The Change in Impedance of a Single-Turn Coil Due to a Flaw in a Coaxial Conducting Cylinder

The problem of detection and location of a small flaw inside a conducting cylinder using an eddy current coil coaxial with the cylinder has been addressed. The electric field at an arbitrary axial and radial position inside the conductor has been obtained from a previous solution of the boundary value problem. An expression for the change in complex impedance due to a small flaw located within a conducting body has been derived and is shown to be a function of the electric field at the position of the flaw. For the case of a degenerate point flaw, this expression is further simplified by using just the value of the electric field at the position of the centroid of the flaw. The overall impedance is shown to be a function of the ratio of the radii of the loop and cylinder and of the conductivity of the material. The expression for the change in complex impedance has been factored into two terms, one dependent on the axial location of the flaw, and the other on the depth of the flaw. The axial location of the flaw is seen to affect only the magnitude and phase of the change in impedance; whereas the depth of the flaw is seen to affect both the magnitude and phase of the change in impedance. Plots of the complex change in impedance as a function of the axial location and depth of the flaw have been provided to illustrate its functional dependence on these parameters.