Re: Current Density?

[Brian McInnes <bmcinnes@PNC.COM.AU>]

Brian Whatcott asks me:
> > (By the way, I find the term "per [unit] volume" rather meaningless,
> > but that is another story.)
>
> This is an interesting comment that I would be glad to see
> developed.   The concept of unit volume in itself is not difficult -
> at least for liquids under gravity: one picks a bottle without leaks
> as a container, and acknowledges that temperature and pressure, maybe
> atmospheric humidity are confounding variables.
> One thinks of a pyknometer and how this relies on mass measurement:
> perhaps that's the cause of Brian's difficulty?
> (a certain circularity...)

My difficulty is that "per unit volume (or whatever) comes across to
me as a cant phrase which we recite because it falls off our lips and
not for any understanding it carries.

per = "for each"; I don't have a problem with its use with the reading
of a value: 5g/cm^3 is read as  grams per cubic centimetre.  I do have
a problem with its use with the phrase "unit volume".

unit volume: this implies there is a unique "unit volume" (or unit
area or unit length).  What if the unit volume is not available?
Materials don't usually come in cubic metres or square metres or
metres.

Why not just the ratio of, say, mass to volume, or, if we anticipate
difficulties with the audiences' grasp of the ratio concept, just mass
divided by volume.

If we were asked to explain exactly what was meant by a statement that
the current density, for example, was 6.2 A/m^2, we would say that if
the conductor had a thickness of 1m^2 (and the current through it was
the same everywhere) then the current through it would be 6.2A.

Brian McInnes