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Re: Ohm's 'law' & minus sign



Chuck Britton wrote:

Has anyone else run into the Pedagogical Position which requires
Ohm's Law to be written with a MINUS sign?!?!?!?!

The justification seems to parallel the addition of the minus sign
known as Lens' Law in the EMF = - d(phi)/dt equation.

I need to be convinced, one way or the other. If it is as 'arbitrary'
as the Lens' Law sign, I'm inclined to leave it OUT!!!

1) I think the sign in Ohm's law is, physically
speaking, completely arbitrary -- but practically
speaking it is very firmly fixed by convention.

To shed some light on this, consider a multi-terminal
resistor (as opposed to the usual two-terminal model).
Take a bunch of resistive goo and stick N leads on it.

Then there will be N voltages (although perhaps only N-1
of them are interesting, because of gauge invariance) and
N currents (only N-1 of which are independent because of
charge conservation).

a) For each lead, it is _entirely_ arbitrary, or conventional,
whether you name the inward and outward current as positive
and negative current, or vice versa.
b) Similarly, it is _entirely_ arbitrary which terminal, if
any, you choose as your zero-reference when exercising your
gauge freedom.

Jiggering either (a) or (b) is sufficient to flip the
sign in Ohm's law for a two-terminal resistor. But why
bother? For purposes of communication, and for purposes
of pedagogy, it makes sense to stick with the conventional
choices of how to orient the voltmeter and how to orient
the ammeter when doing the Ohm's law experiment.

=====================

2) I don't consider the sign in Lenz's "law" to be nearly
so arbitrary.

If you have one coil (the primary) lying next to another
coil (the shorted-turn primary) there will be a minus sign
in the ratio (delta I2)/(delta I1), unless you make some
perversely inconsistent choices as to the orientation of
the ammeters.

Note the spelling on Lenz.