A related approach is to divide the charges into those nearby the point of observation, and those far enough away to allow a multipole expansion. A more general version of this model (which allows the polarization to vary with position) is the customary approach using electric susceptibility or electrical permittivity.Ī more complex model of the point charge array introduces an effective medium by averaging the microscopic charges for example, the averaging can arrange that only dipole fields play a role. In particular, as in the example above that uses a constant dipole moment density confined to a finite region, a surface charge and depolarization field results. The simplest approximation is to replace the charge array with a model of ideal (infinitesimally spaced) dipoles. To the accuracy of this dipole approximation, as shown in the previous section, the dipole moment density p( r) (which includes not only p but the location of p) serves as P( r).Īt locations inside the charge array, to connect an array of paired charges to an approximation involving only a dipole moment density p( r) requires additional considerations.
In particular, truncating the expansion at the dipole term, the result is indistinguishable from the polarization density generated by a uniform dipole moment confined to the charge region. By truncating this expansion (for example, retaining only the dipole terms, or only the dipole and quadrupole terms, or etc.), the results of the previous section are regained. If observation is confined to regions sufficiently remote from a system of charges, a multipole expansion of the exact polarization density can be made. This linear dielectric example shows that the dielectric constant treatment is equivalent to the uniform dipole moment model and leads to zero charge everywhere except for the surface charge at the boundary of the sphere.
0 kommentar(er)
