Lesson Video: Electric Potential Difference Science

Video Transcript

In this video, we will learn what electric potential difference is and how an electric potential difference across a component in a circuit creates a current in that component. We’re going to see that electric potential difference involves doing work on electric charges.

Say that we start out with these two objects. They could be anything. They could be marbles or Ping-Pong balls or balloons. But the important thing about these objects is that each one has an electric charge. Remember that there are two types of electric charge. There’s positive charge and negative charge. And what we’re going to say is this object on the left has a positive charge, and the one on the right has a negative electric charge.

Any time an object has an electric charge, that means it exerts a force on any other object that also has an electric charge. This means that each of our objects will exert a force on the other object. We can tell what sort of force this will be because these two objects have different or opposite electric charges. Objects with opposite electric charge attract one another. The red object will be pulled to the right and the blue object to the left. So the objects will get closer together. And in fact, they’ll continue moving toward one another until they meet. In order to stop this from happening, to keep the charges in place or even to move them farther apart from one another, we would need to exert a force on these charges. That force would need to be at least as strong as the force that pulls the charges together.

Now, say that we did that, say that we push on each one of these objects with a force, we’ll call 𝐹, that is strong enough so that the objects do move apart. By doing this, we’ve done what is called work on these two objects. In physics, this word work has a very specific meaning. It’s equal to the force we exert on some object multiplied by the displacement or movement of that object. Because we exerted a force on both our positively charged and negatively charged objects and we made those objects move because of that force, we did work on them. This all relates closely to electric potential difference. Any time we do work, where that work is spread over some amount of electric charge, then we have created electric potential difference.

Electric potential difference is a long-sounding phrase, but now we know what it means physically. Given a group of objects with electric charge, say, these two objects here, we create electric potential difference when we do work on those charges. This equation shows us how we can get more or less electric potential difference. Working with these two objects, we can increase their electric potential difference by doing more work on them. That could mean applying this force 𝐹 for a longer time so that the charges move farther and farther apart. This means if we wanted to decrease the electric potential difference of these charges, we could of course do less work on them. In that case, they would end up closer together rather than farther apart.

We see though that something else that affects electric potential difference is the amount of charge involved. If we, say, increased the amount of charge on each of these two objects while we kept the work done on the charges the same as it was before, then overall we would decrease their electric potential difference. This idea of electric charges being separated by work is actually behind what makes charges flow in an electric circuit.

Imagine that we have a chunk of metal sitting on our desk. If we looked very, very closely at this metal block, we could see the atoms that make it up. Here, each red dot represents the nucleus of an atom. This nucleus has an overall positive charge, and each little blue dot represents an electron. These have negative electric charge. So all throughout this metal block, we’ve got a bunch of objects with positive and negative electric charges. Just like before, when we only had two charged objects, we can do work on these charges. Now, there’s a bit of a special condition here. Because we’re working with a piece of metal, that means the positively charged nuclei are fixed in place. They can’t move. The electrons, on the other hand, can move. They’re free to move all throughout this block of material.

So if we start to do work on these charges to push them apart, farther apart than they would naturally be, the red dots, the nuclei, will stay fixed in place. But the blue dots, the electrons, will start to move toward one end of this metal block. The charges in the metal will start to look something like this. Notice that now there are many more electrons near this end of the block and far fewer electrons over here. And again, this happened because we’ve done work on these charges. Since we’ve done work over this group of charges, that means there’s an electric potential difference from one end of this block to the other. The way we got this separation of charge so that mostly negative charge was over here and mostly positive charge was here was by exerting a force on these charges.

If we stopped exerting that force, then all these negative charges would go back to the way they were before, evenly spread out throughout this block. But, say, instead we maintain this electric potential difference. That is, we keep pushing on the negative charges toward the right side of the block. Even though they’re attracted to the overall positive side on the left, we don’t let them move that way because of the forces we exert. Set up this way, this block of material is like a cell or a battery. The purpose of a cell in an electric circuit is to supply an electric potential difference. We’ve said that the negative charges at this end of our cell are naturally attracted to the positive charges at this end but that they can’t move that way so long as we maintain this electric potential difference.

Now, say that we take a bit of wire attached to a light bulb and we fasten the ends of the wire to the ends of our cell like this. The negative charges at this end of our cell, which all repel one another, now have a pathway to travel to get towards the positive end of the cell. The negative electrons will flow out this way. The wire itself already has electrons in it. And the movement of electrons from the cell will push them along the wire, causing the bulb to light up and charge to flow all through the circuit as it moves toward the positive end of the cell. This flow of electrons is called electric current.

Any time there’s an electric potential difference across an electric circuit, charge will flow. There will be current. The amount of current depends, in part, on the amount of electric potential difference. Electric potential difference is measured in units called volts. A small cell or battery, for example, might provide 1.5 volts of potential difference. The way our cell here is set up, we’ve seen that the end of the cell with an overall negative charge is here. This is called the negative terminal of the cell. Likewise, this end here, which has mostly positive charges, is called the positive terminal.

We can represent a cell using something called a circuit symbol. A cell with its positive terminal on the left and its negative terminal on the right would be symbolized this way. Notice that the shorter line corresponds to that negative terminal. Likewise, there’s a circuit symbol for a bulb. That looks like this. It’s a circle with two diagonal lines making a cross. When we connect these circuit symbols using straight lines, we’re saying they’re all joined in one continuous circuit. So here is our cell with its positive terminal on the left, here is our bulb, and here is wire connecting the cell and bulb. Because the cell creates an electric potential difference across the bulb, electric charge flows through it.

