# Which are other anomalies like Divergence of 1/r^2?

As one might have learned in the basic science (ex. Electrodynamic theory), when we apply the divergence theorem to the vector function like 1/r^2 with it pointing in the radial direction (like electric filed of a point charge) the direct divergence gives value zero and the integration over a closed surface gives a non zero value. Which violates the divergence theorem. The explanation given is that the function blows at the origin(Delta function).

Can anyone please point out other anomalies like this (like in this case violation of the divergence theorem) in the physics or maths?

It is very important for me and will be really helpful.

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This isn't a violation of the divergence theorem, per se. In physics, we define: $\nabla \cdot \frac{\hat{r}}{r^2} = 4\pi \mathbf{\delta}^3({\mathbf{r}})$ since the definition of divergence is $\nabla \cdot \mathbf{F} = \displaystyle \lim_{V \rightarrow 0} \frac{\oint \mathbf{F}\cdot d\mathbf{a}}{V}$ [1]