Hollow charged spherical shell with charge in the center and another charge outside

Question

I came across this question :

A thin metallic spherical shell contains a charge $Q$ on it. A point charge $q$ is placed at the Centre of the shell and another charge $q1$ is placed outside it. All three charges are positive. What is the force on the charge at the Centre?

Answer options are: - (a) towards left (b) right (c) up (d) zero
According to solution : - its (d) zero
Now I am confused as I know that field inside the shell is zero but there will be field from q1 which will have force F towards left right. So searching for an answer , I came across a point that shell acts as a faraday cage, thus blocking the field outside it.
So I would like you to explain the shielding effect of shell and also if this works only for conducting shells or does it work for non-conducting shells too?

Young Kindaichi · Accepted Answer

I'm going to use the following Corollary (For proof see Section 3.3 Electricity and Magnetism by Purcell)

In the space inside a hollow conductor of any shape whatsoever, if that space itself is empty of charge, the electric field is zero.

Now suppose if the charge $q$ weren't present in the shell, then the field inside this shell would be zero, due to the uniqueness theorem as give above. This fact is independent of whatever is going on with charge $q_1$ or $Q$. If we now reintroduce $q$ at the center of the shell, this induces a total charge $-q$ on the surface of the cavity. This charge is uniformly distributed over the surface because $q$ is located at the center. This charge, therefore, doesn't change the fact that the field is zero at the center of the cavity. The force on $q$ is therefore zero.
P.S. this would not work for a non-conducting shells.

Hollow charged spherical shell with charge in the center and another charge outside

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