Given an uncharged continuum the EM field produces no force on it. Yet in a discrete system we know that atoms are not uncharged locally and momentum can be exchanged due to the electric field(Which Maxwell's equations are suppose to govern).
viz., The transfer of momentum between atoms is due to the electric field(although it's not as simple as the 1/r^2 version). Maxwell's equations should describe the motion of the atoms exactly when one includes the Lorentz force and Newton's second law.
Yet when one moves up to the continuum these microscopic effects no longer exist and the electric field cannot influence the mechanical motion of density if it is not charged.
How can we include this in Maxwell's equations(or probably instead in the Lorentz force)?
I'm thinking that we simply use and it's conservation law(on the same page)
but there doesn't seem to be a way of controlling how well the EM energy is coupled to the material(Some materials will experience a larger motion due to the EM field it experiences).
in both cases though q = 0 for the continuum.
I think was thinking that possibly one could temporarily treat the continuum as being charged even though it isn't which will allow the momentum due to the field to propagate and one could compute forces and such. With proper scaling one might get the same effect as if modeling a discrete material. Effectively one is breaking up the material into positive and negative charge, computing the momentum then subtracting... in a continuum this is 0 but for the discrete case it cannot be zero unless there are no particles.
What is a better way? How can one model the microscopic collision transfer of momentum that can be applied to the continuous case?