that there won't be any field detected by such observer, but this is not demonstrated and sounds strange to me.

The reasoning of these papers is that the electromagnetic tensor is invariant, so if it is zero in the inertial frame it will be zero also in the non-inertial one.

But here we are talking about the electric field only, which is a component of the electromagnetic tensor, so I don't see any a priori reason why it could not be made non-zero thanks to a frame transformation.

My reasoning for being dubious about this is that, intuitively, if one zooms out from the shell and looks at it from the distance, it will look like a point particle, and its field will also look like that of a point particle. As it has been detailed in numerous papers throughout the years (spanning over half a century), an accelerated observer looking at a point charge that moves inertially will detect continuous radiation coming from it. (An accelerated observer at rest relative to a co-accelerated point charge sees instead only a static Coulomb field).

This then seems to imply to me that, if we consider that point charge to be the charged shell as seen from the distance, then for such distant observer the exterior electric field will look just like in the first picture, and therefore I would also expect the interior field, when seen close up, to look the same.

If the spherical shell is accelerated, the field inside is not zero anymore, but it gains a non-null component along the direction of the acceleration, as mentioned, for example, in this paper.

The following picture from the above paper shows the field lines in the xy-plane in the instantaneous rest frame. The shell is undergoing rigid hyperbolic motion along the x-axis (toward the right)

The question I have is the following:

*Assuming that a charged spherical shell is moving inertially, would an accelerated observer (test charge) inside of it detect an electric field like in the image above?*This question is also equivalent to asking the following ones:

*Is there an electric field inside the shell if it is accelerating in an homogenous gravitational field? Will an observer (test charge) in the center of the shell that is not falling along with it, detect an electric field?*I read in a couple of papers that there won't be any field detected by such observer, but this is not demonstrated and sounds strange to me.

The reasoning of these papers is that the electromagnetic tensor is invariant, so if it is zero in the inertial frame it will be zero also in the non-inertial one.

But here we are talking about the electric field only, which is a component of the electromagnetic tensor, so I don't see any a priori reason why it could not be made non-zero thanks to a frame transformation.

My reasoning for being dubious about this is that, intuitively, if one zooms out from the shell and looks at it from the distance, it will look like a point particle, and its field will also look like that of a point particle. As it has been detailed in numerous papers throughout the years (spanning over half a century), an accelerated observer looking at a point charge that moves inertially will detect continuous radiation coming from it. (An accelerated observer at rest relative to a co-accelerated point charge sees instead only a static Coulomb field).

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