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I have no doubt that the formula for C (of the ideal parallel-plate
capacitor, C=eps_o*A/d) is correct. But its derivation, based on
Gauss's Law, is not very convincing. What am I missing?
In the 5th edition of "Physics for Scientists and Engineers"
Serway and Beichner derive the formula as if the field between
the plates were due to two non-conductive plates of charge. In
other words, they multiply E'=sigma/(2*esp_o) by 2 and
produce the correct formula for C. This is on page 807.
But two layers of sigma in a capacitor reside on metallic
plates and each plate produces E"=sigma/eps_o. On that basis
I would expect the net field between the plates to be twice as
large as that used in the derivation. Something must be wrong
with this expectation because it leads to a wrong formula,
C=0.5*eps_o*A/d. Where am I wrong?
The same derivation can be seen in Tipler's book ("Physics
for Scientists and Engineers", page 692) and in several other
textbooks. If each plate alone is contributing E'=sigma/eps_o
then why is it wrong to expect the two plates to produce a
field which is twice as large (inside a narrow gap)?
Ludwik Kowalski