The vector decomposition theorem of Helmholtz leads to a form of the Coulomb gauge in which the potentials are expressed in a form that is totally instantaneous. The scalar potential is expressed in terms of the instantaneous charge density, the vector potential in terms of the instantaneous magnetic field.

The dependence of frictional forces between mica surfaces on humidity, particularly in the low relative humidity range, has been studied with the surface force apparatus. The dynamic shear stress decreased with increasing humidity. When the humidity was lower than 40%, a large static frictional peak was observed before initial sliding. This peak did not reappear after stopping temporarily and resuming the motion but appeared again after the surfaces had been separated, if only for a few seconds, and brought into contact once more before sliding. To clarify the nature of this static frictional peak, frictional forces and adhesion during, before, and after sliding the mica surfaces were studied in detail. The dependence on humidity of shear stress and pull-off force suggests that layering of adsorbed water on and between the mica surfaces is important. The results of the measurements of kinetic shear stress as a function of sliding velocity at different humidities revealed the role of water condensed around the contact zone. A mechanism based on capillary condensation is proposed to explain the role of humidity on friction by adsorption of water layers on the free mica surfaces and at the contact.

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Abstract.By means of the Helmholtz theorem on the decomposition of vector fields, the angular momentum of the classical electromagnetic field is decomposed, in a general and manifestly gauge invariant manner, into a spin component and an orbital component.The method is applied to linearly and circularly polarized plane waves in their classical and quantum forms.