🚀 go-pugleaf

> Dear Joe: I am quoting from your last message and responding by using
capital letters. For those who were not involved I recall that we are
arguing about two capacitors in series. The notation is R and C for
resistance and capacitance; r and e for resistivity and dielectric constant.
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> It could be that the equal charge argument is not needed to obtain the
> textbook formula for series capacitors.

AS CAN BE SEEN FROM A TEXTBOOK DERIVATION, THE PROOF IF REVERSIBLE. IF
THE EQUAL-CHARGES ASSUMPTION LEADS THE EQUIVALENCE FORMULA (1/C=1/C1+1/C2)
THEN THE EQUIVALENCE FORMULA LEADS TO EQUAL CHARGES. IN ANY WAY, WAS ANYBODY
ABLE TO DERIVE THE EQUIVALENCE FORMULA WITHOUT ASSUMING, EXPLICITLY OR
IMPLICITLY, THAT CHARGES ARE EQUAL?

> Or it could be that by some accident of nature the capacitors had
> dielectric properties, leakage characteristics, and size and shape such
> that the criteria Kowalski has set were met, although at first glance
> that seems unlikely.

JOE IS REFERRING TO THE DERIVATION OF Q1/Q2=(R1*C1)/(R2*C2) WHICH LEADS
TO:  Q1/Q2=(r1*e1)/(r2*e2).

OBSERVE THAT THE AREA OF THE DIELECTRIC MATERIAL AND ITS THICKNESS
SIMPLY CANCEL (F O R   E A C H   C A P A C I T O R !) WHEN R*C IS
TURNED INTO r*e. I AM SORRY I DID NOT EMPHASIZE THIS BEFORE. THUS SIZES
AND SHAPES ARE IRRELEVANT. THE RATIO OF CHARGES ON TWO CAPACITORS IN SERIES
DEPENDS O N L Y  ON MATERIAL PROPERTIES. THE "ACCIDENT OF HUMAN NATURE" IS
THAT OUR STUDENTS ARE ASKED TO VERIFY A WRONG THEORY BY USING A SPECIAL
CASE WHICH HAPPENS TO CONFIRM IT. CAPACITORS MADE FROM DIFFERENT DIELECTRIC
MATERIAL WILL HAVE DIFFERENT CHARGES, EXCEPT IF, BY COINCIDENCE, r1*e1 AND
r2*e2 ARE EQUAL.

BUT LET'S WAIT FOR EXPERIMENTAL DATA WHICH, I HOPE, WILL SOON BE ARRIVING
FROM SEVERAL INDEPENDENT INVESTIGATORS. PLEASE HELP TO SOLVE THE DILEMMA,
ONE WAY OR ANOTHER. IT IS OUR PHYSICS.

* Laboratories should be used for "asking or pursuing How do we know..? Why
* do we believe..? What is the evidence for ..? questions inherently
* associated with a given experiment". (A.B. Arons, TPT, May 1993, p279)

           Ludwik Kowalski   Kowalski@apollo.montclair.edu.