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Homework Statement:

In spherical poler coordinates the volume integral over a sphere of radius R of $$\int^R_0\frac{\hat r}{r^2}dv=\int_{surface}\frac{\hat r}{r^2}•\vec ds$$
$$=4\pi$$
Relevant Equations:

In spherical poler coordinates the volume integral over a sphere of radius R of $$\int^R_0\frac{\hat r}{r^2}dv=\int_{surface}\frac{\hat r}{r^2}•\vec ds$$
$$=4\pi$$
In spherical poler coordinates the volume integral over a sphere of radius R of $$\int^R_0\vec \nabla•\frac{\hat r}{r^2}dv=\int_{surface}\frac{\hat r}{r^2}•\vec ds$$
$$=4\pi=4\pi\int_{\inf}^{inf}\delta(r)dr$$
How can it be extended to get $$\vec \nabla•\frac{\hat r}{r^2}=4\pi\delta^3(r)??$$
$$=4\pi=4\pi\int_{\inf}^{inf}\delta(r)dr$$
How can it be extended to get $$\vec \nabla•\frac{\hat r}{r^2}=4\pi\delta^3(r)??$$