Having trouble intuitively understanding why complete circuits are necessary.

A lot of explanations on the internet say that the negative end of a battery has a relative abundance of electrons while the positive end relatively lacks electrons. Thus, when the two ends are connected, the electrons flow from the negative to the positive until there is a balance (zero voltage state).

If this were the case, then why can't you run a wire from the negative end of one battery to the positive end of a second battery and expect current to flow from the electron-plentiful negative terminal of battery 1 to the electron-deficient positive terminal of battery 2?

Take the water example. If you have a big jug of water suspended in the air connected to an empty jug down below, water will flow down and fill the bottom jug. There's no circuit. The water jug up top will simply empty its "charge" down into the water jug below. If you put a water wheel in the middle you would still get work. No apparent circuit needed.

If you rubbed yourself on carpet, electrons rub off the carpet molecules and get attached to you, making you negatively charged with a surplus of electrons. If you touch a metal doorknob electrons will jump from you to the doorknob, but there's no apparent circuit either between you and the doorknob, especially considering the doorknob itself terminates into the wood of the door. Yet there is still current without a complete circuit.

If an internal wire became dislodged inside of a metal case, and the metal case was connected to earth, current would flow from the mains down to literal dirt. But there's also no apparent circuit, just one end with a relative abundance of electrons and another end with a relative deficiency of electrons.

Work is produced when electrons flow, just as a water wheel turns when water molecules flow past the wheel, pushing it. So movement of particles, to me, is the only requirement for work. A complete circuit isn't required if all you want is movement - you just need something to move from A to B, no?

Trying to redistribute electric charge so it is not exactly balanced (equal density of positive and negative charges everywhere), costs huge amounts of energy. Really massive amounts. Imbalances of parts per billion generate ultra-high voltage fields (megavolts or so).

So to a good approximation charges cancel out everywhere. For a current to flow electrons in a wire have to return to where they started, otherwise charge would accumulate at each end of the wire, taking lots of energy and producing massive electric fields.

When you connect +ve of one battery to -ve of another there will be a very short burst of current as the voltages equalize, but remember this is parts per trillion or smaller for fractions of a microsecond, cancelling out whatever tiny imbalance their may have been.

When you connect +ve of a battery to its own -ve terminal the electrons keep flowing because of the work done by the chemical reactions that sustains the voltage difference until all the chemicals are used up.

Consider the negative charge on all the conducting electrons in a gram of copper is about 10,000 coulombs, balanced by the same amount of positive charge on the metal atoms. Then consider that a Van-def-Graff generator might struggle to get to 1 micro-coulomb of charge at 100's of kV... Unbalanced charges are tiny tiny fractions of the balanced charge.

The electrons in the wire in low voltage circuits just shuffle around being replaced by the same amount of charge - in other words current flows in a circuit (current electricity as opposed to static electricity).

Ok, so I guess this is where using the water analogy breaks down, right? With the water analog it’s easy to have one water reservoir be filled while another water reservoir is empty. This obvious and sometimes massive imbalance of water (say, water flowing from a lake into an empty hole dug into the ground) is common to have.

But electrons don’t behave that way, or rather, it’s very very hard to get them to behave this way because electron imbalances are very difficult to maintain. You can have a tub filled with electrons and another tub empty of electrons and when you link the two you will have current that’s non-circuitous, but it’s very difficult to create this.

So speaking very technically, a complete circuit is not strictly necessary for electron flow, but realistically it is necessary due to the fact that electron imbalances are extremely difficult to maintain?

Look at a lightning bolt. There you have a discharge that is not circuitous.

fuzzybabybunny:
Ok, so I guess this is where using the water analogy breaks down, right?

It’s more like a potential energy within a “local” system (or subsystem)…a localised system. In that localised system, if there is a “separation” of charge caused by carrying out the relevant procedures or processes needed to do that (where input energy is involved), then a physical phenomenon is known to occur… creating an electric field of some sort. So… like the kingsman II movie… whatever happens in Italy stays in Italy.

It’s only when you connect batteries together in series where the voltages of series-connected batteries become additive (for the equivalent “overall” battery).