Knowing all this, let’s look now at a few examples.

The picture shows an electron that is near to an atomic nucleus. Do the atomic nucleus and the electron attract or repel one another?

In our picture, we have two objects: an atomic nucleus and an electron. Our question is asking whether the nucleus and electron attract or repel one another. This implies that there’s some force between them. These two objects will have a force between them if they both have an electric charge. Indeed, that’s the case. An electron has a negative electric charge, while an atomic nucleus overall has a positive electric charge. Since both objects are charged, there will be a force between them. What’s more, we know that these objects have opposite electric charges. Whenever two objects have opposite electric charges, they attract one another. There will be a force on the nucleus toward the electron and a force on the electron toward the nucleus. In answer to this question then, we write that the nucleus and the electron attract each other.

Let’s look now at part two of this example.

Which of the following statements is true? (A) The electron can be moved farther away from the nucleus without doing any work. (B) In order to move the electron farther away from the nucleus, work must be done on the electron.

We’ve seen from the first part of this question that there’s an attractive force between the nucleus and the electron. This force will tend to make the electron and nucleus move closer together. In this part of our question, though, we’re imagining moving the electron farther away from the nucleus. To do that, we would need to exert some force that would overcome this attractive force, drawing the electron and nucleus together. So we need to exert a force on the electron, and this force is what would cause it to move farther away. Since we’re exerting a force on the electron over some distance, that means we’re doing work on it. If we didn’t do any work on the electron, there’s no way it could move farther from the nucleus. And so we choose answer option (B). In order to move the electron farther away from the nucleus, work must be done on the electron.

Let’s look now at another example.

A cell does work on the charges within it to create a separation of charge across its two terminals. Complete the following sentence: The potential difference provided by the cell is equal to the blank divided by the blank. (A) Amount of charge that has been separated, amount of work done. (B) Amount of charge that has been separated, distance between the terminals. (C) Amount of work done, amount of charge that has been separated. (D) Amount of work done, distance between the terminals.

Knowing that we’re working here with a cell, let’s clear some space at the top of our screen and consider what’s happening in this cell. This cell contains electric charges. It has positive charges, we’ve shown them here in red, arranged in an orderly grid. And it also has negative charges here in blue. These charges are able to move throughout the cell. We’re told that the cell does work on these charges to separate them. This means it exerts forces on the charges and causes them to move. We mentioned that the red charges, the positive ones, are fixed in place, but the blue negative charges can move. So this force will make the blue negative charges concentrate at one end of the cell.

For that reason, this end of the cell is called its negative terminal. And that means the other end, where there are more positive than negative charges, is the positive terminal. So the cell has done work on the charges within it to create a charge separation. This separation of charges means there’s now a potential difference across the cell.

We want to know which of our four answer options best describes this potential difference by filling in the gaps in our sentence. The first thing we can say about this potential difference is that it depends on the amount of work that was done to separate the charges in the cell. The greater the amount of work, the more negative charges would tend toward the negative terminal, and therefore the larger the potential difference would be. Now, notice that our sentence is describing a fraction. Whatever goes in the first blank is being divided by whatever goes in the second blank. We can think of this sentence in fact as being similar to a mathematical equation for potential difference.

Clearing just a bit more space still, we can write that that equation would go like this. The potential difference provided by the cell, we’ll call it PD, is equal to whatever goes in the first blank of our sentence divided by whatever goes in the second blank. A moment ago, we noted that the more work was done on the charges in the cell, the greater the potential difference across the cell would be. And that tells us what must go in the first blank in our sentence. The amount of work done by the cell must be in the numerator of this fraction. Looking over our answer options, we see that only options (C) and (D) have the amount of work done going in that first blank.

Right away then, we can eliminate options (A) and (B) from consideration. Options (C) and (D) are different in what they suggest for completing the second blank. Choice (C) gives the amount of charge that has been separated. Option (D), on the other hand, describes the distance between the terminals, that is, the physical distance between the positive and negative terminals of our cell.

Now, let’s think for a moment about work as it applies in physical situations. The work done on an object, say, one of these charges in the cell, is equal to the force exerted on that charge multiplied by the distance the charge travels. In other words, the distance these charges move is already included in this idea of work. We don’t need to take that distance into account again, as option (D) suggests. If, instead of distance, we put charge in the denominator of this fraction, then we see that for some fixed amount of work done on the charges, more charge having to be separated means that fixed amount of work doesn’t separate the charge very much. And that means that the potential difference is not so great.

On the other hand, for a smaller amount of charge, a fixed amount of work can push those charges relatively farther apart from one another. Fewer charges to separate then means a greater potential difference again for a given amount of work done. It does make sense then that work would go in the numerator of this fraction and charge in the denominator. For our answer then, we choose option (C). The potential difference provided by the cell is equal to the amount of work done divided by the amount of charge that has been separated.

Let’s finish this lesson by reviewing a few key points. In this video, we learned that electric potential difference, sometimes called potential difference for short, equals the work done to separate electric charges divided by the amount of charge that is separated. And we saw also that electric potential difference across a component in a circuit creates current in that component. Lastly, we learned that electric potential difference is measured in units of volts, abbreviated capital V. This is a summary of electric potential difference.