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



Jack Uretsky wrote:

Hi all-
It will be amusing to see if I can get Ludwik to read the Chapter
on forces in <The Mechanical Universe>, the edition of which
Olenick is the first author. This is not the 95th time that I have
made the suggestion, but we're getting there.

Jack is probably referring to Chapter 11 entitled
"Gravity, Electricity and Magnetism". It comes
after the law of universal gravitation and Kepler
relations were discussed (Ch. 8 and 9) but before
electricity topics are systematically covered in
volume 2.

Coulomb's law first appears in Ch. 10 where it is
written next to the low of gravity. The assumption
is that students are already familiar with the concept
of charge q. (How else can it be? The q1 and q2 appear
in F=Ke*q1*q2/r^2 without any explanation).

The first relation of Ch. 11 is the force law for magnetic
poles, F=Km*p1*p2/r^2. Once again p1 and p2 are not
explained, students are expected to know what the
magnetic pole strength p is. The second relation of the
Ch. 11 is F=p*B where F is the force acting on a pole
while B is a quantity called magnetic field. It was not
introduced as a physical quantity up to this point;
magnetic field was described so far only in terms of
lines from N to S near a bar magnet.

The third relation of the Ch. 11 is F=q*E where F is the
force acting on a charge q and E is a quantity called
electric field. It was not introduced as a physical quantity;
up to this point the electric field was described only in
terms of lines surrounding wires or radiating from charges.
No connection between E and Coulomb's law was made.

A little later B is defined as a physical quantity by the
usual cross product formula. Note that q has not yet been
defined as a physical quantity. In other words B is defined
before q. [Stop it, Ludwik, you wanted to be a reporter, not
a critic. OK, I will control myself. ] A little later the 10.1
formula (Coulomb's law) is shown again but this time Ke is
said to be an experimental constant equal to 9*10^9 N*m^2/C.
The unit of charge, C, has not yet been introduced.

Next to it formula 10.1 (F=Km*p1*p2/r^2.) is presented
again and the unit pole is defined as the product q*v in
the F=q*v*B. The unit of p, 1 pole, is said to be C*m/s;
the unit of charge, C, has not yet been introduced. After
that the authors write: "If we measure the force between
two unit poles, then we can determine the constant Km. In
practice this is not done. Instead we measure the force
between two wires carrying current which we discussed
earlier. The idea, however, is the same: we measure the
force to determine a constant, and the result is
Km=1.00*10^-7 N*s^2/C^2."

Yes, there was a picture of two currents on the previous
page but the concept of current is not introduced until
the second volume. The derivation culminates by showing
that the unit of Ke/Km is m^2/s^2. The authors conclude
that by inserting the above values of Ke and Km one finds
that the square of the Ke/Km is the speed of light,
3*10^8 m/s. The chapter ends with a poem written by
James Clerk Maxwell

*******************************************

What do you like in this chapter, Jack? I like the idea of
trying to follow the real history but I do not like the
way in which it was actually done. I see that neither 4*Pi
nor epsilon_zero are included in Ch 11. But they are
used in volume 2, as in any other text based on SI units.
Ludwik Kowalski