Better to think of the value of charge on one terminal of a particular battery “relative to” the value of charge on the other terminal of that particular battery.

You're not modeling all elements correctly tho.

Take your water-jug - if the top container is sealed, water will not flow - when unsealed, air is allowed to take the place of the water that flows out. So Air completes the circuit.

Take the sparking - with lightning, the air molecules turn into a plasma-like state, creating a path for the high voltage current to flow. With a doorknob, the metal in the doorknob gets charged up while you discharge, with the air similarly breaking down as in the lightning example and creating the electrical path.

Simple batteries are much lower voltage tho, so wires are needed from plus to minus, and from minus to plus to close the circuit. It's not until you get into thousands of volts does air breakdown and become a conductor.

Remember; for every action there is an equal and opposite reaction.

As others have mentioned the analogies can sometimes be more confusing.

Consider the water analogy. Here the common force is gravity. If you imagined the same experiment setup in space without gravity, the result would be much different.

For lightning it is similar, the circuit is completed by a large (physically) capacitor from the air at the cloud level to ground.

If this were the case, then why can't you run a wire from the negative end of one battery to the positive end of a second battery and expect current to flow from the electron-plentiful negative terminal of battery 1 to the electron-deficient positive terminal of battery 2?

Here the lack of "electron flow" is due to there being no difference in potential. Battery 1 negative is at the same potential as battery 2 positive (by the fact that they are connected together).

I'm not sure I helped but I hope you can "see" the completed circuits in the analogies.

Take the water example...

The biggest difference between water and electricity is that electricity need a "path"... A conductor... If you cut a water pipe you get zero resistance and water flows-out all over the place. If you cut a wire you get infinite resistance and no current flows.

If you rubbed yourself on carpet, electrons rub off the carpet molecules and get attached to you, making you negatively charged with a surplus of electrons.

Now, you are essentially a charged capacitor. You don't need a complete circuit because you don't have continuous current flow and the charge just needs to balance-out between you and whatever you touch. If you touch another person, and that other person isn't touching anything else half the charge will flow into the other person. If you touch a (grounded) doorknob, you are "balancing" the charge between you and the earth (which means you'll get completely discharged).

You can't get continuous current because you don't have a complete circuit. Unless... You continue to rub your feet, transferring more electrons to your body.

If you touch a metal doorknob electrons will jump from you to the doorknob, but there's no apparent circuit either between you and the doorknob...

When you get close to the doorknob, the air "breaks down" as an insulator. The air ionizes and the air becomes a conductor. Higher voltage can "jump" a bigger gap. It takes a several kilovolts to break-down the air in a spark-plug gap and it takes millions of volts to get lightening.

especially considering the doorknob itself terminates into the wood of the door.

Wood is a poor conductor but that means the wood door is a good-enough conductor. If the door was plastic (or maybe very-dry wood) nothing would happen... Only a small charge would be transferred to the doorknob and you'd never know.

Also, for the OP..... in electronics circuit theory, a DC current can only flow around a circuital 'loop'. So, for the case of a wire connecting one terminal of charged battery A and one terminal of charged battery B ..... no loop (with a DC voltage source incorporated within the loop) exists....so no DC current.

fuzzybabybunny: Ok, so I guess this is where using the water analogy breaks down, right?

Not completely. Imagine a battery as a tank with a movable wall, dividing it into two chambers. Is pushed into one direction by a spring. Current needs to flow back to fill up the other chamber, else the spring will be stopped by the vacuum suction on its side. It is a little more involved, since you need to get potential energy and spring energy translated to get it into the rest of the analogy, but that is basically it. It is not just a full and an empty chamber. Why would water flow happen in the first place in that situation?

Maybe it is better to have the chambers vertically arranged, with a thick (proportional to the voltage) but weightless wall in between. With that, you only deal with potential energy, but you cannot fill another battery, since the upper chamber needs to be empty to make room to fill the lower one.

If the air surrounding your batteries had a low resistance it would complete the circuit. As it is there is not enough V to track across the air molecules due to the high resistance. Lightning however has enough energy to use the air as a conductor