Evaluation of nonuniform 60-hertz magnetic-field exposures for compliance with guidelines

Magnetic-field exposures are considered in compliance with guidelines if they do not cause the induced electric field or current density to exceed basic restrictions that are based on possible adverse biological responses. Magnetic-field guidelines provide induction models for extrapolating from external field exposures to basic restrictions and vice versa. However, the uniform-field exposures used in these models do not reflect the nonuniform fields often encountered in actual high-field exposures. The purposes of this study were to investigate the relationships between external magnetic-field exposures and induced electric fields in nonuniform 60-hertz fields and to present a method for evaluating the compliance of such exposures with guidelines. Induction factors provide the induced electric field per unit of incident magnetic field. They represent a means of extrapolating from external field exposure to a peak induced electric field. Uniform and nonuniform field induction factors were computed for homogeneous ellipses and ellipsoids, and for an anatomically correct heterogeneous human model. Computations were carried out for three orthogonal uniform fields and for related nonuniform fields at varying distances from three line sources. Analytic expressions were used to compute induced peak electric fields for homogeneous models in uniform fields. A scalar-potential finite-difference method computed induced quantities for all models at 3.6-mm resolution in uniform and nonuniform fields. Equivalent uniform magnetic fields that produce the same peak electric field as a nonuniform field with a known maximum field were derived from the induction factors. To evaluate a nonuniform field exposure for compliance, the equivalent uniform field for the exposure is estimated based on the magnitude of the maximum surface field and the distance from the line source. Compliance is achieved if the equivalent uniform magnetic field is below the magnetic-field limit. Equivalent uniform magnetic-field exposures are computed for two actual electric utility tasks, as examples.