Gattosilvestro ha scritto:
> Non ho scritto che il calcolo di eps0 lo ha fatto Coulomb, o qualcun
> altro ai suoi tempi.
> Lo hanno fatto in tempi più recenti dopo l'adozione del Sistema
> Internazionale.
> Solo che la F = q1q2/4pi*r^2*eps0 è sempre nota come Legge di Coulomb,
> anche se espressa con le grandezze del SI.
>
> Già che sto scrivendo espongo un altro modo per calcolare eps0: con il
> condensatore.
Queste sono varianti inutili: la questione sta a monte.
Ho il sospetto che staimo girndo in tondo...
Posso ripeterti quello che ho già detto, e tu mi replicherai con
quello che hai già detto...
Chissà se può servire che ti citi Maxwell?
============================================Dal "Treatise on Electricity and Magnetism" (1873)
Prefazione, pag. 4:
If, as in the astronomical system, the unit of mass is defined with
respect to its attractive power, the dimensions of [M] are [L^3 T^-2].
vol.2:
620. EVERY electromagnetic quantity may be defined with reference to
the fundamental units of Length, Mass, and Time. If we begin with the
definition of the unit of electricity, as given in Art. 65, we may
obtain definitions of the units of every other electromagnetic
quantity, in virtue of the equations into which they enter along with
quantities of electricity. The system of units thus obtained is called
the Electrostatic System.
If, on the other hand, we begin with the definition of the unit
magnetic pole, as given in Art. 374, we obtain a different system of
units of the same set of quantities. This system of units is not
consistent with the former system, and is called the Electromagnetic
System.
629. Of the two systems of units, the electromagnetic is of the
greater use to those practical electricians who are occupied with
electromagnetic telegraphs. If, however, the units of length, time,
and mass are those commonly used in other scientific work, such as the
metre or the centimetre, the second, and the gramme, the units of
resistance and of electromotive force will be so small that to express
the quantities occurring in practice enormous numbers must be used,
and the units of quantity and capacity will be so large that only
exceedingly small fractions of them can ever occur in practice.
Practical electricians have therefore adopted a set of electrical
units deduced by the electromagnetic system from a large unit of
length and a small unit of mass.
The unit of length used for this purpose is ten million of metres, or
approximately the length of a quadrant of a meridian of the earth.
The unit of time is, as before, one second.
The unit of mass is 10^-11 gramme, or one hundred millionth part of a
milligramme.
768. THE absolute magnitudes of the electrical units in both systems
depend on the units of length, time, and mass which we adopt, and the
mode in which they depend on these units is different in the two
systems, so that the ratio of the electrical units will be expressed
by a different number, according to the different units of length and
time.
It appears from the table of dimensions, Art. 628, that the number of
electrostatic units of electricity in one electromagnetic unit varies
inversely as the magnitude of the unit of length, and directly as the
magnitude of the unit of time which we adopt.
If, therefore, we determine a velocity which is represented nu
merically by this number, then, even if we adopt new units of length
and of time, the number representing this velocity will still be the
number of electrostatic units of electricity in one electro magnetic
unit, according to the new system of measurement.
This velocity, therefore, which indicates the relation between
electrostatic and electromagnetic phenomena, is a natural quantity of
definite magnitude, and the measurement of this quantity is one of the
most important researches in electricity.
771. Since the ratio of the electromagnetic to the electrostatic
unit of electricity is represented by a velocity, we shall in future
denote it by the symbol v. The first numerical determination of
this velocity was made by Weber and Kohlrausch *.
[...]
The value of v obtained by MM. Weber and Kohlrausch was
v = 310740000 metres per second.
772. Two other methods for the determination of v lead to an
expression of its value in terms of the resistance of a given con
ductor, which, in the electromagnetic system, is also expressed as a
velocity.
773. [...]
The value of v, as found by Thomson's method, was 28.2 Ohms*;
by Maxwell's, 28.8 Ohms.
786. The quantity V, in Art. 793, which expresses the velocity of
propagation of electromagnetic disturbances in a non-conducting medium
is, by equation (9), equal to 1/sqrt(K mu).
If the medium is air, and if we adopt the electrostatic system of
measurement, K = 1 and mu = 1/v^2; so that V=v, or the velocity of
propagation is numerically equal to the number of electrostatic units
of electricity in one electromagnetic unit. If we adopt the
electromagnetic system. K = mu^2 and mu = 1, so that the equation V=v
is still true.
===========================================So già quello che mi risponderai: Maxwell dice che per es. nel sistema
elettrostatico K (quello che oggi si chiama 4pi*eps0) = 1.
Vero, e ti posso aggiungere che in un brano che non ho citato (art.
781) afferma esplicitamente che esiste un mezzo per la luce e per le
onde e.m. e che lui si propone di dimostrare che il mezzo è lo stesso,
le onde sono le stesse.
Però in precedenza hai visto che assume sempre come fondamentali
M,L,T, e nel sistema elettrostatico l'unità di carica è definita di
conseguenza: quindi K=1 *per definizione*.
Ti ho anche citato un brano della prefazione, dove M. osserva che si
potrebbe eliminare anche la cost. di gravitazione G; e assumere come
fondamentali soltanto L e T.
(Incidentalmente, quello che si fa in "Gravitation", dove anzi c'è una
sola gr. fondamentale: la lunghezza. Così [M]=[L], e per es. la massa
del Sole è circa 1.5 km.)
--
Elio Fabri