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Write an expression for potential at the point outside a uniformly charged spherical shell outside on the surface and inside the shell.
Solution
We have seen in chapter $1$ that for a uniformly charged spherical shell, the electric field outside the shell is as if the entire charge is concentrated at the centre and electric field obtained due to point charge.
The potential outside the shell and on the surface of shell,
$\mathrm{V}=\frac{k q}{r}(r \geq \mathrm{R})$
where $q$ is the total charge on the shell
$\mathrm{R}$ is the radius of the shell
$k$ is the coulomb's constant
The electric field at a point inside the shell is zero. Means the potential inside the shell is constant and its magnitude is same as potential at the surface of the shell.
$\therefore \mathrm{V}=\frac{k q}{\mathrm{R}}(r \leq \mathrm{R})$
