In a Conductor, All the Charges Must Lie On the Surfaces. In Addition To the Charge q On the Inner Sphere, Note That Induced Positive And Negative Charges Can Strategically Be Distributed On the Surfaces Of the Outer Conduction Shell. Which Results In No Net Charge On the Shell.
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For a system of concentric sphere and shell with a given charge on the sphere the charge densities, field and the potentials are calculated at different points. With that the coulomb force on a charge due to system of point charges calculated.