Forces on Moving Magnets due to Eddy Currents

TLDR

A moving magnet or coil above a conducting plate experiences magnetic lift and drag forces due to induced eddy currents. The study examines how these forces relate to magnetically supported high‑speed vehicles. Lift and drag are computed for various thin‑plate coil geometries, with high‑speed lift approaching the image‑force limit and drag decreasing as velocity⁻¹. The lift‑to‑drag ratio is geometry‑independent, while lift’s velocity dependence varies with geometry, and a superconducting coil can achieve a lift‑to‑weight ratio of up to 2000 at 300 mph 0.1 m above the plate.

Abstract

A magnet or a current-carrying coil, moving with constant velocity above a conducting plate, will experience magnetic lift and drag forces from the eddy currents induced in the plate. The lift and drag forces are calculated for various coil geometries on the assumption that the conducting plate is thin. For this model, the lift at high speeds approaches the force between the coil and its ``image'' located directly below it, and the drag force falls off as (velocity)−1. The ratio of lift to drag is found to be independent of coil geometry, but the velocity dependence of the lift is greatly affected by the geometry. The ratio of lift to coil weight can be as high as 2000 for a superconducting coil moving at 300 mph at 0.1 m above a conducting plate. The relevance of the calculation to magnetically supported high-speed vehicles is discussed.