Lorentz Force on Dielectric and Magnetic Particles

Abstract

The well-known momentum conservation theorem is derived specifically for time-harmonic fields and is applied to calculate the radiation pressure on 2-D particles modeled as infinite dielectric and magnetic cylinders. The force calculation results from the divergence of the Maxwell stress tensor and is compared favorably via examples with the direct application of Lorentz force to bound currents and charges. The application of the momentum conservation theorem is shown to have the advantage of less computation, reducing the surface integration of the Lorentz force density to a line integral of the Maxwell stress tensor. The Lorentz force is applied to compute the force density throughout the particles, which demonstrates regions of compression and tension within the medium. Further comparison of the two force calculation methods is provided by the calculation of radiation pressure on a magnetic particle, which has not been previously published. The fields are found by application of the Mie theory along with the Foldy-Lax equations, which model interactions of multiple particles.