Conducting sphere with chrage in centre

[Taylor_1989]

Homework Statement

Consider a conducting sphere of radius $R_1$. Inside it there is a cavity, spherical in shape, with it origin at the same point as the conducting sphere and of radius $R_2$ $(R_1>R_2)$. Assume there is a point charge equal to $+Q$ at the origin.

Use Gauss law to calculate the value of the electric field, E

Homework Equations

The Attempt at a Solution

I have no working because I am looking at this from a logical perspective and just want to know if my logic is correct.

my assumption is that this sphere with cavity is electrical neutral, so with the charge in the center being positive, then this will induce negative charge onto the inner shell, so then the electric field on the outside the shell will be the same, as the electric field insie the cavity and the, region between the outter surface and the cavity will be 0

Is this logic correct

 

[kuruman]

... then the electric field on the outside the shell will be the same, as the electric field insie the cavity ...

Mostly correct except that the field inside the cavity has the same radial dependence as the field outside the sphere but it cannot be construed to be same.

Now what? You are asked to find the electric field using Gauss's Law. Logic alone will not do that.