A metallic spherical shell has an inner radius {{rm{R}}₁} and outer radius {{rm{R}}₂} . A

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2. Electric Potential and Capacitance

medium

A metallic spherical shell has an inner radius ${{\rm{R}}_1}$ and outer radius ${{\rm{R}}_2}$. A charge $\mathrm{Q}$ 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 ?

Option A

Option B

Option C

Option D

Solution

As charge in spherical cavity $+Q$, the charge induced on inner surface of spherical shell will be $-Q$ and accordingly the charge induced on outer surface will be $+Q$.

Surface charge density on inner surface of spherical shell. $\sigma_{1}=\frac{-Q}{4 \pi R_{1}^{2}}$ and surface charge density on outer surface of spherical shell $\sigma_{2}=\frac{+Q}{4 \pi R_{2}^{2}}$.

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