# Negative Electrostatic Potential Energy for a system of two point charges

This thing has been confusing me for some time now. When I try to find the potential energy of a system of two charges by evaluating the work done to bring them into a certain configuration, I get a negative value. Please correct me. Here's my work. $$U(r)=\int_{\infty}^{r}\vec{F}_{ext}.\vec{dr}$$ $$=\int_{\infty}^{r}\frac{kQq}{r^2}dr$$ (since $$F_{ext}$$ and $$dr$$ are in the same direction) $$=kQq\left(-\frac{1}{r}+\frac{1}{\infty}\right)$$ $$=-\frac{kQq}{r}$$