Electromagnetic-force distribution inside matter

Using the method of finite difference time domain, we solve Maxwell's equations numerically and compute the distribution of electromagnetic fields and forces inside material media. The media are generally specified by their dielectric permittivity ε(ω) and magnetic permeability μ(ω), representing small, transparent dielectric and magnetic objects such as platelets and microbeads. Using two formulations of the electromagnetic force density, one due to Lorentz and the other due to Einstein and Laub, we show that the force-density distribution inside a given object can differ substantially between the two formulations. This is remarkable, considering that the total force experienced by the object is always the same, irrespective of whether the Lorentz or the Einstein-Laub formula is employed. The differences between the two formulations should be accessible to measurement in deformable objects.