Maxwell’s Equations

To describe the electromagnetic behavior of an eddy-current probe coil, and with the goal of becoming equipped to interpret the measured impedance of an eddy-current coil, this chapter describes expressions of Maxwell’s equations in full and under the quasi-static regime that is of direct relevance to eddy-current NDE. From Maxwell’s equations, equations governing the electromagnetic fields can be expressed in various ways. Interface conditions on the electromagnetic field is also provided. The interface conditions are needed, along with the governing equations, to set up a bounded system of equations that can be solved for the fields generated by eddy-current probe coils. Similarly, suitable governing equations and appropriate interface conditions provide the mathematical framework by which the influence of a test-piece—with or without a defect—on the probe impedance can be described.