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I am trying to find the potential $V$ inside a sphere using the method of image charges.

I have a conducting spherical shell. The charge $q$ is inside the sphere. The sphere is ungrounded and is an equipotential because it is a conductor.

If I place an image charge $q'$ outside the sphere, I can make it equipotential if it is grounded i.e. potential$ V=0$ on the sphere. But since it is not grounded, there is some potential $V_0$ on the sphere.

To make the equipotential $V_0$ on the sphere, I can put another image charge $q''$ at the centre except that that is not allowed because I can't put image charges inside the space that I'm investigating.

Where else can I put the image charge? No matter where I put it outside the sphere it will not give me the $V_0$ equipotential on the sphere. How do I solve this?

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Your first image charge made the spherical shell an equipotential (@ V=0). So, by superposition, you can now add a uniform surface charge density to the shell, and it will stay an equipotential, but no longer at zero...

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