I mean physicists when they have to create a field they draw it with the same direction of the force, (gravitational, electric for example) i know that the magnetic field acts only on moving charges and i also know that the force is a relativistic effect of lorentz contraction, but why creating a field and making it perpendicular to a force? why not representing the magnetic field vector perpendicular to the force? Trying to answer myself, please tell me if i got it or if it's wrong: so, we are trying to find a vectorial field, we know from experiments that the force created by this field is proportional to the velocity of entry of a charge and to the strenght of the field, the force is a vector. the field is a vector, the velocity is a vector, the only way we can get a vector F from v and B also vectors so that F is proportional to both is by cross product, this implies that the F is perpendicular to B so we make a vectorial field perpendicular to the force. basically we see that the force changes direction with the velocity and that has to be because of another vector acting on the velocity is this correct?