electrostatics - Force when distance between charge is zero

According to coulomb law

$$F = \frac{q_1q_2}{r^2}$$

I want to know what happens to force when $r=0$. If $F \to \infty$ then the charges can't be separated! But if an unlike charge of higher magnitude is placed beside any of $q_1$ or $q_2$ then it gets attracted. Can anyone clear me out?