Theory of the measurement of thickness and conductivity of cylindrical shells by an inductive method

Abstract

We consider the case of a solid cylinder of arbitrary conductivity, covered by a thin shell of conductivity σs. The coated cylinder is assumed to be located inside a primary exciting coil, and also inside a secondary detection coil. A time-varying current in the primary induces currents in the sample, and these currents are reflected at the secondary. We derive expressions for the time constants of the decay of the secondary voltage. We relate the dominant time constant to the conductivity and the thickness of the shell. If the conductivity of the shell is known, then the simple measurement of a time constant allows the determination of the thickness of the shell. The special case where the conductivity of the inner cylinder is zero is analyzed in detail. The method of measuring the thickness of the shell by induction is shown to be of practical importance in the case of thin metallic films deposited on a cylindrical substrate. We show that the dominant time constant for this case depends linearly on the thickness of the film. Thus measurements on a cylindrical shell are shown to be more convenient than measurements on flat films, where the dominant time constant is proportional to the square of the thickness of the film.