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batteries (again)



Another set of questions about batteries:

Does an electric field always exist between the terminals of a battery?

When a conductor is placed in contact with the terminals of a battery, is the electric field constrained to exist only within the conductor?

If there is an electric field that exists outside the conductor near the terminals of a battery, is there a flow of charge (say ions in the air) in that region, and if so, is it measurable?

Thanks

Justin Parke