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Let us take a conducting spherical shell with no charge on it initially. Now if we put a charge $+q$ on its surface (by either method of induction or contact), would charges be induced on the inner surface of the shell? If charges are induced then aren't charges induced at the centre of the shell too? What happens inside the shell cavity when we charge the shell by method of induction(what do the induced charges inside the shell do when we charge the shell)?

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If you have a spherical shell with no charge on it initially and then you put a charge on its surface. This charge will distribute over a surface. There will be no induced on the inner shell. Why? Let us suppose there is a charge on the inner surface then there will be a non-zero electric field inside the conductor which is not possible (Electric field inside the conductor is always zero). There will be no induced at the center of the shell (It's shell ).

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