There are two concepts I keep reading about that seem to be conflicting each other. Firstly, whenever there's a potential difference between two points, and those points are connected, electric current will flow between them, evening out the potential difference. And secondly, electricity needs a closed circuit to flow.
Consider a closed circuit that is floating (battery powered or isolated). If I were to connect the ground clip (connected to earth ground) on my oscilloscope probe anywhere in the circuit, it would be reasonable to assume that the electric potential at that point is different between that point, and earth ground.
Because the clip is connected to ground with a low resistance path, and because the potentials are different, it makes zero sense to me whenever people say that no current will flow through there. If current is the movement of electrical charges, how is it physically possible that connecting a different potential would not result in charge movement?
What I find even more confusing, is that people often quote how the earth has "infinite" capacity to dissipate charge, which does make sense, but then it would act as a capacitor with infinite capacitance? Or at least measurable non-zero capacitance, and since it is so large, there should be a non-trivial amount of current flowing to earth at least in the moment when the ground clip is connected.
On a similar note, if I we just consider a capacitor with no return connection as in this image
I find it very hard to believe that applying a potential difference to one side of the capacitor would not repel the charges on the other side, and even push out the charges at the end of the wire to act as a capacitor against its environment.
I do understand that in the case of a small capacitor this effect might be small enough for us to ignore, as the capacitance of a small wire is probably beyond what we can even measure with test equipment?
But in the case of connecting to earth ground, such as this
how come the "infinite capacitance" of earth ground doesn't cause the charges to flow there through a low resistance path? I would understand if the argument worked for something like batteries, where one could probably say that unless electrons flow in the battery it would not produce more electrons out of it (I'm not sure if this really is true), but in that case I would imagine there would be other power sources for which this is not true, such as if there was a capacitor on the circuit, and the earth ground connection would allow it to discharge itself into earth (because of potential difference) with low resistance quickly.