What's the equation of kinetic energy of charged particle?

I was looking for equation of motion. I came up with a solution but it doesn't satisfy me. Cause I was trying to find motion of that particle using Lagrangian. We know that $$W=\int \overrightarrow{F}\cdot d\overrightarrow{l}$$

$W=T$ for some cases and I came up with $T=qV$. In Euler-Lagrange, kinetic energy has velocity as function, in $T=qV$ there's no velocity directly, the equation actually tells me that particle is gaining kinetic energy from potential (more precisely, potential is converting into kinetic). At first sight, I wrote that $T=\frac{1}{2}m{\ddot{r}}^2$ what if particle is massless(?) so it's not very helpful. Where I took $$L=0.5m{\ddot{r}}^2-\frac{1}{4\pi {ϵ}_0}qr$$ if I try solve Euler-Lagrange using that Lagrangian then I get $m\ddot{r}=\overrightarrow{E}$. How force is equal to electric field? It totally doesn’t make any sense to me, their dimension doesn't match either. None of these equation satisfy me. what I think that is I got wrong result for taking kinetic energy which doesn’t apply to charged particle. So what's the kinetic energy of charged particle?