Electricity begins with electric force. Electric force can be explained by saying matter has a property called charge.

Written by Willy McAllister.

### Contents

• A good way to learn about charge is to understand its historical development. The idea of charge came about to explain the existence of electric force.

• There are two types of charge. Benjamin Franklin gave us the names for charge, Plus and Minus. The same (like) charges repel each other, and different (unlike) charges attract each other.

• Charles Augustin de Coulomb worked out how the electric force behaves. He showed the electric force is proportional to the product of the two charges $(q_1, q_2)$, and inversely proportional to the square of the distance between the charges. This is called Coulomb’s Law.

$F_e \propto \dfrac{q_1 \, q_2}{r^2}$

• The smallest charged objects we know of are two sub-atomic particles, the electron $(-)$ and the proton $(+)$. They have the same charge, with opposite signs.

• You can specify a specific amount of charge two ways, in units of coulombs or as some number of electron charges, $e^-$.

• The definition of $1 \,\text{coulomb}$ is the amount of charge that moves past a point in a wire in $1\,\text{second}$ when the current is $1\,\text{ampere}$.

• One coulomb is equivalent to the combined charge of $6.242 \times 10^{18}$ electrons.
The charge on an electron is $e^- = 1.602 \times 10^{-19}$ coulombs.

## Eels and amber

Let’s start 5000 years ago. For the moment, pretend you never heard of charge or electricity, and forget you know anything about atoms. Around 5000 years ago, the Egyptians knew if you touched an eel it could give you a shock. They didn’t know why it happened, but they used to tell sick people to touch eels, and sometimes it made them feel better (other times probably not). This very first practical application of electricity was in medicine.

Back in those days, the Greeks made jewelry out of a pretty stone called amber. Amber isn’t really a stone, it is fossilized resin from trees. Resin is a goopy substance trees make as a defense to fight off insects and cover wounds when a branch gets broken. Sometimes when this goopy stuff drips from the tree it turns into a solid (fossilizes) and gets the name amber. Amber is basically a natural version of plastic.

So Egyptian or Greek aristocrats lounging around wearing their fancy amber jewelry would pet their cats. They noticed light things like feathers or their own hair were attracted to the amber. Today we have a word for it, the triboelectric effect. “Tribo-“ in Greek means “rub”, so you can call it the “rubbing-electric” effect if you want.

You create the same effect by passing a plastic comb through your dry hair, or rubbing a balloon on your sweater. The comb makes your hair stand up, and the balloon sticks to things and repels other rubbed balloons.

The Greek word for amber is ἤ λ ε κ τ ρ ο ν.

λ ε κ τ ρ ο ν
eta lambda epsilon kappa tau rho omicron nu
e l e k t r o n

I bet you can guess what we use this word for.

## Making sense of electric force

So we have these observations of nature: rubbing cats or balloons. We observe this invisible “amber force,” sometimes attraction, sometimes repulsion, depending on what was rubbed. So from the very beginning we could tell there were two kinds of electric force, attraction and repulsion. Stranger yet, the force acts at a distance. The two objects don’t have to be touching, yet we see this obvious pushing or pulling force between them. This is super weird (and super fascinating!).

Maybe amber force is the same as magnetism?

This rubbing-cats force seems kind of like magnetism, which has two kinds and the same force at a distance property. But electric force has to come from a different place. Magnetism is a property of certain kinds of rocks called lodestones (a rock that contains iron). This electric force comes from the friction between amber and cat and has nothing to do with iron. As you study electrical engineering or physics you will learn that electricity and magnetism are very closely related. When these ideas come together we merge their names and call it electromagnetism.

Gravity has the same force at a distance thing, but there is only one kind of gravity (only attraction). So it is a very different kind of force.

The best explanation anyone has come up with (so far) to make sense of electric force is: Physical objects (matter) displaying this electric force possess a property called charge.

What is a "property of matter"?

Matter has a number of properties: mass, color, volume, squishiness. These are not little things that are inside the matter; they are aspects of the matter itself. When an object attracts or repels nearby objects we say it has the property of charge. Charge is not some little tiny piece of stuff tucked inside electrons and protons, it is a property of those particles.

## Making sense of charge

Great! Now we know why there is electric force. It’s because objects have charge!

So what is charge? Uhh…

To this day, we have no idea why this rub-the-cat electric force exists, just like we don’t know why gravity exists. It just does. We made up a story about charge to make us feel like we know what’s going on. The idea of charge, real or not, leads us in the right direction for understanding electricity.

