In the modern world, we seem to take magic for granted. By simply pressing little buttons, we induce all manner of tasks to helpfully complete themselves. We don’t need to light candles or lamps; we just flick a switch and there is light. We don’t need to collect and meticulously arrange firewood to start a fire; we just flick other switches and a heater or oven spontaneously provides heat. Flick yet more switches and we can see and hear our family from across the world, keep food from spoiling, or have our clothes washed. If you could take a person from almost any time in human history and bring them into your house, it would take mere moments for you to prove to them that you are a magician.
We call this magic electricity. Electricity is the silent, invisible power that runs our lives. It has revolutionised human existence, making commonplace what once seemed impossible. Yet it has become so mundane that we now notice its absence — signalled by the abrupt breakdown of our trusted appliances — more readily than its presence. Occasionally, a fault allows electricity to escape from its wire containment and we catch a frightening glimpse of its power in the form of sparks that could kill us with a touch. It is difficult to imagine how these dangerous sparks can possibly be used to play music or freeze our leftover lasagne. But as children we quickly learn that electricity is simply a power beyond our reckoning; not to be questioned, never to be meddled with, but always to be relied upon. It is as enigmatic as it is ubiquitous.
But of course, electricity is not magic. It is a product of science. By comparing it to older, simpler technologies, we can come to understand how it works and why it is such a powerful tool. This will allow us to understand why this mysterious force that was once an academic curiosity became a cornerstone of society.
A World of Water Wheels
Before approaching electricity, it is helpful to consider a more basic technology — the water wheel. Many important processes for human society, like grinding grain to produce flour, require a large amount of energy. This energy can be provided by a person’s manual labour, but this is exhausting and time-consuming. The water wheel provides an alternative. It uses the fact that a stream of flowing water, such as a river, contains energy due to the motion of the water. If you position a wheel so that the water passes over one side of it, this energy will cause the wheel to turn. This turning wheel can then operate a mill that grinds the grain. So, a water wheel is a mechanism for harnessing the energy in water to perform a useful task without human labour.

The ultimate force on which water wheels depend is gravity. Gravity pulls water from higher places to lower places, which is what causes it to flow. It means that water sitting at a high elevation, such as the top of a hill, or the source of a river in the mountains, has stored energy that can be converted to energy of motion as it falls. This stored energy is called gravitational potential energy because it is associated with the potential of the water to start moving by flowing downwards. So, water wheels ultimately work by capturing some the gravitational potential energy of water as it is released through the water’s flow.
In principle, the energy harnessed by water wheels could do a lot more than grind grain. A large volume of fast-flowing water passing over a water wheel could theoretically be used to turn the high-power motors of appliances like fans and refrigerators. The energy of a water wheel could be transformed to heat energy to heat your home or oven, by using a mechanism that rubs against the wheel to create friction. In theory, with enough energy it could even be possible to generate enough heat in this way to cause a metal filament (like that in an incandescent light bulb) to glow, giving artificial lighting. In fact, since any form of energy can theoretically be converted into any other, in principle any appliance could be operated by the gravitational potential energy harnessed by water wheels.
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We could imagine a world based on this idea. Water would be provided to the roof of every home by a grid of pipes. This water would then be allowed to flow from the roof to the floor. Water wheels would harness the energy of this flow and use it to power all of our appliances. It would be a modern, post-industrial world, but one devoid of electricity. Unfortunately, this system is completely unfeasible. The fundamental reason is that incredible quantities of water would be required to power each home. Indeed, a typical Australian household consumes about 15 kWh (or 50 MJ) of energy each day. To generate that quantity of energy by water flowing from the top to bottom of a five-metre-high home would require at least a million litres of water every day.1 This is the equivalent of half an Olympic swimming pool of water each day, or multiple large domestic rainwater tanks of water each hour, being provided to the roof of every house. Clearly, an alternative approach is needed.
From Water Wheels to Electronics
This alternative is electricity. Fundamentally, electricity is a force like gravity. Gravity causes objects with mass to attract each other. Objects fall down to the Earth because the Earth is so massive that it strongly pulls everything towards it. Similarly, the electric force causes objects with opposite electric charges to attract each other. The most important type of object with an electric charge is the electron, which is one of the fundamental particles of nature that make up all atoms. Its charge is negative, which means that if you prepare a metal plate that has a strong positive charge (called a positive terminal in electronics), electrons will be pulled towards it, just as water at the top of a hill is pulled down towards the ground.
This means that electrons have energy associated with electricity analogous to the energy of water associated with gravity. Specifically, electrons that are held away from a positive terminal have stored energy called electrical potential energy, just as water at the top of a hill has gravitational potential energy. If you release these electrons, they will flow towards the terminal, just as water flows in a river, releasing their potential energy as they do so. This energy can be harnessed by placing a mechanism (called a resistor) in the path of flowing electrons, just like a water wheel in the path of flowing water. This energy can be converted into other forms to power a wide range of appliances, just as we imagined with the energy of water wheels. Realising this potential is the art and science of electronics.
This is what happens when you flick a switch. Electricity is provided to our home through wires, just as water is supplied through pipes. A switch that is off blocks the flow of this electricity, just like a tap that is off blocks the flow of water in a pipe. When we turn on the switch, this barrier is removed and electricity is allowed to flow through the wire. The wire directs this flow through the appropriate electronic components that harness the energy of the flow just as a water wheel harnesses the energy of the flow of water. For example, it may be directed through a resistor that creates friction to heat a heating element in an oven, or to heat a metal filament so much that it glows in an incandescent light bulb. Alternatively, it can be sent through an electric motor, which uses magnets to harness the energy to turn a wheel. Computers and modern light bulbs depend on components like diodes and transistors that use the energy of electrons’ flow in yet more sophisticated ways. But in all cases they use the same fundamental principle discovered by inventors of the water wheel millennia ago; potential energy released by flowing particles can be harnessed to power useful processes.

