electricity - Why are circuits considered loops?

So, I know that when you're talking about something like a circuit that includes a battery, a circuit LOOKS like a loop, but that's merely because of the fact that the power supply is physically close to the output.

However, this doesn't have to be the case, right? Batteries are just self-contained because it's convenient, but you could drain a power source by connecting it to ANY positively charged endpoint, if I understand this right.

Are circuits therefore considered loops just because it's convenient to think of it that way? As a river cannot flow in a circle, neither can electricity because it would work out to a net zero potential thus meaning no movement!

Answer

Most circuits are considered loops because charge in conductive materials tends to equalize electrostatic potential differences relatively quickly. Take a long wire/rod for instance. Let's say you can add electrons to one side of it. At first you start with 0 electrons. When you add the first electron, there's nothing else around so it can go basically wherever. When you add the second electron, it will push the first electron as far away as possible to try and create charge balance in the rod. This first electron moving is actually a tiny current and its movement could be used to extract work from it (because it took work to add the second electron to the system). Adding a third electron will push the second electron to the middle. The second electron's movement is half of the first so you could only extract half the amount of work out of it. The first electron is at the other end and hasn't moved at this point. If you keep adding electrons to the rod at one end, the movement of the other electrons will be less and less. Soon, you'll be at thousands of volts and not capable of extracting any work out of it because there's simply nowhere for the electrons to go.

Instead, what if we took electrons off of one side and added it to the other side? Now every electron you do this to will cause all the other electrons to move in response in one direction the same amount. Now you can extract a uniform amount of work out of the system for each electron you move. But what have you done? You've created a loop with your hand moving single electrons at a time. This is why most circuit utilize a loop. There's something that pushes electrons in one (or maybe both) direction. In your case, it's a battery, but generators and various other methods can be used to "pump" electrons to extract work from them at a different location.