Linear Dielectrics

The polarization of a dielectric results from an electric field, which lines up the atomic or molecular dipoles. In many substances, the polarization P is proportional to the electric field E. The general expression relating the components of P to the components of E can be written in the form
            P_x=∈_o χe_xx E_x+ χe_xy  Ey+ χe_xz Ez
            P_y=∈_o χe_yx E_x+ χe_yy  Ey+ χe_yz Ez
            P_z=∈_o χe_zx  E_x+ χe_zy  Ey+ χe_zz Ez                    … (1)

The nine coefficients χ_exx, χ_exy, and so on, constitute the electric susceptibility tensor. This situation is quite common in crystals. A crystal is generally easier to polarize in some directions than other, and in this case we use Eq. (1).


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