Analytical calculation of the force between a rectangular coil and a cuboidal permanent magnet

This paper concerns the analysis of the force between a rectangular coil and a cuboidal permanent magnet. The magnetic flux density distribution due to the permanent magnet is determined using the surface charge method, and an analytical equation is obtained for the Lorentz force on a cuboidal current carrying volume. These analytical results are used to calculate the Lorentz force on a rectangular coil modeled using four current carrying volumes. The calculations are verified both by measurements and numerical integration. These results can be used in the design and real-time control of planar actuators for industrial levitation/positioning platforms or other (ironless) actuators