By coupling I mean the two separated spherical dome shells are connected with each other with a rod/wire in which the potential in the connecting rods is not the same or equal to zero as in the shell..Because electrons cannot tunnel via infinite potential?How possible is it to achieve and what can I do to achieve this?

How can I achieve this via quantum mechanical approach or the use of dielectric function model?

See the attachment for the geometry of the problem at hand.

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