A solid conducting sphere of radius $a$ has a net positive charge $2Q$. A conducting spherical shell of inner radius $b$ and outer radius $c$ is concentric with the solid sphere and has a net charge $-Q$. The surface charge density on the inner and outer surfaces of the spherical shell will be
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(a) Surface charge density ($\sigma$) $ = \frac{{{\rm{Charge}}}}{{{\rm{Surface area}}}}$
So ${\sigma _{inner}} = \frac{{ - 2Q}}{{\,4\pi {b^2}}}$ and ${\sigma _{Outer}} = \frac{Q}{{\,4\pi {c^2}}}$
So ${\sigma _{inner}} = \frac{{ - 2Q}}{{\,4\pi {b^2}}}$ and ${\sigma _{Outer}} = \frac{Q}{{\,4\pi {c^2}}}$
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