# Why do electrons flow from a lower potential energy to a higher potential energy?

So I understand that the term "voltage" refers to the potential energy difference between two points. So, in a 5v battery, there is a 5v difference between the positive and negative ends. When these are connected in a circuit, the electrons naturally want to flow from one end to the other.

My question is, why do they do this? What exactly is it that makes electrons want to flow from lower potential energy to higher potential energy?

Also, does the potential energy difference between two points (voltage) determine the speed at which the electrons travel?

• Everything is "flowing" from the high potential energy to the low one. – Eugene Sh. Nov 27 '17 at 17:52
• Note that Franklin had it wrong the electrons flow from negative to positive, but we conform to the standard that electricity "flows" from positive to negative. In this case think of it is why does the stone want to roll down hill, same deal there is a surplus on one end and a void on the other causing a flow. and/or like a pumping action where the energy source creates an inbalance that the circuit desires to balance by moving the electrons, they simply want to balance by moving into available slots – old_timer Nov 27 '17 at 18:07

You're confusing (electrostatic) potential (aka voltage) with potential energy.

An electron has a high potential energy when it is at a location associated with a more negative value of potential, and a low potential energy when at a location associated with a more positive potential.

The reason is that electrical charge has two types: positive and negative which exert attractive forces on each other but repulsive forces on themselves. A more positive potential is produced by an accumulation of positive charge (which attracts negatively charged electrons) and a more negative potential is produced by an accumulation of negative charge (which repels electrons).

The choice of defining one type of charge as negative and the other as positive was made arbitrarily, before the electron (with negative charge) was identified as the primary current carrier in metallic conductors. By the time that was discovered it was too late to go back and re-define the charge polarities for the convenience of engineers. In any case, the "mixed-up" polarity definition should help you remember that electrons aren't the only charge carrier and when other carriers are present they might behave differently from electrons.

Electron flow mostly comes down to the fact that opposites attract and likes repel.

So, if you have more electrons than protons in one place, the electrons tend to repel each other, and flow from that place to somewhere else that there are more protons--ideally they'll be attracted to a place where there are more protons than electrons, but even if that's not available, a place where there's less of an over-abundance of electrons will do.

As to speed of movement of electrons: it depends on what exactly you're talking about. An electron normally orbits the nucleus of an atom at a fairly fixed speed. Voltage doesn't affect that to any significant degree.

A signal propagating through a conductor normally travels at around 2/3rds the speed of light. What matters in this case isn't the voltage or the conductor itself--it's the dielectric constant of the insulator surrounding the conductor (a lower dielectric constant yields faster propagation).

Voltage is the ability to overcome electrical resistance--to get more electrons to flow through a conductor, despite higher electrical resistance.

For a loose analogy, think of a person pushing a heavy weight. Higher voltage is equivalent to a person who's stronger, so he can push a heavier weight. Being able to push a heavy weight doesn't necessarily mean he can run particularly fast.

In order to understand electricity you have to go down to the atomic level.

The simplified model of an atom states that it has a nucleus of protons and neutrons that is surrounded by electrons that orbit around it.

The protons have a positive charge, and the electrons have a negative charge. Which is which polarity was discovered after the concept / standard of positive and negative voltages was created.

Normally there are an equal number of electrons as there are protons. The charges thereby cancel out and there is no net charge on the atom as a whole.

However, the electrons are only loosely bound to the atom and it is relatively easy to force an atom out of orbit. When this happens the atom then has a positive charge and becomes an ION. The free electron of course has a negative charge. As such, there is now a force between the ION and the free electron pulling them back together. This force is the electrical potential between the two.

With a battery or other power supply, the mechanism of the battery of power supply, forces large numbers of electrons to leave their atoms and accumulate at the negative terminal, sort of like parting the sea. This means there is a force pulling between the two which we can measure as the voltage across the terminals. The makeup of a battery or power-supply is such that the electrons are held apart and can not return through the supply.

When you connect a wire, or load, across the terminals you provide a path for the electrons to return to their natural state back at the ions.

However it is not quite as simple as that.

In the wire between there are more atoms with their electrons buzzing around them. When current flows what actually happens is electrons hop from atom to atom in a kind of long chain, akin to a bucket brigade. As each electron hops forward it leaves an ion behind it which attracts an electron from the previous atom and on and on down the wire.

How fast the electrons move will depend only slightly on the voltage across the terminals. How many of them are moving at once does depend on the voltage. In reality, individually, they move quite slowly.

It's like these people walking on the bridge.

They are all walking about the same speed, but there are so many more people jostling to cross at the top that the total "current" of bodies is large. The poor guy in white on the girder is all alone, the "current" on that path is small.

For conservative fields, like the electric (electrostatic) field, the force on a charged particle with charge $q$ due to the electric field is given by: $$F = -q\frac{dV}{dx}$$ From Newton's Law we know that any particle will move in the direction of the net force applied to it. In the absence of any other force there will just be the electrostatic force applied to the particle (given by above equation). And it is clear from the equation that the force is in the direction of decreasing V (because negative $dV$ makes the right hand side positive). Thus any charged particle will move from a region of higher potential to a lower one if acted upon by only the electrostatic force.

All have answered very well. Let me explain it in another way:

Consider two points A and B. Let A be in higher potential (more positive charges) and B be in lower potential (less positive charges). The direction of the net electric field is always from higher potential to lower potential (i.e., from A to B). Now force, F on a charge q in this electric field E is given by: $$F = q.E$$ where F and E are vectors.

now we know that here q is negative for an electron. So its obvious from the equation that the force on electrons is in the opposite direction to the electric field. Hence, electrons will move from B to A. i.e, from lower potential to higher potential.

You have it the wrong way round.

When we have a battery, and connect a conductor between the terminals, we notice that a current flows. We notice that this current deposits heat in the conductor.

If we do careful experiments, measure the current, measure the power, we find that their ratio is well-behaved, and we can identify it with the voltage of the battery. If we put batteries in series, their voltages add, and it all works.

As to why this all happens, nobody knows.

There are all sorts of 'explanations', which are really ways to do sums to predict what happens, at various levels. With volts and amps, we are doing sums with circuit theory. With electron charge and fields, it's electronic physics. With photons and QED, it's quantum mechanics.

You can use any of them to explain what's going on, if you take for granted the validity of the underlying assumptions. If you ask why, then you find yourself going deeper and deeper down the rabbit hole, and the ultimate answer is 'because that's the way the universe works'.

• so his title should be "Why do electrons flow from a higher potential energy to a lower potential energy?" – barlop Nov 30 '18 at 2:20