= Electric field for a radial power-law charge density
{title2=$\mathbf E(r)=\frac{Ar^{p+1}}{\epsilon_0(p+3)}\widehat{\mathbf r}$}
Let the spherically symmetric <volume> <charge density> be $\rho(r)=Ar^p$, with $p>-3$ so the origin contains finite charge. Integration gives $Q(r)=4\pi Ar^{p+3}/(p+3)$. <Gauss's law> yields the radial <electric field> $\mathbf E=Ar^{p+1}\widehat{\mathbf r}/[\epsilon_0(p+3)]$ for $r>0$. The field tends to zero at the centre if $p>-1$; finite enclosed charge alone does not guarantee a regular central field.
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