Consider a positive charge $Q$ at the origin.What is the work done in bringing a unit positive charge from infinity to zero.
We know that the work done in bringing the charge from infinity to $r$ is the electrostatic potential $$V(r)=\dfrac Q{4\pi\epsilon_0 r}$$
But what is the work done to bring it from infinity to $0$, i.e,when $r=0$?
Can we bring it initially from infinity to $r$ and then from $r$ to $0$?
Then what is the work done in bringing a unit charge from $r$ to zero?
Best Answer
It would take an infinite amount of work to bring the charge to $r=0$ where $Q$ is, regardless of whether you start infinitely far away or finitely far away. The repulsive force between the two charges gets infinitely strong as they get infinitely close, and you have to work against it.