Closed-form resistance and self-inductance of transformer-induced eddy currents in long plates
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2026-08-01
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Springer Science and Business Media Deutschland GmbH
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Eddy currents play a key role in a wide range of applications, including induction heating, non-destructive testing, braking, and non-contact damping. The determination of their equivalent electrical parameters, particularly resistance and self-inductance, is essential for physical interpretation and for the validation of numerical models, yet explicit closed-form formulations remain scarce. In this work, closed-form expressions are derived for the resistance and self-inductance associated with transformer-induced eddy currents in conducting plates with large aspect ratios. The analytical formulation enables the evaluation of the induced magnetic field, magnetic flux, and Joule losses, leading to compact expressions for the equivalent electrical parameters and a consistent RL circuit representation of the system. The proposed expressions provide an analytical benchmark for the validation and interpretation of numerical models of transformer-induced eddy currents in long conducting plates. The results are compared with existing analytical approximations obtained under more restrictive assumptions, demonstrating consistency while providing a physically consistent analytical description within the assumptions of dominant longitudinal currents and large aspect ratios.
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Mauraza, M., Elejabarrieta, M. J., & Cortés, F. (2026). Closed-form resistance and self-inductance of transformer-induced eddy currents in long plates. European Physical Journal Plus, 141(8). https://doi.org/10.1140/EPJP/S13360-026-08021-9