The image charge inside the conducting sphere without producing any electric field In the method of images for a grounded conducting sphere, we calculate the position of image charge at $$\frac{R^2}{r}$$, due to which there should be an electric field inside the conducting sphere which violates Gauss' law. I know it's a misconception but I am confused.
 A: The image charge there does not mean that "there should be an electric field inside the conducting sphere", there should be no net electric field in the conductor.
It just mimics the electric field distribution outside the sphere.
The electric field distribution outside the conducting sphere should be the same as
the situation that there is no conductor there but an image charge placed there. It says nothing about the electric field inside the sphere.

The figure here is a cartoon diagram of an induced grounded conducting sphere (from Wikimedia commons), which may help you understand the situation.
A: The point of the method of images is to create a separate system whose boundary conditions are the same as the original problem. Then by uniqueness of solutions to Poisson's equation we can use this new configuration to find the field in the region of interest.
In other words, if we have our charge outside of the conducting sphere, the field due to this configuration outside of the sphere looks just like if we had the image charge configuration and we were only looking at the field outside of where the sphere would be. This is why in the method of images you only put image charges in regions where you are not calculating the field in. 
