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While it is true that the notion of current often--as when it flows
in a thin wire--has a strong directional sense to it very much LIKE a
one dimensional vector, I don't see how one can rigorously treat it
as a vector.
Suppose I have a REAL wire with some current flowing in it. I
challenge anyone to give me an operational procedure to rigorously
associate a useful "vector current" with a specific position (or
cross section or whatever) of the wire.
John Denker wrote:
We would have big problems with the Biot-Savart law (among other
things) if [current were not a vector.]
I disagree. It is true that I am guilty of having pointed out to
classes that it might seem somewhat odd to use "I dl_vector" (as most
textbooks do) as the infinitesimal source element in the Biot-Savart
law. Superficially, at least, it might seem more attractive to
associate the direction of the source element with the current itself.
As a practical matter, however, one usually comes to realize the
advantage of associating the direction with the dl_vector after doing
some complicated integrals using the Biot-Savart law.
More to the point, the Biot-Savart law really OUGHT to be written
using "j_vector dV" (where dV is an infinitesimal volume element) as
the infinitesimal source element, but I'd just as soon skip the
unnecessary headaches THAT would surely cause in an introductory
course.
--
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>
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