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this is a conceptual question which is bothering me for quite some time, we have 2 spherical conducting shells , suppose inner shell is given some charge $Q$, now charge induced on outer surface would be like this -- (sorry I didn't show that charge $Q$ would get distributed over surface of inner shell, but that is obvious)

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1) Now we know that since the shells are conducting so there shouldn't be any electric field between the region between both the shells, but there is an electric field due to inner shell which is $\cfrac{KQ}{x^2}$ where x is distance from inner shell which is greater than its radius.

2) what I think it might be a special case of electrostatics, as the field lines over the surface of inner shell would be radially outwards perpendicular to its tangential surface, so there is no component of electric field due to which charges shall redistribute on surface of inner shell, so even though there is electric field between the shell, but its in static condition so in accordance with electrostatics.

Is the logic in point (2.) correct? or is there any other reasons for this?

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  • $\begingroup$ The force due to charges present on outer shell would participate in redistributing. $\endgroup$ – Shreyansh Pathak Apr 28 at 16:17
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There is no reason for not having and electric field in the middle, between the interior and exterior shells. If that region is not a conducting solid and it is just empty space, there is a field as you suggested $$ \vec{E} = \frac{KQ}{r^2} \hat{\mu_r}$$ and the outer shell has no impact on this. The field would redistribute the charges in the outher shell so that $-Q$ lay in the interior surface and $+Q$ would lie in the most exterior surface of the outer shell.

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  • $\begingroup$ I think there are some reasons , which states there should not be any electric field between shells , like gauss law , as net charge enclosed by the closed surface between shells is $0$ it means electric field should be $0$ as well , but there is electric field due to inner shell , which means the whole argument of mine is violating gauss law $\endgroup$ – maverick Apr 28 at 17:02
  • $\begingroup$ A Gaussian sphere lying in between the other shells would enclose the central shell only and the charge enclosed is $+Q$ if I understood your question. $\endgroup$ – Nelson Vanegas A. Apr 28 at 17:06
  • $\begingroup$ yes I understood now , what you meant thanks for your help and time! $\endgroup$ – maverick Apr 28 at 17:14
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Electric field inside an enclosure like the region between shells need not be zero. Or more precisely is rarely zero. If it is a single walled enckosure-like a spherical shell and if the charges are free to move so that they can distribute themselves, only then the electric field is zero. Here since the inner sphere has all the charge... it is obvious that there is nothing to cancel the effect of one charge.

(usually in a solid sphere the charges in front of a point would cancel the effect of charges behing... this does not happen here)

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