Viewpoints in Mechanics
- Each theory or theorem has a viewpoint, which dictates how it starts. In
order to take advantage of parallelism to foresee the directions of the theory's
development so that we may move forward, solidify our understanding and simplify our theory, we must shift our point of view from time to time.
Electrostatics and magnetostatics are similar. If we regard E and H as a pair, we have
formally parallel equations [Born, p.76, (1) & (2)]. This is the reason
why we call H the magnetic field. However, from the viewpoint of the influence
of matter, we should physically regard E and B as a pair [Born, p.1,
In order to obtain the scalar and vector potentials for polarization and magnetization
[Born, p.77, (19) & (20)], we start with the entire set of Maxwell's equations
[Born, p.76, (3)-(6)] using [Born, p.72, (1)-(4)] (in vacuum) as the model.
[Born, p.77, (19) & (20)] can be regarded as the general solution of the
differential equations [Born, p.76, (3)-(6)]. It
is unnecessary to use auxiliary concepts such as polarization charge
densities or magnetization current densities. In order to obtain [Wangs, p.143,
(10-6)], [Wangs, §10-2] shows that we may as
well start with more inspiring and directly related [Wangs, p.114, (8-21)]. In order to obtain
[Wangs, p.314, (20-6)], [Wangs, §20-2] shows
that we may as well start with [Wangs, p.300, (19-21)] rather than the entire
set of Maxwell's equations.