Re: On 1/4*Pi*epsilon in Coulomb's law

[Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>]

"Timothy S. Sullivan" wrote:

> ... Everything about physics isn't perfectly rational. Some
> things just have to be accepted (although you do want to keep
> it to a minimum, of course.) ...

"To keep it to a minimum" we must be trying to improve what
we can. Nobody is in a better position for identifying bad things
than us, teachers.

Ludwik Kowalski wrote:

> ... Perhaps a new sequence of teaching electromagnetic
> topics can be invented to match the SI system. I do not
> think that the SI will go away very soon and new
> sequences are worth trying. Another approach is to
> invent a better system of units for our traditional
> sequence (which begins with electrostatics). ...

Let me try the second approach; it is much easier than
the first. Suppose a new unit of electric charge, to be
named chunk, is introduced. One chunk is defined by
making the Coulomb's law coefficient dimensionless
and equal to unity. In other words, one chunk is a charge
which acts on a charge of the same magnitude with a
force of one newton when the distance is one meter. It
is not difficult to show that 1 chunk is about 10.5 mC.
All other electrical units would be based on chunk, (as
they used to be based on the esu in the old CGSE system).

Inventing arbitrary names for new units (such as chunk) is
probably not desirable. Therefore I will be using traditional
names with the prefix "x", such as xcoulomb (xC), xvolt (xV),
xtesla (xT), etc. The logical sequence to follow, in defining
units for new electrical concepts, will be the same as in the
told CGSE system. The only difference is that X-units will
be based on meter and kilogram while the CGSE units were
based on centimeter and gram.

The essential difference between the X approach and the SI
approach is the rule which does not allow to define a new
unit in terms of a unit to be introduced later. I am aware
of disadvantages of X units; they would differ from practical
units used by technologists. But they would be logically
consistent with the way we teach. The old maxim, "do not
accept things without understanding" is worth cultivating.
Some X units will be much larger, or much smaller, than
the corresponding SI units. But that is a small price to pay
for avoiding dogmatism.

The X unit of E is N/xC while the unit of V is xV (or J/xC).
Note that 1 xV is about 10^5 times larger than one volt
because 1 xC is smaller than 1 C by the same factor. The
unit of current, xA, defined as xC/s, is close to 10.5 microA
while the unit of resistance, xohm, is xV/xA. ). The unit of
magnetic field, xT is N/(xA*m). As in mechanics we define
new units at the same time as the corresponding physical
quantities are introduced. It is so simple! Note that 1 xW,
equal to 1xV*1xA is the same as one watt (J/s). Also note
that material constants, epsilon and mu, would be
dimensionless, as they used to be when they were first
introduced by Faraday and Weber.

Would I really want X units to be used in teaching? Probably
not. Why not? Because some formulas based on X units would
differ from the corresponding SI formulas. To coexist with the
SI system, which is not going to disappear, I would reluctantly
introduce the 1/4*Pi factor into the Coulomb's law. This would
be necessary to preserve the invariance of formulas; the appearance
of a formula should not depend on the choice of units. Thus all
units of my modified system, if it were to be used, would differ
from the units of the above X system by a factor resulting from
the presence of the Heviside's 1/ 4*Pi factor in Coulomb's law.
Ludwik Kowalski