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Re: SI and electric charge



With regard to your last paragraph, how do you determine that
two charges are "identical"?
Regards,
Jack

On Thu, 3 Jan 2002, Ludwik Kowalski wrote:

"John S. Denker" wrote:

... I hope we can agree that good metrology is not
necessarily good pedagogy, and vice versa. ...

Certainly.

... Again: pedagogy is not the same as metrology,
or history, let alone the history of metrology. ...

Tangential remark: The fundamental laws of physics don't
require any particular number of units. In MTW (Misner,
Thorne, Wheeler _Gravitation_) they use centimeters for
almost everything: cm of distance, cm of time, and cm of
mass.

I would not teach introductory physics that way.

Also: Metrologists speak of "base units" in contrast to
"derived units". There are various units that form the
"base" of SI, but these cannot be considered "basic" in
the sense of "fundamental" or "absolute". They are
more-or-less arbitrarily chosen, which makes them about
as non-fundamental as they could possibly be.

You are ABSOLUTELY correct. That is why introducing C
before A is inconsequential, as far as the SI is concerned.
But this sequence is pedagogically desirable, in a first
physics course.

To my way of thinking, derived units are derived from
the "base" units _without_ introducing any new fudge
factors in the derivation. That means that the number
of base units is roughly equal to the number of arbitrary
fudge factors.

For example, if we consider meter and second to be "base
units" then the derived unit, m/s, is associated with the
"fudge" factor of 1. Likewise with m/s^2 derived from the
definition of acceleration, or with N derived from F=m*a.
But the k, in Newton's law of universal gravitation, is
not a fudge factor. It is a quantity to be measured. In
Coulomb's law, on the other hand, according to my
proposal (see below), k~9,000,000,000 is a fudge factor.
The same k is not a fudge factor when A is defined
before C. This (common practice today) turns k into a
quantity to be measured, like G. I would prefer k to be
a fudge factor and the coefficient in the Biot Savart law
to be a measurable quantity. At present that coefficient
is fudge factor defining A (indirectly).

Was the term "fudge factor" used by me the same way
as what JohnD had in mind? If not then another terms
should be found to distinguish coefficients "by definition"
from coefficients "by measurements".
Ludwik Kowalski

... It turns out that the magnitude of an electric force
between two charges (q1 and q2) is proportional to the
product q1*q2 and inversely proportional to the square
of the distance (d^2) between their centers. This
observation ... is known of Coulomb’s law.

F = k*q1*q2 / d^2

where k is the proportionality constant. The value of that
constant can be chosen arbitrarily in order to define a unit of
electric charge. For the purpose of this introduction the unit
of electric charge, one coulomb, C, we will defined by
declaring that k=8,987,551,000. This is equivalent to saying
that the electric charge is one coulomb if it attracts or repels
an identical charge with a force of nearly nine billion newtons
when the distance between the centers of two charges is one
meter.


--
"But as much as I love and respect you, I will beat you and I will kill
you, because that is what I must do. Tonight it is only you and me, fish.
It is your strength against my intelligence. It is a veritable potpourri
of metaphor, every nuance of which is fraught with meaning."
Greg Nagan from "The Old Man and the Sea" in
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