# Why are electrons not pushed out from the conductor at an open circuit under the influence of a power source?

Frequently, electric current is compared with water flow. For example, if I make a hole in a water tank, water will flow till the tank pressure and the atmospheric not become equal or the tank becomes empty. Why does this not happen with electricity?

• It does if the voltage is high enough to break down the insulating effect of open air. That's called lightning ;) – Majenko Sep 24 '14 at 10:42
• Because that's the definition of an open circuit. – user207421 Sep 24 '14 at 23:55
• One way to think about this is by taking the energy into account. When water flow pushes out of an open pipe, it "goes towards" a lower energy. On the other hand, electrons in a circuit are in a lower energy state, compared to free electrons. So while water dripping from a pipe loses energy (gravitational potential energy), electrons would need to gain energy in order to be freed - imagine a water flow pushing against a hill. The thing is, the hill is ginormous in the "open circuit" case :) – Luaan Sep 26 '14 at 14:39

You're imagining an open circuit to look like this:

A better analogy would be this:

The pipes in a circuit aren't surrounded by free space for the water to flow -- they are tunnelled through a rock. Where there is no pipe, there is just rock and the water does not flow.

• Good visualization. More wordy: the energy barrier for electrons to "leak" is extremely high, and only occurs when the "pressures" (voltages) are extreme or when they are (stretching the metaphor now) "boiled" away by incoming photons via the photoelectric effect. – Nick T Sep 26 '14 at 0:44
• If you're using water to visualise how electricity works, it's also important to remember that the "circuit" (pipework) either lies flat, or is in space where there is no gravity. – Roman Starkov Sep 27 '14 at 21:04

The water analogy is very limited and does not model the way electrons move in a wire. It should always be used with great care.

Electrons drift very slowly (about 1m/hour) by jumping from atom to atom. Current appears to flow instantaneously in a complete circuit but will not flow in an incomplete circuit (no electric field to move the electrons).

Inside a wire the conductivity is high (lots of 'free' electrons buzzing about randomly) and a small electric field (a voltage difference at each end of the wire) can produce a current. Outside the wire the conductivity is very low and there is no electric field to overcome the attraction of the positively charged metal ions in the wire should an electron leave the surface of the wire.

Water (molecules) on the other hand will simply flow out of the end of the pipe because the force pushing the water in at the open end (due to air pressure) is less than the force pushing the water out of the system (air pressure + gravity + pump?).

Water can escape because the inside and outside of the pipe is essentially the same medium and the molecules are acted upon by pressure (air and pump) and gravity (inside the pipe) and gravity (outside the pipe).

Is it possible for electrons to escape the wire?

Yes.

For electrons to escape their 'metal container' there must be sufficient energy supplied to break the bonds that tie them to the metal ions. This can be done with high energy photons (see photo electric effect and work function) or heating the metal (thermionic emission). Of course if this is done in air the electrons can't get very far before being absorbed so it needs to be done in a vacuum.

If the electric field is very high (as in charged clouds) the resulting spark is lightning.

• Hi Jim, Just to be clear the drift of electrons in a metal due to external E fields can be slow. But the thermal motion is very fast. (something like 1/2mv^2 = 3/2 kT say v^2 = kT/m I get ~ 2x10^5 m/s assuming an effective mass of 1.) – George Herold Sep 24 '14 at 14:38
• @GeorgeHerold absolutely correct and thanks for clarifying (+1). I've tried to avoid getting into maths details over thermal motion (fast, random movements in all directions but essentially net zero movement overall) vs drift velocity (slow migration in hops in the general direction of the applied field). – JIm Dearden Sep 24 '14 at 17:02
• I have a question - If electrons move so slowly how do so many of them (6241,509,324,000,000,000 per amp per second?) move to create the current? – asawyer Sep 26 '14 at 13:32
• @asawyer You need to think about the wave, not just the individual particles. When you push on a stick, (almost) the whole energy of your push will be transferred to the other side, even though the atoms on one side didn't move all the way to the other side - the energy was propagated in a wave over the electrons and atoms, without having to move them too much. A bad but fitting analogy would be Newton's craddle. – Luaan Sep 26 '14 at 14:31
• @Luaan Ah ok that makes perfect sense. – asawyer Sep 26 '14 at 14:38

Making a hole in a water tank so that water can escape is the same as a short circuit in electronics. Blocking a water pipe is the same as open circuiting a connection.

Remember, the water tank is a "water flow insulator" and is the same as a blocked pipe.

It's all a question of pressure equalization.

With the water it's not the water's pressure that is equalizing, but the atmospheric pressure acting upon the water. The air pushes down on the water and pushes it out of the hole until the inside and outside pressures are equalized.

Connect a wire between two poles of a battery and the pressure between the two poles can equalize.

