A numerical study of the use of magnetometers to detect hidden flaws in conducting objects

Superconducting quantum interference device magnetometers can be used to detect flaws in conducting objects by measuring the magnetic fields produced by flaw-induced perturbations in an otherwise uniform applied electric current. We examine the electric-potential and magnetic-field distributions from prolate spheroidal flaws in a homogeneous conducting plate. Beginning with Laplace’s equation in prolate spherical coordinates, we derive analytical expressions for the potential distribution outside of prolate spheroidal flaws exposed to either a uniform axial or transverse applied current. The influence of the flaw over the uniform field is practically negligible for radial distances three times that of the boundary surface of the flaw. Because the magnetic field due to the perturbation of the uniform currents by the flaw arises from the discontinuity of the component of the current tangential to the surface of the flaw, the magnetic field can be evaluated numerically using the analytical expressions for the current at the flaw surface. In the far field, B falls off as the inverse square of the distance from the flaw, consistent with the flaw acting as a current dipole. The dipole strength is determined by flaw volume and orientation, and the dependence of signal strength upon the direction of the current can be used to infer the shape of the flaw.