Electromagnetism in Linear, Homogeneous and Isotropic Materials: The Analogy Between Electricity and Magnetism in the Susceptibility and Polarization

Through the years, the asymmetry in the constitutive relations that define the electric and magnetic polarization, <b>P</b> and <b>M</b>, respectively, by the relevant vector field, <b>E</b> and <b>H</b>, has been imprinted, rather arbitrarily, in Maxwell's equations. Accordingly, in linear, homogeneous, and isotropic (LHI) materials, the electric and magnetic polarization are defined via <b>P</b> = χ_eε₀<b>E</b> ('P-E, χ_e' formulation; 0 ≤ χ_e < ∞) and <b>M</b> = χ_m<b>H</b> ('M-H, χ_m' formulation; -1 ≤ χ_m < ∞), respectively. Recently, the constitutive relation of the polarization was revisited in LHI dielectrics by introducing an electric susceptibility, χ_ε, which couples linearly the reverse polarization, P~ = -<b>P</b>, with the electric displacement <b>D</b> through P~ = χ_ε<b>D</b> ('P-D, χ_ε' formulation; -1 ≤ χ_ε ≤ 0). Here, the 'P-D, χ_ε' formulation is generalized for the time-dependent case. It is documented that the susceptibility and polarization of LHI dielectric and magnetic materials can be described by the 'P-D, χ_ε' and 'M-H, χ_m' formulation, respectively, on a common basis. To this end, the depolarizing effect is taken into account, which unavoidably emerges in realistic specimens of limited size, by introducing a series scheme to describe the evolution of polarization and calculate the <i>extrinsic</i> susceptibility. The engagement of the depolarizing factor N (0 ≤ N≤ 1) with the accompanying convergence conditions dictates that the <i>intrinsic</i> susceptibility of LHI materials, whether electric or magnetic, should range within [-1, 1]. The 'P-D, χ_ε' and 'M-H, χ_m' formulations conform with this expectation, while the 'P-E, χ_e' does not. Remarkably, Maxwell's equations are unaltered by the 'P-D, χ_ε' formulation. Thus, all time-dependent processes of electromagnetism described by the standard 'P-E, χ_e' approach, are reproduced equivalently, or even advantageously, by the alternative 'P-D, χ_ε' formulation.