A metallic spherical shell has an inner radius R1 and outer radius R2. A charge Q is placed at the centre of the spherical cavity. What will be surface charge density on (i) the inner surface, and (ii) the outer surface?


Since the spherical shell with an inner radius R1 and an outer radius R2 is metallic, there are free electrons in the shell. The positive charge Q is placed at the centre of the spherical shell as shown in the figure below.


The charge Q will cause equivalent negative charge -Q to be induced on the inner surface while there is equivalent positive charge +Q induced on the outer surface.



Surface charge density is given by



Therefore, Surface charge density on the inner surface is



Surface charge density on the outer surface is



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