Integral expressions for self and mutual inductances of circular coils with rectangular winding cross sections

The method of extracting inductance based on formulas has been widely used due to its simplicity and efficiency. The literature primarily includes various formulas for inductance, which have been derived using different approximations. A detailed comparison of their accuracy and applicability is generally unavailable. This makes it challenging to select the most suitable option for applications that require high precision in the results. In this paper, an expression for the self- and mutual inductance of coils with rectangular cross sections is derived, which does not involve any approximation except for the absence of axial and radial currents. The accuracy of the formulas is verified by comparing them with the results obtained previously in various limiting cases. The Gaussian units are used throughout the paper.