Re: [Phys-l] current vector

[Jack Uretsky <jlu@hep.anl.gov>]

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:

> Bernard Cleyet wrote:
>
> "I think Moses can do a better job, but a stab -- your example is like a
> parallel plates cap. connected by a wire.  Here the current and current
> density are identical, except for pinch, skin, size, etc. effects.  So
> I'm stuck -- what's the problem?"
>
> I, personally, do not see a problem here either, although I do not agree
that the current and current density are identical, even in this example. At
the risk of getting annoying by repeating myself, 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. I also want to add
what I should have mentioned from the very beginning, that in cases 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
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