The whole “acting at a distance” thing has always been puzzling, but we don’t have a better explanation. When we study electrostatics, we draw lines of force leading away from charges flowing out into nothing. We play-act that these lines are real and we stick with this theory as long as it produces great results, which it does. This is a problem for physicists to ponder on while electrical engineers go off to build stuff.

## Benjamin Franklin

In 1752 Ben Franklin nearly killed himself while flying a kite in a lightning storm. He wanted to show that lightning was made of electricity. He could tell because the key attached to the wet kite string gave off sparks and tingled his knuckles, the same as if you shuffled your feet on the carpet and touched a doorknob.

Franklin thought of electricity as an invisible electric fluid. While doing rubbing experiments he theorized that rubbing caused one object to lose some invisible electric fluid while the other object gained fluid. Franklin coined the word charge and gave us the names of the two charges, “positive” and “negative”.

What's in a name?

The names $+$ and $-$ made sense. If you let equal amounts of the two charges come together you get zero charge (neutral). So charge seems like it can be described with positive and negative numbers because of the way charges combine. But Franklin could have chosen another pair of words instead of the signs we use for numbers. Like maybe "in" and "out" or "red" and "blue". After all, there are two kinds of magnetism. The poles of a magnet are not called $+$ and $-$, they are called North and South. In some ways I wish he had picked different names. The choice of number signs for charge causes some confusion when we pick the direction of positive current flow.

Franklin coined a number of electrical terms: battery, charge, conductor, plus, minus, condenser (another name for a capacitor).

So now we have a name for this electricity stuff. Charge!

## Charles Augustin de Coulomb

Even if we can’t explain why there is electric force, we can describe what it does. The first person to do a good job of this was French physicist Charles Augustin de Coulomb, in 1784. This was 30 years after Franklin, but still 113 years before the discovery of the electron in 1897 (J.J. Thomson). So Coulomb (and Franklin) worked with the idea of charge without knowing about electrons or protons or atoms.

Coulomb invented a very sensitive instrument to measure electric force, the torsion balance. He did experiments putting different amounts of charge on spheres (two little cannonballs) and measuring the electric force between them with his sensitive torsion balance. Then he worked out an equation that gave the same result as his data.

Coulomb's torsion balance (optional)

The torsion balance is based on twisting a fine wire. It works the same as if you tie a rope to a car tire and hang it from a tree. If you sit quietly in the tire, it takes only a very small nudge to make you twist back and forth. Coulomb drew this illustration of his torsion balance for a publication.

Two spheres are placed inside a chamber (Figure 1). The sphere on the left (b) sits still while the sphere on the right (a) is mounted on an arm (P and Figure 3) hanging from the thin torsion wire. If electric force is present, the sphere on the right twists as it hangs from the torsion wire. The chamber is sealed to prevent breezes from messing up the measurement. It is made of glass so you can see inside. A charge is placed on the twisting sphere. The fixed sphere starts out uncharged. You let the twisting sphere swing back and forth until it comes to rest at some position. Then some charge is placed on the fixed sphere by touching the post holding it in place (m and Figure 5) by the clamp that looks like chopsticks. This causes the twisting sphere to rotate either towards or away from the fixed sphere, depending on the sign of both charges. The amount of twist is measured on the scale (Q) going around the chamber. The other figures are close-up views of the important bits and pieces of the main instrument.

How did Coulomb himself measure charge? (optional)

Coulomb did not have very good control over exactly how much charge was applied to the spheres, but he did have good control of ratios of charge. One sphere had "some charge" and was attracted to the other sphere that had "some charge". He was quite smart about how he applied the charge. For example, start with no charge on the two spheres. You can tell they are uncharged because they don't attract or repel anything. Now put some charge on one sphere. It now has some amount of charge, let's call it $q$. ($Q$ or $q$ are the variable names Coulomb used for charge, and we still use them today.) If you touch the charged sphere to the uncharged sphere, they will share $q$ evenly between them. You don't know what the charge is precisely, but you know they are both charged the same, both with a charge of $q/2$. Can you think of a way to charge a sphere with $q/4$?

Coulomb demonstrated that the electric force is proportional to the amount of charge on each object and inversely proportional to the square of the distance between them $(1/r^2)$. We call it Coulomb’s Law.

$F \propto \dfrac{q_1\,q_2}{r^2}$

The $\propto$ symbol means “proportional to”. We will replace it with an $=$ sign by including a constant of proportionality in the equation in this article on electric force.

Check out this marvelous 1959 educational video with Professor Eric Rogers from Princeton University demonstrating electric force. You can see Professor Rogers transfer charge from his “charging arrangement” machine to one balloon and then sharing that charge with another.

