THIS TEXT IS CLEARLY PIECES OF DRAFT!!! DON'T TAKE IT FOR YOUR STUDIES!!! Call me crazy/ignorant or dive with me :)

Focus on the symmetry of influences between two charges ${\displaystyle q_{1}}$ and ${\displaystyle q_{2}}$ distant of ${\displaystyle r}$.

${\displaystyle ({\frac {r}{c_{0}}})^{2}\mathbf {F} ={\frac {\mu _{0}}{4\pi }}q_{1}q_{2}\mathbf {\hat {r}} }$

${\displaystyle {\frac {r}{c_{0}}}}$ could be read as "the time required for light (or information) to travel a distance of r in empty space" (seconds)

${\displaystyle {\frac {\mu _{0}}{4\pi }}q_{1}q_{2}}$ does only depend on the charges

A force (N, or kg.m/s² according to Newton) times the square of a time (s²) is constant for a pair of charges (H.C²/m, thus also kg.m).

Other writing:

${\displaystyle \mathbf {F} =({\frac {q_{1}}{|\mathbf {r} |/c_{0}}})({\frac {q_{2}}{|\mathbf {r} |/c_{0}}}){\frac {\mu _{0}}{4\pi }}\mathbf {\hat {r}} }$

${\displaystyle ({\frac {q}{|\mathbf {r} |/c_{0}}})}$ may be the influence of an electric charge ${\displaystyle q}$ at a distance ${\displaystyle r}$ (after "charge information" ${\displaystyle q}$ traveled during the time ${\displaystyle {\frac {|\mathbf {r} |}{c_{0}}}}$ in direction ${\displaystyle \mathbf {\hat {r}} }$).

Inserting some well-chosen vector, may this quantity be associated to the magnetic spin? and vector product giving a vector in one or the other direction?

The force appears as an interaction of influences from both charges, each one locally. Problem, this distance would have been traveled only by the information coming from the other charge.

Other idea: the information traveled half path, met the other information to interact and get back "updated" to the initial charge. Another writing, making a supposition that symmetric influence "appears" at medium distance between both charges:

${\displaystyle \mathbf {F} =({\frac {q_{1}}{(|\mathbf {r} |/2)/c_{0}}})({\frac {q_{2}}{(|\mathbf {r} |/2)/c_{0}}}){\frac {\mu _{0}}{16\pi }}\mathbf {\hat {r}} }$

This is a very "quantum"-related approach, imagine "information travelers" :\ but would follow Einstein's idea of: interaction only if information has been exchanged (no interaction over space-time cone).

Singularities? (r=0)