Re: Flat conductors (was I need help).

[Ludwik Kowalski <kowalskiL@MAIL.MONTCLAIR.EDU>]

Thanks, David. I suspect I was not the only one to be confused
because of the lack of sufficient theoretical knowledge. Now I
know what it was about and I do not feel bad for being confused.
If I had another life to live I would start investing in theoretical
physics and in mathematics. But physics can be fun at any level,
especially when resource people are available, like on Phys-L.
Ludwik Kowalski

David Bowman wrote:

> Sorry to butt in (but merely being sorry will not stop me) regarding
> the conversation between Ludwik K. & John D.:
>
> > At my level of familiarity with physics no wavelength is
> > used to describe electrostatic or d.c. phenomena. That is
> > why I am confused.
>
> This seems to be the source of your misunderstanding.  You are
> correct that these phenomena do not entail wave phenomena.  But when
> John uses the term 'wavelength' he is *not* referring to a wavelike
> *motion* in time of any medium.  Rather he is imagining the
> dissipative/diffusive behavior of the system as being decomposed
> spatially in terms of various spatial Fourier modes, and then is
> looking at the temporal behavior of each such mode.  Since these
> Fourier modes form a complete set, *any* disturbance pattern in space
> at any instant of time can always be written as a superposition of
> them.  Each such mode involves sine (or cosine or complex exponential)
> dependence as a function of a spatial coordinate/distance.  Each such
> basis sine wave disturbance *does* have a spatial period.  It is quite
> reasonable for John to call this spatial period a *wavelength*.  It
> is just that each such spatial disturbance does *not* propagate in
> time as a wave because the behavior of the phenomenon is diffusive
> (i.e. as in a parabolic PDE) and not wavelike (i.e. as per a
> hyperbolic PDE).
>
> Thus according to John's (and normal common usage in theoretical
> physics) terminology he can speak of a wavelength without necessarily
> meaning any kind of wavelike propagation behavior.  The wavelength
> is just the spatial period of an elementary Fourier basis mode in
> space.
>
> > I suppose you are referring to a
> > transient adjustment of some kind. Whose equation of
> > motion and what kind of disturbance?
>
> The equation is a diffusion equation (a parabolic PDE) and the
> disturbance has a sine wave shape in space at each instant of
> time.  As time goes on the disturbance does not move in space.
> It just weakens exponentially with time where the decay time is
> proportional to the square of the disturbance's spatial period.
>
> > You are most likely
> > correct but I can not follow what you are saying. But I
> > am always happy to learn new things.
> > Ludwik Kowalski
>
> Maybe this translation helps?
>
> David Bowman
> David_Bowman@georgetowncollege.edu