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Looking for some intuition on this question:

We all learn from Gauss's law that inside a charged conducting spherical shell there should be no electric field. What about if the sphere contains a neutral plasma?

On the one hand, due to Debye shielding, a test charge placed near the sphere's boundary (but on the inside) should not be able to 'see' the charge on the more distant side of the sphere because it's effectively screened out by the mobile charge carriers in the plasma. It should therefore experience a net force from the nearest sphere wall which is unbalanced on the other side. On the other hand, Debye shielding only occurs because the mobile charge carriers move around in response to the initial electric field. So if the initial electric field is zero, perhaps Debye shielding should never occur in the first place.

Is it possible that either situation could occur depending on initial conditions/perturbations? Like, with a perfect charge distribution on the sphere and a perfectly homogeneous plasma there will still be zero electric field, but small perturbations could result in a self-reinforcing electric field inside the sphere?

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  • $\begingroup$ I am a little confused here. If I placed a single proton inside an otherwise empty conducting spherical shell, why would there be no electric field inside the inner boundary of the shell? The conductor itself, will of course, create an equal and opposite electric field within the material resulting in zero net electric field inside the conducting material. However, that doesn't mean there will not be an electric field inside the space contained by the shell. Am I missing something? $\endgroup$ Jul 21 '21 at 14:54
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The overall charge on a conducting sphere does not create an electric field inside the sphere, this is something many beginners ask about.

But a plasma is by definition ionized. Electron mobility is higher than the ion mobility, and so the outer region of the plasma will accumulate a small positive charge while the inner surface of the sphere picks up a small negative charge. This will create a detectable radial field in this rather thin region.

The other forces you surmise do not occur. For a force to be exerted, a net field must be present. But the plasma is conductive. So if you take any arbitrary sphere inside it, there is no field within that sphere. Thus, there can be none anywhere in the bulk of the plasma. Specifically, there is no rogue field to exert a force on your charged particle.

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