Benzene forms the electron shell configuration of two rings of

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Benzene forms the electron shell configuration of two rings of electrons, parallel to the molecule, shown here http://upload.wikimedia.org/wikiped...e_Orbitals.svg/750px-Benzene_Orbitals.svg.png

so my question is, if an electron beam is run through the center of the benzene, would the resultant magnetic field cause the electrons to flow in a systematic way in the ring?
 
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This actually seems like a viable theory at first, although I am unsure how the electrons would flow stability wise, as the ring structure you mention is not in fact a perfect ring. However you could influence the electron trend.

An interesting question to pose is, if you go the electrons to flow in a specific way, what would happen if the electron beam stopped an a second beam going the opposite way through the benzene molecule started. Theoretically the exact opposite force would be applied to the electrons.
 


It's not only a viable theory, but a well-known phenomenon called http://en.wikipedia.org/wiki/Aromatic_ring_current" .
 
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Then reversal of the flow could theoretically apply exact opposing force to all of the electrons.
 


The two rings of a delocalized orbital are not separate entities, just as two lobes of a single p-orbital are not separate. I think the figure describing the delocalized orbital is a little exaggerated. Two rings should meet at each carbon site in the same way as the lobes of their constituent p_z orbitals do.
 
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From the BCS theory of superconductivity is well known that the superfluid density smoothly decreases with increasing temperature. Annihilated superfluid carriers become normal and lose their momenta on lattice atoms. So if we induce a persistent supercurrent in a ring below Tc and after that slowly increase the temperature, we must observe a decrease in the actual supercurrent, because the density of electron pairs and total supercurrent momentum decrease. However, this supercurrent...
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