Derivation of the Korteweg-Helmholtz Electric and Magnetic Force Densities Including Electrostriction and Magnetostriction from the Quasistatic Poynting´s Theorems

The Korteweg-Helmholtz electric and magnetic force densities for quasistatic systems including the Coulomb-Lorentz force density on free charge and free currents; polarization and magnetization force densities; and electrostriction and magnetostriction force densities are derived from Poynting´s theorem. In this derivation, stationary frame linear constitutive laws are used for dielectric, magnetic, and ohmic conducting media with dielectric permittivity epsiv(rho) and magnetic permeability mu( rho), which can be functions of mass density rho, itself a function of position and time, and sigma is the ohmic conductivity which can be space and time varying. Using the quasistatic Galilean transformations for electric and magnetic field variables with conservation of mass and Poynting´s theorem, results give a modified Poynting vector, differing from the usual Emacr times Hmacr by a compressibility term, but with the usual electroquasistatic and magnetoquasistatic energy densities, power dissipation density, and Korteweg-Helmholtz force densities straight forwardly derived.