The dynamics of a charged particle with velocity $\textbf{v}$ in electromagnetic field is dominated by the Lorentz force
$$\textbf{F} = q(\textbf{E}+{\textbf{v} \times \textbf{B}}), \tag{1}$$
and the corresponding Lagrangian is
$$L = \dfrac{1}{2}mv^2 - q\phi(\textbf{r},t)+q\textbf{v} \cdot \textbf{A}. \tag{2}$$
My question is: How to derive the equation $(1)$ just from $(2)$ ?
