Theoretical models for the remote field effect

The Remote Field Effect is used extensively for testing of thick tubular products where deep penetration into (primarily ferromagnetic) materials is required (1). The testing apparatus consists of two coils, one generating a magnetic field, the other is used as a pickup coil. The distance between the two coils is normally large (of the order of two coil diameters). The operating frequency is low, normally below 100 Hz. The method has been assumed in the past to rely on a special effect, and therefore the name Remote Field Effect. One of the most remarkable aspect of the method is its equal sensitivity to inner and outer defects in thick ferromagnetic tubes. This effect could not easily be explained by direct induction and therefore, many models have been proposed. The common model used is that of a wave propagating from the inside of the material to the outside and then back again (2). We propose a theoretical model that shows the effect to be merely that of induction at large distances (3-5). The field equations are solved directly using first an analytic Bessel function approach and then using an integral approach. Both of these models confirm the basic results associated with the remote field effect and also include the velocity of the coils. The models described here are general and applicable to other induction applications.