Analysis of direct current potential field around multiple spherical defects

A method for evaluating the distribution of electrical potential around multiple spherical defects was proposed. As the method is based on the known solution for a single defect, the electric field can be efficiently analyzed in comparison with the other methods, such as the finite element method. The electric field in a conductive material with multiple spherical defects at random locations is estimated by the method. The analysis shows that the increase in the potential difference normalized by the potential difference without defects, Δ V/V₀, is in proportion to the product of the volumetric density of defects and the mean of cubed defect radius, n _t[r³]_m. The universal relationship is independent of the location of defects and the distribution of defect radius. Thus, the damage due to the multiple defects can be evaluated by the increase in potential difference.