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Re: [Phys-l] current vector



Rauber, Joel wrote in part:

Moses Fayngold wrote:

| The 8 currents in this example are NOT vectors. The vectors
| indicated in 8 brackets, are NOT currents. They are current
| densities averaged each over its respective octant.

Why do you say these are not currents, but rather current densities?

Because the expressions in the brakets are (and can only be) obtained
using ADDITIONAL information about local current density distribution.
You cannot derive them from CURRENT ONLY, this will give you just
(1/8)(dQ/dt) for each of them. Unless you introduce by hand
(as John has done) the corresponding unit vectors sticking out of the
respective octants.

>So I do not see any way you can interpret the above as a
current density.

I did not interpret anything. I did not say current density.
Current density avaraged over an octant is not identical to
local current density, as the averaged lifetime is not identical
to individual lifetime.


This is a bit like saying that Gauss law proves the electric field is
not a vector because the r.h.s is proportional to Q_enclosed which is
clearly not a vector.

You put into my mouth what I have never said, and then you dispute with
it.

It only proves that electric flux is not a vector. And your statement
only proves that flux of current density is not a vector.

Thank you for help. Your argument reiterates my own and proves
again my point with 100% accuracy. Current = flux of current density.
Flux of current density is not a vector. Corollary: current is not a vector.
Your analogy with the electric field flux also works fine.
The electric field is analogous to current density. Both are vectors.
The electric field flux is analogous to current density flux (=current).
Both are scalars. The expression for current in terms of current density
is mathematically equivalent to expression for electric flux in terms of
electric field. In some textbooks electric field is called electric flux
density, and magnetic field - magnetic flux density.


I don't think John would deny defining something different from the I_f
that occurs in the expression I_f = dQ/dt. So what. Its not all that
conventional; but it may be a useful definition in certain
circumstances, like getting the signs correct in the discharging
capacitor problem that sparked this thread.


I am not against introducing new definitions - there would be no progress
without it. But each time you do it you should say it explicitly and
unequivocally: here I introduce a new definition different from the
conventional one in this or that. In this case it has not been done, and
what is introduced is not new and is not current, but an analog of current
element (see one of my previous posters.)


Moses Fayngold,
NJIT