Lorentz force (EM), what happens if

[fluidistic]

I'm wondering what happens (or if it makes sense) if in the formula $$\mathbf{F} = q (\mathbf{E} + \mathbf{v} \times \mathbf{B})$$ we replace $$v$$ by Lorentz factor, that is $$\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$$.
I realize that in the new formula I'm cross-producting a scalar with a vector, but I could assignate a direction to Lorentz factor.

For example, would this changed formula be more accurate than the non modified one? Or does it make sense?

 

[Vanadium 50]

It doesn't make sense.

Apart from the problem you identified, the dimensions no longer match. What problem are you trying to fix anyway? The Lorentz force equation is exact - often one uses it to define the electric and magnetic fields.

 

[fluidistic]

It doesn't make sense.

Apart from the problem you identified, the dimensions no longer match. What problem are you trying to fix anyway? The Lorentz force equation is exact - often one uses it to define the electric and magnetic fields.

Thanks for the reply.
I wasn't trying to fix anything, it occurred to me by chance. I wasn't aware that the Lorentz force was exact, nice to know.

Thanks a lot for the information.