## Coulomb - the unit of charge

Early electrical scientists needed a way to talk about amounts of charge. Since they didn’t know about electrons and protons they couldn’t define amounts of charge based on those particles. So charge was first defined based on a certain current flowing in a circuit.

The first definition of charge was,

$1\,\text{coulomb}$ is the amount of charge that flows in $1\,\text{second}$ when the current is $1\,\text{ampere}$.

The unit of charge was named the coulomb, in honor of guess who.

An example circuit you could build would be a $1\,\text{volt}$ battery connected to a $1\,\Omega$ resistor. Ohm’s Law tells us the current will be $\text I = \text V/\text R = 1/1 = 1 \,\text{ampere}$. When that is happening, there is $1 \,\text{coulomb}$ of charge passing by every second at every point in the circuit, by definition.

You can think of a coulomb as a bucket of charge, like a bucket of water. You can scoop smaller amounts of charge out of the bucket to get milliliters or teaspoons of charge. We actually use terms like microcoulomb $(\mu\text C)$ or nanocoulomb $(\text{nC})$. Thinking of charge as a continuous fluid is the way Franklin thought about it.

The definition of a coulomb assumes you know what an ampere is, and vice versa.

One ampere is the current you get when $1\,\text{coulomb}$ of charge is passing by every second. One coulomb is how much charge passes by in a second when the current is one ampere. These are circular definitions. To break the circle the ampere is also defined with specific conditions for an experiment you can do in a laboratory. There have been several different definitions of that experiment over time. One of the original definitions of the ampere was based the current it takes to electroplate a certain weight of silver onto a surface,

The ampère is represented by that quantity of current which is capable of depositing 4.025 grammes (62.10 grains) of silver per hour or 0.001118 grammes per second.

This was known as the silver ampere.

It’s amazing, but the classical fields of electrostatics (what we are studying here) and electrodynamics developed in the mid-to-late 1800’s did not predict or depend on the existence of the electron.

## Electron

The electron was discovered in 1892 (J.J. Thomson). We now know the smallest charged objects are two sub-atomic particles, the electron $(-)$ and the proton $(+)$. The amounts of charge on the electron and proton are identical, with opposite signs. The mass of electron is $1000\times$ less than a proton, but the charge of the two particles is identical. Nature made it that way.

The electron gets the $-$ sign and the proton the $+$ sign because of the way Franklin stated his “one fluid” theory of electricity so long ago. The material he though was lacking electric fluid had picked up extra electrons from the other material used to rub it. There was no way to know this at the time. The important point to remember is the signs/names we use for charge are arbitrary. There is nothing naturally “negative” about the electron’s charge; its only true property is that it is unlike the charge of the proton. It’s just a name.

The variable name we use for the charge of an electron is $e^-$, with the $^-$ written after the $e$. If you want to express the charge of a proton it can be written as $e^+$.

We use the expression $e^-$ for the charge on an electron. Sometimes you will see $e^-$ to indicate an electron itself. The context of the discussion will tell you which.

## Measuring charge with $e^-$

Now that we know about electrons, we have a second way to think about an amount of charge. In addition to coulombs, we can measure charge in terms of number of electron charges. Think of a coulomb of charge as a bucket full of sand, where each grain of sand is an electron charge, $e^-$. Electron charge is a useful way to talk about charge at the atomic level. Down at the level of atoms there are not so many grains of sand and each one matters.

So what is the relationship between the coulomb unit and an individual electron charge? How many grains of sand $(e^-)$ are there in a bucket of one coulomb?

Electrons are really small, and one coulomb of charge is a ton of electron charges.

In terms of electron charges,

$1$ coulomb $= 6.242 \times 10^{18} \,e^-$

This number is measured by experiment. That’s $6.242$ billion billion electrons! That is a lot of electrons moving in one ampere of current. So it’s no wonder when we deal with everyday currents we don’t count the electrons of sand, but instead talk about current in more convenient every-day number of amperes (coulombs/second).

If we take the reciprocal we derive the charge on an electron in terms of coulombs.

$e^- = \dfrac{1}{6.242 \times 10^{18}} = 1.603 \times 10^{-19}\,\text{coulomb}$

## Summary

The concept of charge explains why there is electric force.

There are two types of charge. Like charges repel, and unlike charges attract.

Franklin and Coulomb gave us the terminology and equation that describes the effect of charge.

You can talk about charge either in units of coulombs or by counting electron charges. Pick whichever way suits the discussion best.

Photo credits

Ant in Amber

Princeton PSSC Coulomb's Law