### Video Transcript

An acetate rod is rubbed with a cloth duster, giving the acetate rod a net positive charge and the duster a net negative charge. Which object has gained electrons? Which object has lost electrons?

Okay. So in this question, we’ve been given an acetate rod and a cloth duster. We rub the two against each other resulting in a net positive charge for the acetate rod and a net negative charge for the duster. So in this question, we’re discussing static electricity, the transfer of charges from one of these objects to the other. We need to work out which object has gained electrons and which object has lost electrons. So let’s represent the acetate rod with a blue cylinder and the cloth duster with this weird-looking cloth-like thing.

Now before we rub them together, we know that both of these are neutral. They’re not charged either way, neither positive nor negative. And this is because, generally, objects tend to be neutral. They don’t have an overall charge on them. This is because the number of electrons in these objects tend to be equal to the number of protons in these objects. And so the total charge on them, when we get count for all the protons and electrons, tends to be zero. In other words, we can say that for the acetate rod, the number of electrons, capital 𝑁 sub e, is equal to the number of protons, capital 𝑁 sub p.

Another way to think about this, is that the number of negative charges in the acetate rod is equal to the number of positive charges. And so the total charge on the rod is zero. Similarly, for the cloth duster, we can say that the number of electrons in the cloth duster, this time lower case 𝑛 sub e, is equal to the number of protons, lowercase 𝑛 sub p. So notice the following. The number of electrons in the cloth duster is equal to the number of protons. And the number of electrons in the acetate rod is equal to the number of protons in the acetate rod. However, these numbers do not have to equal each other. All that we know is that the acetate rod has a certain number of electrons and protons. And those numbers have to be the same. And the cloth duster has a certain number of electrons and protons. And those numbers have to be the same.

So now we can see what happens when we rub these two together. And here we are rubbing the two objects together. And this obviously is going to result in a transfer of charges. We’ve been told in the question, if we read it carefully, that the charges that are being transferred are electrons because the question is asking us which object has gained electrons and which object has lost electrons. Therefore, some electrons will be transferred from one object to the other. Now, let’s see what happens when we take these two objects apart from each other. Specifically, let’s see what happens to the number of protons and electrons in each object.

Well, we know that the number of protons in each object has to stay the same because the protons are not being transferred. So earlier on in the video, we saw that the acetate rod has capital 𝑁 sub p protons. After the cloth duster is rubbed on the acetate rod, the acetate rod still has capital 𝑁 sub p protons because like we said, the protons are not being transferred. So the number of protons stays the same. However, the number of electrons does change. We’ll call this capital 𝑁 sub e, with a superscript “new”. The new tells us that this is the new number of electrons after the electrons have been transferred from one object to the other.

Now we know that electrons are negatively charged, and protons are positively charged. We also know from the question that the acetate rod has a net positive charge. In order for this to happen, the number of protons in the acetate rod must be larger than the number of electrons in the acetate rod. This is because if there are more protons, then the overall charge on the acetate rod will be positive. Therefore, the new number of electrons in the acetate rod is less than the number of protons remaining in the acetate rod.

We can apply the same logic to the cloth duster. We can say that the new number of electrons in the cloth duster is lowercase 𝑛 sub e, with a superscript “new”. We also know that the cloth duster has a net negative charge. So it must have more electrons than protons. Therefore, the number of electrons, lowercase 𝑛 sub e with a superscript “new”, is greater than the number of protons, lowercase 𝑛 sub p. And from this we can see that the acetate rod has lost electrons and the cloth duster has gained electrons. This is the only way that the acetate rod will have a net positive charge and the duster will have a net negative charge.

And so our final answer is that the cloth duster has gained electrons and the acetate rod has lost electrons.