Why Electricity?
However, while electronics are fundamentally similar to water wheels, they have a decisive advantage that explains why electricity is ubiquitous in modern society while water wheels are a relic of the past — efficiency. While powering a typical household using water wheels would require a thousand tonnes (i.e., a million litres) of water each day, a microscopic mass of electrons is sufficient to provide the same electrical energy. Indeed, at the standard Australian mains voltage of 240 V, just 0.0001 grams of electrons contains the required 50 MJ of electrical potential energy. This is why electricity is a feasible basis for powering the modern world in a way that water wheels never could be. It does not require the transport of unwieldy quantities of matter; microscopic particles in thin metal wires are sufficient.
The reason for this difference is that electricity is a much stronger force of nature than gravity. Gravity is an extremely important force at large scales; it is what keeps us on the surface of the Earth, and the Earth orbitting around the Sun. However, it only becomes significant through the accumulated effect of huge amounts of mass. In fact, while gravity is the most accessible of the fundamental forces of nature, which is why it has been used since ancient times in technologies such as the water wheel, it is actually the weakest of the forces. Building the modern world depended on harnessing a far stronger force: electricity. The electrical force between two electrons is more than a million trillion trillion trillion (10^42) times stronger than the gravitational force.2 The energy that can be harnessed from the flow of electrons in electricity is correspondingly much larger than that which can be harnessed from the flow of water under gravity, which is what makes electricity such a powerful tool.

Electricity therefore reminds us of the importance of exploratory science. Until modern times, electricity was a mere curiosity. It was observed in lightning, electric fish and amber rods that could attract feathers after being rubbed on a cat. No-one could have guessed then that it could be used to light up our homes and cities, cook our food, talk to each other from across the world, or transport us across a country. But curiosity was reason enough for early modern scientists to want to understand it. Their investigations uncovered the immense, hidden strength of the electrical force, and how it could be used to harness energy from the flow of electrons. Today, the electrical energy of electron flow powers our lives. Our modern world is epitomised by an abundance of bright shining lights that could all be said to glow with the flow.
The gravitational potential energy contained in a mass m of water falling from a height h on the Earth is E=mgh, where g is approximately 10 m/s^2. Therefore, the mass of water falling required to generate energy E is m = E/gh = E/50. Therefore, it requires one million kilograms of water, or one million litres, to generate fifty million joules (50 MJ) of energy. This is the amount of water that would be required if the water wheels were 100% efficient; in reality, far more water would be required. For comparison, it takes more than five years for a typical Australian household to consume the water that would be required by this energy system every day.
Let G be the universal gravitational constant, k be the Coulomb constant, q be the charge of an electron and m be the mass of an electron. Then, the ratio of the electric force to the gravitational force between two electrons separated by any distance, r, is:
Thanks again Paul. I am wondering if you have a view on what seems to have been a bit of a debate [here seen in YouTube] about whether electrons actually do “flow” in wires… https://youtu.be/bHIhgxav9LY