Lorentz force law from potentials ?

is the following derivation correct (ignoring for simplicity's sake a few factors of c):

for a single charged particle, instantaneously located at [math]\vec{r}[/math], in the Classical limit, the fields from said particle, at point [math]\vec{r}'[/math]:

[math]\Phi(r') \propto \frac{q}{r}[/math]

[math]r = \sqrt{ \left( \vec{r}' - \vec{r} \right) \circ \left( \vec{r}' - \vec{r} \right) }[/math]

[math]\vec{A}(r') = \vec{v} \Phi(r')[/math]

the potential generate the force fields:

[math]\vec{E} = -\nabla \Phi - \frac{\partial \vec{A}}{\partial t} = -\nabla \Phi - \vec{a} \Phi - \vec{v} \frac{\partial \Phi}{\partial r} \frac{\partial r}{\partial t}[/math]

the force felt by a test charge [math]q'[/math] at [math]\vec{r}'[/math]:

[math]\vec{F}' = q' \left( \vec{E} + \vec{v}' \times \vec{B}\right)[/math]

[math]\frac{\vec{F}'}{q'} = -\nabla \Phi \left( 1 - \left( \vec{v}' \circ \vec{v} \right) \right) - \vec{a} \Phi - \vec{v} \left( \left( \vec{v}' - \vec{v} \right) \circ \nabla \Phi \right)[/math]

i think the above is equivalent to

http://en.wikipedia.org/wiki/Lorentz_force#Lorentz_force_in_terms_of_potentials