Theory for the eddy current characterization of materials and structures: applications to nondestructive evaluation and geophysics

Two problems are studied. First, a new method is presented for calculating the electromagnetic field in two conjoined conducting halfspaces in the presence of current sources in either or both halfspaces. The method allows the two halfspaces to differ in the conductivity, permeability, and permittivity. The full Maxwell's equations are used; the quasistatic results may be derived as a particular limit The method is unique in that it depends only on the solution of two variables; the components of the magnetic field, B^, and the current, ] j, normal to the interface between the halfspaces. The second problem involves the determination of the fields induced by a current source in one halfspace with an arbitrary 3D inhomogeneity in the other. New, coupled integral equations for the fields are written down strictiy in terms of B^, ] and the external current source. The same formalism, used to generate the new integral equations, is also shown to yield the standard dyadic volume integral representations. Finally, it is shown that the formalism is a useful way of deriving various asymptotic results. The weak scattering limit (the Bom approximation) is derived as an example.