Why is the formulae for force as a result of electromagnetic forces given by:

Question

anonymous · Answer

$$F=q(E+\frac{v}{c} \times B)$$

kociela · Answer

first one comes how we have measured the electric field; so E = F / q what in turns leads to coulomb law ( not sure which one was first, but the coulomb law is derived from experimental results, theoretical should exist but don't know is there one yet ) 

In the second one i think it should be 
F = q * v x B and and can be formulated to E = v x B  
this gives the E and B perpendicular by each other which holds experimentally. that looks like it could be derived from equation compilation by Maxwell and trigonometric wave forms        ( A_c = A * sin k(x-v*t) ) which would give experimental background in the end. 

Forward from this to theoretical backgrounds goes little over my head by now. But it's possible.