Re: [Phys-l] current vector

[John Mallinckrodt <ajm@csupomona.edu>]

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>