The depolarization field in polarizable objects of general shape

Abstract

The polarization of particles or biological cells is commonly investigated by measuring the impedance of suspensions or by a variety of single particle methods, that exploit different force effects. For biological cells the most striking frequency-dependent changes in polarizability result from structural (Maxwell-Wagner) polarization phenomena. Explicit solutions of the Laplace equation are available only for objects with finite surfaces of the second degree. Thus, dielectric models consider the structural properties of cells by assuming spherical or ellipsoidal geometries, since only in very few cases is the effective local field $E_{i}(r)$ in the presence of a dielectric object known. This concerns dielectric bodies of special shape, which are exposed to a special electric field $E_{0}(r)$. In the present paper an approximation procedure is presented for the general case, allowing to calculate the depolarization field $E_{i}(r)$, which is generated in the presence of an arbitrarily shaped dielectric object, introduced into a field space $\vec {E}_0 (\vec {r})$. Contrary to recent numerical methods (finite element technique), which require extensive computer resources due to the unavailability of analytical solutions, the here presented approach results in closed analytical expressions. The applicability of the method is demonstrated for a non-ellipsoidal cylindrical dielectric by measuring its dipole moment in a microwave field. The accordance with the calculated results is found to be one order of magnitude better than it would be in the commonly practiced procedure, where the cylinder is substituted by a spheroid of the same axis relation.