2-D quasi-static solution of a coil in relative motion to a conducting plate

Purpose - The aim of this paper is to present a method for calculating the electromagnetic fields, forces and current density distribution using Fourier series for a two-dimensional quasi steady state model consisting of a conducting uniform plate moving relative to an arbitrary current source with time harmonic excitation. Design/methodology/approach - The presented solution is valid for an arbitrary source. A specific source is chosen consisting of a single coil made up of two-time harmonic current filaments. The solutions are derived and presented in a form that allows its expansion to include an arbitrary number of spatially shifted coils conducting arbitrary harmonic currents. Findings - The analytical solution is compared to simulations produced using commercial finite element analysis software, ANSYS Maxwell2D and COMSOL, and is found to be in good agreement. The analytical solution provides a direct method to analyze the spatial harmonics in the system and can be computationally significantly faster especially at high relative speeds between the primary source and conducting plate. Originality/value - The presented Fourier series solution is applied to simple 2-Dmodel of a single coil with AC current excitation moving relative to a conducting plate. An analytical solution and analysis of this system has not been presented before, to the authors' knowledge, using Fourier series or any other method.