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Here's the scenario:

Let's say I have a circuit in a vacuum chamber with a current

*i*, that flows through it and a constant voltage source and resistance in the circuit. One section of the circuit is a piece of gold (or any other conductor) foil with arbitrary dimensions.

What would happen if the gold foil were bombed with a stream of elections from an external source, say an electron gun? Would some electrons from the gun enter the foil and join the circuit, increasing

*i*?

Does this have anything to do with the probability density of an electron passing through a potential barrier? In other words, does the probability that the electron is found within the potential barrier (the foil) correspond to the amount of electrons which enter the circuit?

Thanks in advance