# Electric field at $r=0$

How does classical physics justify the existence of an electric field at $r=0$?

Is this an edge case, an ambiguity, a "does not exist"?

Is this a trivial case or indicative of an actual fault in classical electrodynamics?

Obviuosly the math breaks down because the denominator is $r^2$...What I want to know, is this significant or a trivial case?

• The force goes like $1/r^2$ for two point-like charges very far away from each other: once the charges approach, their sizes and the charge distributions come into play and the field is more than regular at $r=0$. – gented Nov 14 '16 at 21:21

To put it in another way. A point charge $e$ could be thought of as made up by many $de$ tiny charges at one spot, but you'll require an infinite amount of energy to bring two (or more) of these charges from infinity to a single and the same point.