# Why is there electric field inside conductor in between shells if inner shell is charged?

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)

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?

• The force due to charges present on outer shell would participate in redistributing. Apr 28 '20 at 16:17

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.
• 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 Apr 28 '20 at 17:02
• 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. Apr 28 '20 at 17:06