Coupling of Continuum Mechanics and Electrodynamics: An Investigation of Electromagnetic Force Models by Means of Experiments and Selected Problems with Analytical and Numerical Methods

In the literature, many models of electromagnetic momentum are proposed. Each model implies a form of the electromagnetic force density, which acts as a source in the mechanical momentum balance. The debate as to which model of the electromagnetic force is “correct” for arbitrary materials and processes is ongoing. Most authors argue in favor or against specific models by virtue of thought experiments, e.g., with light waves.
The topic of this talk is to show that experiments conducted on a macro scale can conclusively eliminate models from the pool of generally applicable force models. Any electromagnetic force model predicts a total force that acts on a body as well as a local force distribution. Both predictions can be used experimentally. To do so, experiments are conceived and conducted on a macro scale in order to test the theoretical mechanical predictions of some selected electromagnetic force models. By comparing theoretical results with experimental findings, certain candidates for a generally applicable electromagnetic force model can be excluded.
The talk starts with the examination of the total electromagnetic force that acts on a body in an experiment with a magnetostatic setup. Here, the total axial force between two equal coaxially aligned permanent cylindrical magnets is investigated analytically. An analysis shows that (most) electromagnetic force models yield equal predictions for the total force in static settings—this is also the case in this experiment. However, in this example, the cylinders are treated as rigid bodies. More insight into the correctness of an electromagnetic force model can be obtained by analyzing the implications of local distributions of electromagnetic force with deformable bodies, e.g., with elastic behavior.
The first demonstrated example that analyzes implications of local effects is an elastic and linearmagnetic sphere that is placed in an external magnetic field. The induced magnetic field and the magnetization yield model-dependent predictions of electromagnetic force densities on the surface. These cause (elastic) magnetostrictions that are computed for small strains with the method of Hiramatsu and Oka. With the different employed electromagnetic force models, varying deformation shapes are obtained. For this example, no experimental data are available. However, the results motivate future experiments in this field, either for this magnetostriction problem with a spherical geometry, or a similar problem.
Another example is given that shows the implications of local effects: a droplet of silicone oil that is submerged in castor oil. The oils do not mix due to the surface tension between them. In the experiment, a homogeneous electric field that acts on the oils is activated. Due to the different permittivities of the oils, a deformation of the immersed drop can be observed. The surface stress tensor is modeled and the surface displacements are computed analytically. The solutions show different model-dependent predictions of the deformation shape. As this experiment has previously been conducted and discussed in the literature, the computed displacements can be compared with experimental photographs.
The presented examples show that it is possible to reduce the pool of candidates of valid electromagnetic force models by comparing theoretical predictions of deformations with conducted experiments, on a macro scale. The displacement (or velocity) scales in problems with fluids are considerably larger than, e.g., in the shown magnetostriction problem. Therefore, experiments with fluids seem promising for future work.