Electrostatics – Clarification About Electric Fields Within Conducting Shells

Question

If I were to have a conducting shell that has a charge of $+q$ on the shell itself, there would be no electric field inside the conducting shell itself as if I were to apply Gauss's Law to the inside, there would be no enclosed charge and thus no electric field inside.

However if I were to have a neutral conducting shell but a point charge of $+q$ was placed inside the shell, then there would be an electric field within the shell and outside the shell as from Gauss's law there is an enclosed charge.

Are those two claims above correct? I'm not really sure about the second one as if a charge is placed inside, then electrons within the conductor will move such that they will negate out the charge inside the cavity so I am not sure what happens to the electric field in case two.

Answer 1

Your claims are absolutely correct.

1. Region between the outer and Inner surfaces of shell : In second case, there will be no Electric field inside the region between the outer and inner boundaries of the conducting shell.
2. Region enclosed by the inner surface of shell : There will be an Electric Field in the region enclosed by the shell because the application of Gauss Law is valid here and it gives the Electric Field due to the charge kept inside the shell.
3. Region on the exterior of the outer surface of shell : Also outside the shell, there will again be non-zero Electric field because of the charges induced on the outer surface of the shell. Electric fields due to the charge +q present inside the shell and the charge induced on the inner surface of the shell -q cancel each others effect outside (on applying Gauss' Law). The only contribution to the electric field outside is from the +q charge induced on the outer surface of the shell.

NOTE : Net electric field (due to all the charges inside, on the body and outside the conductor) in the Conductor's body is always Zero in ELECTROSTATIC Condition so conductor becomes as an Equipotential body because of the absence of electric field.