# Maxwell's equations from continuum limit

In appendix A.6 of Schroeder's Thermal Physics, he mentions (in regards to classical fields):

The usual approach is to first pretend that the continuous object is really a bunch of point particles connected together by little springs, and eventually take the limit where the number of particles goes to infinity and the space between them goes to zero. The result is generally some kind of partial differential equation (for instance, the linear wave equation or Maxwell's equations) that governs the motion as a function of place and time.

I take the part in parentheses to mean that there's some way to derive Maxwell's equations from the continuum limit of some sort of system of springs. I'm familiar with deriving the wave equation from a system of springs, but have never heard of obtaining Maxwell's equations and can't seem to find anything that mention it other than this somewhat vague reference. I'm not even sure what the "springs" would be for this case unless we're talking about oscillations of the electromagnetic field. in which case the derivation would seem kind of circular to me. Is this some remnant of aether theory or something? An explanation of the procedure would be appreciated.

• I am not completely sure but here it goes: While not exactly springs, I think the author might be alluding to the derivation of macroscopic Maxwell equations from microscopic ones, by, for instance, considering a spacial averaging over bounded and free charges/currents, which will, at first approximation, include vibrational effects of atoms/molecules around their center of mass. Take a look of section 6.6 in Jackson's book, Classical Electrodynamics, 3ed, and the references suggested in there. – secavara Mar 9 '18 at 1:37
• Apparently, this is how Maxwell derived his equations. – flippiefanus Mar 9 '18 at 4:22