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A metallic spherical shell has an inner radius $\mathrm{R}_1$ and outer radius $\mathrm{R}_2$. A charge $\mathrm{Q}$ is placed at the centre of the spherical cavity. What will be surface charge density on
(i) the inner surface
(ii) the outer surface?
(i) the inner surface
(ii) the outer surface?
Solution:
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Verified Answer
As we know that the surface density is $\left(\sigma=\frac{Q}{A}\right)$ As per given data the charge placed at the centre of the spherical cavity is positively charged. So, the charge ( $-\mathrm{Q})$ created at the inner surface of the sphere, due to induction by charge $+Q$ at centre and due to this charge created at outer surface of the sphere is $+Q$.
So, surface charge density $(\sigma)$ on inside the surface
$$
=\frac{-\mathrm{Q}}{4 \pi \mathrm{R}_1^2}
$$
Now, surface charge density $(\sigma)$ on outside the surface
$$
=\frac{+Q}{4 \pi R_2^2}
$$
So, surface charge density $(\sigma)$ on inside the surface
$$
=\frac{-\mathrm{Q}}{4 \pi \mathrm{R}_1^2}
$$
Now, surface charge density $(\sigma)$ on outside the surface
$$
=\frac{+Q}{4 \pi R_2^2}
$$
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