electric permittivity and capacitors

I asked myself do I really understand why capacitors have greater
capacity with greater dielectrics.
http://en.wikipedia.org/wiki/Permittivity
It appears to be simple: well polarized and arranged medium serves as
a transmission line from plate to plate. Also the field E is smaller
in the material with all the +-+-+-+-+- sums leading to zero.... so
this fits into energy going down inside capacitor with a great
dielectric.

.

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