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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
            Px=∈o χexx Ex+ χexy  Ey+ χexz Ez
            Py=∈o χeyx Ex+ χeyy  Ey+ χeyz Ez
            Pz=∈o χezx  Ex+ χezy  Ey+ χezz Ez                    … (1)

The nine coefficients χexx, χexy, 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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