State the formula for electric field intensity due to uniformly charged spherical shell.

Answer: Outside the shell \(E = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r^2}\); on the surface \(E = \dfrac{\sigma}{\varepsilon_0}\); inside \(E = 0\).

For a shell of radius \(R\) carrying charge \(q\) (surface charge density \(\sigma = q/4\pi R^2\)), at a point at distance \(r\) from the centre:

• outside \((r > R)\): \(E = \dfrac{q}{4\pi\varepsilon_0 r^2} = \dfrac{\sigma R^2}{\varepsilon_0 r^2}\) (the shell behaves like a point charge at its centre);
• on the surface \((r = R)\): \(E = \dfrac{\sigma}{\varepsilon_0}\);
• inside \((r < R)\): \(E = 0\).