Divergence of r̂ over r² ↩

aliases: []
shorthands: {}
created: 2021-10-20 18:40:54
modified: 2022-01-10 04:13:03

In every point, is radially outward, this gives the sense that this has a positive divergence everywhere, but this is not true:

But applying the divergence theorem gives us a different result:

The solution: all the divergence is compressed into the point , where blows up.
The mathematical object in the origin is called the Dirac delta function, so the divergence of the vector field is:

Corollary

It follows from this that the Laplacian of is:

Because