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Is it true that most of the electric flux is in the acid between
the [battery] plates, as in a charged capacitor? I think so.
I don't think so. There is no field and no flux in the
electrolyte of an unloaded battery.
in addition to the electric force (Fe=q*E) each carrier
[in space between the plates] experiences another force, equal
and opposite to Fe.This non-electric force was labeled as emf.
This is a fairy tale. Further speculation along this
line is not going to be helpful.