Question

coulomb's law does't work when charge are moving why is that?

Answer 1

This is a Physics question and it would be better to post it in that group.

Answer 2

Nonetheless, the short answer is Coulomb's law still applies: i.e., there is an attractive force between two charges q1 and q2 at a distance r still follows
\[ F_c = \frac{kq_1q_2}{r^2} \]
But in addition, moving electric charges induces magnetic currents, which then act in other ways on other electric charges.

So in other words, with moving charges, Coulomb's law only tells you on part of the picture when the charges are in motion.