Re: [Phys-l] Current as Vector

[John Mallinckrodt <ajm@csupomona.edu>]

Brian writes:

>   Let us suppose I have a cube of graphite a kilometer on a side.

That's one honkin' big piece of graphite!  (Nevertheless, I'm all for 
the analysis of extreme cases when it helps to make a point.)

> And suppose I consider a situation near the middle of this mass.
> Suppose I have a driving voltage field in an x direction,
> another driving field in the y direction, and a third  field
> in the z direction.

I will assume that I can replace

 "driving voltage field in an x direction, another
  driving field in the y direction, and a third
  field in the z direction"

with the more standard

 "electric field."

> Should I say that the current in the middle of this mass is a
> scalar, now I don't have the invisible directional constraints
> of conductive wires in air that allow me  ..er.. you to talk as though
> directionality is a given?

I simply don't know what you mean by "the current in the middle of 
this mass,"  but the situation is entirely standard.  Unless the 
graphite is in crystalline form it has an isotropic conductivity and 
the current density (a vector) at any point is proportional to the 
local electric field (another vector.)  If it is in crystalline form 
then we need to use the conductivity tensor instead.

If you really still want to know some "current," then you'll first 
have to specify an open surface and distinguish its two sides so that 
I may calculate the value of the current (a signed scalar) across 
that surface from the flux of the current density.

--
John "Slo" Mallinckrodt

Professor of Physics, Cal Poly Pomona
<http://www.csupomona.edu/~ajm>

and

Lead Guitarist, Out-Laws of Physics
<http://www.csupomona.edu/~hsleff/OoPs.html>