Stick a bung in the hole of the tank and the water can no longer flow - the pressure difference between the inside and the outside is now fixed. Add a very high resistance between the two poles of a battery and the current can no longer flow (or flow very slowly - the bung has a drip). The higher the resistance the slower the flow.

Air has a typical resistance (according to Wikipedia) of around $1.30×10^{16}\Omega/m$ to $3.30×10^{16}\Omega/m$, with a breakdown voltage of around 300kV/m (which is the pressure at which the bung gets forced out of the hole in the tank).

Water and electricity don't work the same way. Sometimes water in pipes is used as a analogy for current in wires, but that analogy breaks down in the case you are asking about.

Actually the analogy is still valid if you remember that air doesn't conduct electricity, but air conducts water flow easily. To make the water flow analogy more accurate, you'd have to envision everything except the interior of pipes to be made of some solid material. Imagine everything that is air actually being some hard rubber, for example. Water wouldn't flow out of a open-ended pipe because it can't go anywhere.

## Energy Levels

This effect is usually explained by the concept of energy levels. The materials are divided into three groups: insulators, conductors and semiconductors.

### For conductors...

From the point of view of energy levels (atomic), for the conductors, there is no energy gap between the valence band and the conduction band. Then, with very little energy, the electrons can be set in motion.

### For insulators....

For insulator, the energy gap between the valence and conduction bands is much larger, which means that a lot of energy is needed to locate an electron in the conduction band.

### Then, in a open circuit...

In an open circuit, the insulation surrounding the conductor has a much higher level of energy than these. Under normal conditions, electrons from the insulated conductor, do not have enough energy to reach the conduction band of the insulator.

### But...

However, if the energy applied to the conductor is increased significantly, it can achieve a jump to the insulating material; this effect is electric discharge or dielectric rupture.

• Thank you. Great answer. Nevertheless, it did not help me. I understand why there is no current in dielectrics. According to my idea of the electric current electrons must be pushed to the outside world of the conductor. But they abut against the end of the wire as in barrier. What keeps the electrons inside the material when the electromotive force acts on the conductor? – user3131972 Sep 24 '14 at 14:09
• @user3131972 Think about it: how electrons move from one type of conductor, to another type, e.g from copper to aluminium? They can move because the energy level of electrons in copper match the aluminium (aprox). From conductor to insulator, the energy levels are so much different, then for the electrons go into the insulator, we must provide a very much energy. – Martin Petrei Sep 24 '14 at 14:17
• @user3131972: There is no "outside world" per se, there is only "something else". In this case the "something else" is the insulator called "air". – Ignacio Vazquez-Abrams Sep 24 '14 at 18:50

Electrons are trapped in a metal because of the work function of that metal. The work function is a measure of the energy of the electron in the metal to it's energy in free space. (or in the vacuum.. the presence of air is just an added complication.) The electrons in a metal are always in a lower energy state than the vacuum state. If a strong enough electric field is applied to the metal the electrons can over come the work function and leave the metal. (think about a vacuum tube cathode.) A water analogy is fairly easy. Water is in a bucket or trough with tall sides. (But it's better to just think about real electrons.)

Any difference between the number of electrons in a particular region and the number of protons in that region will cause nearby electrons to be attracted or repelled as needed to equalize the numbers. The only reasons electrons would want to leave a region would be either that there were too many electrons in the region relative to the number of electrons, or that a nearby region had a shortage of electrons (relative to protons). A "perfect" one-amp power supply will move one coulomb of electrons (that's a rather large bucket load) from one terminal to the other every second. If no electrons leave the terminal which is receiving all those electrons from the supply, it won't be long before the electrons get so overcrowded that they'll start to leave even if that would mean the place they're going would be somewhat overcrowded (since it would be less overcrowded than the place they're leaving). Likewise, if no terminals enter the terminal from which the supply is taking the electrons, its electron shortage will quickly become severe enough to cause it to start grabbing electrons from anything nearby, even if that would cause an electron shortage nearby (since it would be less dire than that of the terminal that's grabbing the electrons).

As electrons leave one terminal and enter the other, this will reduce the urgency with which those terminals will need to expel or acquire electrons. Note that in relative terms, it takes an amazing small surplus or shortage of electrons to create an essentially irresistible force. The mass of electrons in a conductor cannot quite be viewed as incompressible, but it's very close. In very rough relative terms, if a typical material had a swimming pool's worth of electrons, the difference between a severe shortage and severe overcrowding would be less than a drop.

Imagine this:

For electricity, the pipe heals itself. The wall thickness is the distance to the nearest other conductor. It may seem kinda weird to think of moving things through a solid pipe wall like a wire through air, but if you ignore that part of physics, the analogy works.

If the "wall" is too thin to hold the pressure, it punches through, which we call an arc. This works at very small scales too, like a 5V chip arcing internally when powered with 12V.