### Electricity and Magnetism

In the last quiz, we talked about the flow of electricity in a loop of wire connected to a battery. Sometimes, we can even see electricity in a lightning strike or a discharge of sparks from a power line.

But what is electricity? Is it a substance? Is it a form of light? Are only certain objects capable of carrying electricity? Or is it hiding in every material?

After centuries of study, our modern view is that electricity is the movement of certain particles, each of which has a property called electric charge. These particles make up everything around us, even objects that aren't obviously "electrified."

Electric charge is an abstract concept because it's often invisible to us. But in this quiz, we're going to approach the idea with an analogy you can see directly: grains of sand that are either red or yellow.

# The Sand Grain Analogy

Imagine we find ourselves in a desert with nothing but sand as far as the eye can see. At first glance, it seems like the sand is bright orange — but if we lean in, we see that the grains of sand come in two colors, red and yellow.

Why should they be so evenly mixed? Curious, we scoop some sand into two piles and start moving only the yellow grains from pile $\textrm{A}$ to pile $\textrm{B}$.

Pile $\textrm{B}$ starts looking more yellow as we add more yellow grains. How does the color of pile $\textrm{A}$ change after some time?

# The Sand Grain Analogy

Instead of the yellow sand grains, we might have decided to move the red sand grains.

Starting from two orange piles, we spend some time moving red grains from pile $\text{A}$ to pile $\text{B}.$

How do the colors of the piles change after we've been doing this for a while?

# The Sand Grain Analogy

Select one or more

In our sand grain analogy, the red and yellow grains represent particles that carry the two types of electric charge. Like mass or spin, electric charge is an immutable property of fundamental particles.

Physicists have discovered a menagerie of particles over the years, but in this course on electricity and magnetism, we will mostly be concerned with the two most stable charge-carrying matter particles: protons and electrons. Along with neutrons, these are the particles that make up the atoms within you and around you.

All the matter around us is made of atoms, which contain charged particles: electrons and protons.

We can't see electric charge, so how do we know electric charge is a property of particles? And how do we know there are only two kinds of charge, but not one or three or ten? How do we know electrons and protons carry different kinds of charge? For some answers, let's turn back to the sand grain analogy.

# The Sand Grain Analogy

As we're moving yellow grains from pile $\text{A}$ to pile $\text{B},$ something strange starts to happen. It becomes harder to pull the grains out of pile $\text{A}.$ Some force is pulling them back. Spooky!

Furthermore, to place the yellow grains on pile $\text{B},$ we have to push against another invisible force even before the grains touch the pile. The more yellow pile $\text{B}$ gets, the stronger this force becomes.

Curiously, you take two individual yellow grains and start to bring them together. What do you expect to happen?

# The Sand Grain Analogy

If we repeat this experiment with red grains, we see the same thing happen: the red grains push each other apart.

But what about grains of different colors? If we try to push a yellow grain and a red grain together, what would we expect to see based on our observations?

# The Sand Grain Analogy

The force between two grains that are the same color is repulsive — it pushes the grains apart. On the other hand, the force between two grains that are different colors is attractive.

Before we started separating the sand, we had no difficulty removing yellow grains from one orange pile and adding them to the other. So, piles that are an even mix of the two kinds of sand don't attract or repel incoming grains of red or yellow sand.

What can we conclude from this?

# The Sand Grain Analogy

In the sand grain analogy, we found a difference between how two grains interact that depends on whether they are the same color or not.

The structure of a helium atom, containing two protons, two neutrons, and two electrons

Like our made-up example with sand grains and color, the electric charge carried by electrons and protons endows them with observable behaviors. In fact, these behaviors map exactly onto the sand grain interactions:

• Electrons are repelled by other electrons.
• Protons are repelled by other protons.
• Protons and electrons are attracted to each other.

These forces are present deep within the matter around you. Every atom contains electrons, along with oppositely charged protons and uncharged neutrons.

Electric charge is everywhere, yet we rarely notice electric forces between everyday objects. Why might this be?

# The Sand Grain Analogy

Most matter is neutral (i.e. it has no excess electric charge), but under some circumstances, even neutral objects can be attracted to charged objects. Does this contradict our theory, where only imbalanced piles of sand feel forces?

Unlike grains of sand, in many materials some of the electrons are able to move around — at least a little — inside the material. This is especially true in metals, where some electrons can move freely throughout the metal.

Let's consider what would happen if we placed a neutral copper ball near a charged copper ball, which we've arranged to have more protons than electrons. With protons shown as red and electrons shown as yellow, which image shows the distribution of charge inside the neutral copper ball?

# The Sand Grain Analogy

Soon, we'll see how electric forces are stronger between nearby objects than between faraway objects.

As a result, when this charge redistribution is induced in the conductive ball, the yellow side will be attracted more strongly than the red side is repelled. As a result, the ball feels a weak attraction to the red ball despite its charge neutrality. In this way, some neutral objects can feel electric forces.

In the next quiz, we'll apply the ideas we've just developed, and see how to create charge imbalances in the real world.

# The Sand Grain Analogy

×