Related: How is the curl of the electric field possible? According to my information: $$\nabla \times \frac{\hat{r}}{{|\mathbf{r}|}^2} = 0 $$ for all $\mathbf{r}$ ( including $\mathbf{r}=0$; compare with $\nabla \frac{\hat{r}}{{|\mathbf{r}|}^2} = 4 \pi \delta(|\mathbf{r}|)$ that is zero excep...