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At 01:27 PM 3/22/2006, John M., you wrote:You have described a situation in which it is impossible to obtain a quantity with the units of Amperes unless you choose a particular area through which you are going to watch the current flow, thereby imposing the directional constraints that you trying to avoid. Conversely, if you allow me to choose whatever area I wish, then I can obtain a current of completely arbitrary magnitude, so the concept "the current in the middle of this mass" is completely ill-defined.
Brian wrote:
I certainly can find counter examples to the assertion that resistance
is a scalar. Plastic films show notable non isotropism.
You don't need exotic materials to make resistance "dependent" (in
some sense) on "direction." For instance, what is "the resistance"
of a 1 cm x 2 cm x 3 cm block of graphite?
Nevertheless, in my book, resistance is a SCALAR property of a) a
given object and b) a well-specified electrical connection scheme*.
If the object is anisotropic, the anisotropy is expressed through a
conductivity TENSOR relating the local current density (a VECTOR) to
the local electric field (another VECTOR). That anisotropy is taken
into account along with the connection details when determining the
SCALAR resistance.
* I recognize that resistance may also be a function of applied
voltage, temperature, and perhaps other things, but that doesn't
detract in any meaningful way from the point I am trying to make.
--
John "Slo" Mallinckrodt
Since you raised the idea of resistance properties in bulk, perhaps
I can return the favor and raise the properties of current in a
bulk material.
Let us suppose I have a cube of graphite a kilometer on a side.
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.
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?