Calculation of Mutual Inductance between a Circular Coil with a Rectangular Cross Section in front of a Conductor Plate and its Image Coil (1st report)

For some measuring technics, such as a distance gauge and none destructive tesing, it is important to know mutual inductance between a circular test coil with a rectangular cross section, being faced to a metal plate, and its image coil. We calculated it by two double integrals of two co-axial single circular loops, along radii and axes of the coils. But the result was an integral of a Hankel inverse transform type with products of two same infinite series of Bessel functions. We rearranged the series of the integrand in ascending powers of α^2,which was index of the thickness for the radial direction and was smaller than 1,and then integrated the 1st and the 2nd term without approximate calculus. The result was tabulated numerically and compared with the measured values. Unless the thickness of a coil for the radial direction is thick and the coil is near by the surface of the conductor, then the mutual inductance to the image coil can be calculated by the table in effective accuracy.

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