Effective resistance and reactance of a conductor of trapezoidal cross-section placed in semiclosed slot

The paper is an extension of a previous one and discusses the distribution of current in a conductor which has a cross-section in the form of a symmetrical trapezium and is placed in a slot with a narrow opening. An approximate solution is obtained by assuming that the upper and lower surfaces of the conductor are defined by concentric cylinders. It is found that the current density at any point may be expressed as an infinite series of Bessel functions, each term involving an arbitrary constant which is determinable by reference to the assumed boundary conditions. From this result, the complex impedance per unit length of the conductor is determined and hence also the effective resistance and the internal reactance.