# Magnetic Field and the Speed of Light

Is it just a historical choice that both magnetic field and the Lorentz force equation include the speed of light? I figure that whoever wrote up the equations (in cgs!) could have put both factors of $c$ in either the force equation, or have define the magnetic field as being smaller by a factor of c- but they didn't. Any ideas why?

For the reference, the electromagnetic field tensor in CGS has a form $$F_{\mu\nu}=\left(\begin{array}{cccc}\hphantom{-}0&\hphantom{-}E_x&\hphantom{-}E_y&\hphantom{-}E_z\\-E_x&\hphantom{-}0&-B_z&\hphantom{-}B_y\\-E_y&\hphantom{-}B_z&\hphantom{-}0&-B_x\\-E_z&-B_y&\hphantom{-}B_x&\hphantom{-}0\end{array}\right)$$
• Just because if we absorb it into the magnetic field, then the field tensor $F_{\mu\nu}$ would consist of values $E_{x,\,y,\,z}$ and $cB_{x,\,y,\,z}$. And we prefer to make it of $E_{x,\,y,\,z}$ and $B_{x,\,y,\,z}$, without any factors. – firtree May 7 '13 at 18:39
• Then you may start with en.wikipedia.org/wiki/Electromagnetic_tensor (there is actually a $1/c$ factor in that article, because it is written in SI). A CGS survey can be found in Landau and Lifshitz volume 2 "The Classical Theory of Fields". – firtree May 7 '13 at 18:50