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Re: [Phys-l] current vector



By George! This is the second instance of a post from Jack
pointing to a difference between the physics and the maths
of an experimental measurement concerning current.
This may possibly be the first time ever, but I can see exactly
where Jack is centered in this matter, and it seems usefully
reasoned: pragmatic and experimentally based. It doesn't
get much better than that!

Brian

At 03:49 PM 2/25/2006, Jack Uretsky, you wrote:
Hi all-
The language is breeding its own confusion. Current is not a
scalar, nor a vector, nor a tensor. Current is a current, defined by the
method of making a physical measurement. Scalars, vectors, tensors and the
like are mathematical quantities. Physical quantitities and mathematical
quantities live in different universes. A priori, they have nothing to do
with each other.
->BUT sometimes mathematical quantities may be used to represent
physical quantities, under carefully circumscribed conditions. When such
conditions prevail, then the logic of mathematics permits us to make
predictions about the outcomes of physical measurements.
The "current" discussion is about flow of charge, a conserved
quantity. When a conserved quantity flows, the flow is describable by a
divergenceless vector field (a vector is associated with each point of
space, the vectors connect continuously except at points where there are
sources - leads to Gauss' law).
It may be that integrating the vector field over a region gives
rise to constructs, "currents" that are also describable as vectors.
These are as meaningful as any other description.
So "qv" is not a vector, it represents a charge times a velocity.
I may usually be represented by a vector, which is quite a different
proposition.
Take advantage of your freedom! You may represent physical
quantities by vectors whenever the representation is accurate. But do not
confuse the physics and the mathematics. They are not the same.
Regards,
Jack




On Sat, 25 Feb 2006, Fayngold, Moses wrote:
//// current is an integral
characteristic of the process of charge transfer and a scalar, whereas the
current density is a local characteristic and a vector. ///when we do
have a certain direction singled out, (like in case at hand), we use what is
called the CURRENT ELEMENT: dI = Idl - that is the product of current I and
the incremental displacement vector dl along the direction of propagation.
This is suited specifically to treat the problems mentioned in this
discussion and also when we have thin current filaments (see, e.g., J.D.
Jackson, Classical Electrodynamics, 3-d ed., John Wiley & Sons, p. 175 and
further on.), and shows again that current itself is a scalar quantity. A
moving point charge
qv mentioned by John Denker, while being a vector, is NOT a current, but
yet another example of a current element.

Moses Fayngold,
NJIT


Brian Whatcott Altus OK Eureka!