= Electric field of a uniformly charged spherical shell
{title2=$E_r(r)=0\ (r<R),\quad E_r(r)=Q/(4\pi\varepsilon_0r^2)\ (r>R)$}
Place the same positive <electric charge> $Q$ uniformly on the <sphere> of radius $R$, with no external field. Every concentric interior <Gaussian surface> encloses zero charge; <spherical symmetry> then makes the interior <electric field> zero. Outside, it is again $Q/(4\pi\varepsilon_0r^2)$. At $R$, the inner and outer limits differ by $Q/(4\pi\varepsilon_0R^2)=\sigma/\varepsilon_0$, with <surface charge density> $\sigma=Q/(4\pi R^2)$. The ideal surface charge makes the field discontinuous, so the plot displays one-sided limits rather than assigning a single field value on the charged sheet. An isolated charged conducting sphere in <electrostatic equilibrium> realizes this exterior/interior pattern.
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