Limits in mechanics

  1. [Wangs, p.204, l.-17-l.-6] treats a volume current density and a surface current density as parallel concepts, while [Fan, p. 85, l.6-l.20] treats a surface current density as the limit case of a volume current density. Therefore, if we want to visualize a surface current density as a volume current density, all we have to do is add a tiny thickness to the surface in [Wangs, p.205, Fig. 12-6 (b)].

  2. A charge density that is zero in 3-dim can be nonzero in 2-dim. If this is the case, how do we define the surface charge density? [Born, p.5, (18)] gives a proper definition. In contrast, both [Wangs, (2-16)] and [Wangs, (12-10)] are inadequate. The former fails to relate it to the 3-dim charge density and the latter fails to specify that dh0. [Wangs, (9-24)] gives unnecessary details, which make the definition more artificial and confusing. For example, it is hard to visualize how r is related to the surface charge density except through its contribution to the total charge.

  3. When we discuss the law of refraction, what does the theoretical expression l00 mean [Born, p.125, l.-10]?
    Answer. In practice, we mean that the wavelength is relatively small when compared with the radii of curvature of the incident wave and of the boundary surface [Born, p.125, l.-9-l.-7].