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Re: EPSILON_ZERO, Coulomb, et cetera



At 11:58 AM 3/1/00 -0500, Ludwik Kowalski wrote:
Here again I am going to start teaching electricity. What will
I do with epsilon_zero this time? I always curse those who
decided to place epsilon_zero into the Coulomb Law.

I'm not sure WHY you dislike epsilon_0. I'm guessing it might be
1) You would like the force law written in simpler form,
with fewer symbols.
and/or
2) You object to the arbitrariness of the definition of
Coulomb, for reasons having nothing to do with simplicity per se.
or
3) Perhaps I've missed the point entirely.


After introducing Coulomb's law in terms of F=k*Q1*Q2/r^2,
where k is simply a proportionality constant, I will say this.

Let us invent our own unit of Q and call it S (after Satan). The
immediate consequence of this is that the unit of k must be
N*m^2/S^2. What is the numeric value of k? It depends on
how large is one S. If S is large then k is small, and vice versa.

OK, fine.

Suppose we arbitrarily declare that a point charge Q is 1S when
the force it exerts on another point charge of 1S, situated 2 meter
away, is 7 N. Why seven? Because each week has exactly seven
days. And why two? Because it is the smallest even number.

OK, you can be arbitrary if you want. Your "whys" obviously offer no
better logic than the conventional choices, and (for reasons discussed
below) are in fact worse.

What must the numerical value of k be to reflect this arbitrary
choice of the unit of charge? The answer, according to Coulomb's
law, is k=28 N*m^2/S^2. By a similar kind of reasoning the SI
designers adopted another unit of Q named Coulomb, C. A point
charge of one microcoulomb acts on another point charge of
that magnitude with a force of 1 N when the distance between
charges is 9.4815 cm. Why 9.4815? Why not? Any choice is as
good as any other choice, at least in principle, as long as we all
agree to respect it.

Do you object because it is arbitrary, or because it is not a round number?

You will presumably not be surprised to learn that the Coulomb is not
defined in terms of the electrostatic force law. I'm not 1000% sure of the
history, but the Coulomb is defined currently (so to speak) in terms of the
ampere.second, and the ampere is defined by the magnetostatic force
law. That in turn is still a bit arbitrary, but it *is* a round
number: 0.2 microNewtons per ampere squared, exactly.

Are you willing to introduce a new unit of current, perhaps the Armageddon,
defined to be one Satan per second? By so doing you would unplug your
physics teaching from whatever intuition the students might have (or hope
to have) about 15-amp circuit breakers.

The name
given to epsilon_zero, "permittivity of free space", can not be
appreciated in this introductory physics course.

Einstein said a theory should be as simple as possible, but not simpler.

There _is_ an electrostatic force law, and there _is_ a magnetostatic
force law, and the product of the two force constants has something to do
with the speed of light. You redefine one of those constants to be unity,
but you cannot redefine both to be unity unless you also set the speed of
light to be unity -- which would be fine with me but I don't recommend it
for a course at the level you seem to be asking about.