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A new method for solving problems in three-dimensional electromagnetic induction in which the Earth is represented by a uniformly conducting half-space overlain by a surface layer of variable conductance is presented. Unlike previous treatments of this type of problem the method does not require the fields to be separated into their normal and anomalous parts, nor is it necessary to assume that the anomalous region is surrounded by a uniform structure; the model may approach either an Eor a B-polarization configuration at infinity. The solution is expressed as a vector integral equation in the horizontal electric field at the surface. The kernel of the integral is a Green's tensor which is expressed in terms of elementary functions that are independent of the conductance. The method is applied to an illustrative model representing an island near a bent coastline which extends to infinity in perpendicular directions.

and magnetic fields at power line frequencies (50 and 60 Hz) in humans have been the subject of intensive scientific inquiry and considerable public concern during the last two decades. As a part of the scientific effort, extensive evaluations of induced electric field and current density in the human body have been performed. Realistic, heterogeneous, high-resolution models of the body have been analyzed using various numerical methods. Exposures to uniform and nonuniform electric and magnetic fields are considered, thus accounting for typical environmental and occupational scenarios. Numerical values of the average and maximum induced electric field and current density are given for various organs and tissues. Effects on the dosimetric measures of changes in the tissue conductivity, model resolution and organ modeling in situ, and isolation are discussed. It is shown that results from various laboratories agree reasonably well. It is also shown how the macroscopic numerical evaluation of induced fields can be further extended to model more refined cellular system. This is demonstrated for gap junction connected cells.

Contact currents occur when a person touches conductive surfaces at different potentials and completes a path for current flow through the body. Such currents provide an additional coupling mechanism to that, due to the direct field effect between the human body and low-frequency external fields. The scalar potential finite difference method, with minor modifications, is applied to assess current density and electric field within excitable tissue and bone marrow due to contact current. An anatomically correct adult model is used, as well as a proportionally downsized child model. Three pathways of contact current are modeled: hand to opposite hand and both feet, hand to hand only, and hand to both feet. Because of its larger size relative to the child, the adult model has lower electric field and current-density values in tissues/unit of contact current. For a contact current of 1 mA [the occupational reference level set by the International Commission on Non-ionizing Protection (ICNIRP)], the current density in brain does not exceed the basic restriction of 10 mA/m2. The restriction is exceeded slightly in the spine, and by a factor of more than 2 in the heart. For a contact current of 0.5 mA (ICNIRP general public reference level), the basic restriction of 2 mA/m2 is exceeded several-fold in the spine and heart. Several microamperes of contact current produces tens of mV/m within the child's lower arm bone marrow.

Abstract. In this paper, the use of the standard finite difference time domain (FDTD) algorithm is extended to quasi-static electromagnetic field problems. While straightforward application of the standard FDTD algorithm at very low frequencies leads to excessively long simulation times, we show that for linear structures this problem can be circumvented by using a ramp excitation function. The use of appropriate absorbing boundary conditions such as Berenger's perfectly matched layer is also shown to be necessary. By combining two plane waves in opposite directions, a uniform_ electric or magnetic field can be created so that the electric and magnetic field solutions are decoupled, as required in quasi-static analysis. Calculations of the induced fields and currents in a human model exposed to power line frequency fields provide a realistic example of an application of this novel FDTD technique.