= Net charge from the asymptotic radial electric field
{title2=$Q=4\pi\epsilon_0\lim_{r\to\infty}r^2E_r(r)$}
For a spherically symmetric <electric field> in <vacuum>, integrate <Gauss's law> over a sphere. Its <electric flux> is $4\pi r^2E_r(r)$, so taking the enclosing <radius> to infinity gives the displayed total charge, whenever that limit and total charge exist. In particular, a radial field decaying faster than $r^{-2}$ can be nonzero locally while its total source charge is zero. The origin must also be checked: a point charge contributes a nonzero limiting flux as $r\to0$.
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