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

Jordan Morelli (Queen’s University, Kingston, Canada)
Ryszard Palka (Department of Power Systems and Electrical Drives, West Pomeranian University of Technology, Szczecin, Poland)

ISSN: 0332-1649

Article publication date: 3 July 2017

149

## Abstract

### 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-D model 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.

## Citation

Abdelqader, M., Morelli, J., Palka, R. and Woronowicz, K. (2017), "2-D quasi-static solution of a coil in relative motion to a conducting plate", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 36 No. 4, pp. 980-990. https://doi.org/10.1108/COMPEL-07-2016-0312

## Publisher

:

Emerald Publishing Limited