Hello Physics forum, I have come here seeking for some experienced help about a doubt that to some extent is not letting me advance on my studies of electromagnetism. Basically is about the magnetic (B) field, and more specifically, about the force at each point of the vector field (The lorentz force), the thing is that I find no explanation for the equation or at least, not about the cross product that is used for the magnetic part of the force and it makes me very uneasy to continue studying all the other laws (For example, Faraday's law. ) that require such a basic definition of the magnetic field, without undestanding the why of such mathematical definition. to this point I have been able to understand most of the logic of most of the variables and functions of the system, except for this one, i don't know if anybody knows of an explanation of why the magnetic force is equal to vxB? Does it requires more advanced knowledge? or maybe it is just an empirical law without an actual mathematical proof or process to be obtained? This last possibility leads me to my other question, which is a little less problematic. Does the minus sign of Lenz's Law has some kind of mathematical proof, or it is an experimental after thought? Thanks beforehand.