# Lorentz force (EM), what happens if

1. Oct 20, 2009

### 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?

2. Oct 20, 2009

Staff Emeritus
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.

3. Oct 20, 2009