RiddlerA said:
Imagine a conductor with 3 points A→B→C... Now if A is connected to a current source, there will be no current flow unless the circuit is closed right? Does this mean that there will be no electron flow at all in the conductor regardless of the voltage of power source?
(This was answered in another thread, but I don't seem to be able to find it.)
ALL conductors have a capacitance. A conductor's potential may be described by the total charge on it and its capacitance. [Circularly, you could equally say the capacitance of a conductor is a function of the potential on it for a given charge, etc..]
Anyhow, your wire has a capacitance and when you connect another conductor to that wire, they will share their charge until their potentials are equal. IF they have the same potential, no charge will flow.
If you were to connect the wire to an isolated battery, the wire would tend towards the potential of the battery terminal you connected it to, but equally the battery's whole potential will lift to that of the wire. Imagine a 500kV distribution line was isolated instantaneously with 500kV (with respect to ground) on it at the moment of isolation. It is acting like a capacitor, it has a potential of 500kV. If you bring a teeny battery up to it, the battery will get pulled up to the 500kV potential.
If you were to now bring a current source that was tied to ground up to your wire charged to 500kV, then which way do you think current would flow, how much charge would flow, and what would the end potentials be? What happens if it were charged to -500kV?
So your question is incomplete, because you've said nothing about either the current source, or the charge on the wire before connection.
Treat everything as a capacitor and this will make sense. Most 'wires' have a capacitance so small it is ignored. But this is the way you need to think about it if either a) you have a very long wire, and/or that runs very close to an earth, and/or b) are discussing high voltages. If neither a nor b, then you can naively say that no current flows.