winnie said:
Rick,I entirely agree with the point that if you run a conductor between two bodies that are at different voltage, then current will flow through that conductor, even if there is no closed path. Furthermore, I agree that this current will flow for as long as the voltage difference is sustained, again if there is no closed path.
That is the only point I have been making from the very outset. If you have a difference in voltage, you will have a current flow (given a conductive path). It makes no difference if there is a return or not. In most cases, the voltage difference cannot be sustained, and that is the reason why I came up with two examples where the voltage could be sustained.
winnie said:
But if one were to somehow run a conductor from Earth to Moon, just how much current would flow, and for how long would it be sustained?
The current would follow Ohm's Law such that the voltage difference divided by the resistance of the wire would determine the current. How long this would last is dependent on how much charge difference exists, and how quickly the charge is replenished via the original mechanism that put the charge there in the first place. Capacitance is not the mechanism that put the charge on these bodies in the first place.
winnie said:
My understanding is that the Earth-Moon system would simply be a charged capacitor, and that the conductor would discharge it. But you seem to be saying implying that the Earth-Moon voltage difference is somehow permanent and that the current flow would be sustained indefinitely.
If the charge was put there by capacitive effects, what put the charge there in the first place? If the conductor is the means for discharging the capacitor, then how did it get charged in the first place. Where is the voltage reference that permitted this charge to be developed to begin with?
Where is the "zero potential" referenced from? Where is the return path when we are dealing with millions of miles? What about the voltage difference that existed before we added the conductor between the bodies?
Until we add that wire, we have two bodies at some unknown voltage between them, so how does this define a capacitor? What charged one body relative to the other? Where is the circuit path?
winnie said:
if you belive that the current would flow forever, then just say that; though if the latter, please explain what maintains the voltage difference.
No. The current would (or may) not exist forever. If and when the two bodies reach equilibrium, then no current would flow. However, the mechanism that created the charge difference in the first place is likely larger than what we could bleed off with a simple conductor. In a sense, two massive bodies such as this will result in a near-infinite charge differential, and the voltage will remain so long as we do not have a conductor large enough to equalize the charge. I don't know the answer, but I would speculate that this conductor would have to be extremely massive to pass the necessary charge.
The same rationale is necessary for the helicopter. If the charge transmission was rapid enough, then we would not see a voltage difference between the line and the helicopter. There would be no arcing.
All of the previous discussions have made the assumption that a capacitance exists,
and this much is true. However, they all assume that this capacitance is the primary mechanism, without ever going through the mathematics of what this capacitance would be. An electric motor has a capacitance in its windings, but this capacitance is not what makes the rotor turn. Just because you can prove that it is there does not mean you have proven that it is the primary mechanism.