Electric fields induced by low frequency magnetic fields in inhomogeneous biological structures that are surrounded by an electric insulator

Electric fields induced by low-frequency magnetic fields into inhomogeneous structures, which have electric conductivities and dielectric permittivities of typical biological substances, are evaluated. Closed-form approximate and numerical solutions are obtained for nonconcentric cylinders with different electric properties (such as bone embedded in muscle), which are surrounded by a good electrical insulator (such as air). It is shown that even a single inhomogeneity in an otherwise homogenous cylinder, which is exposed to a uniform, axially directed magnetic field, can lead to substantial deviations from the direction and distribution of the induced electric field that would exist in the homogenous cylinder. Thus the induced field is not everywhere circumferential, nor does it magnitude at all angular positions increase linearly with the radial distance. Radially and circumferentially directed field components depend on size, electrical properties, and eccentricity of the inhomogeneities. Equations as well as graphical presentations are given that describe the induced fields when the enclosed inhomogeneities consist either of eccentrically located single cylinders or pairs of coaxial cylinders with different electrical conductivities or dielectric permittivities.