Video: Electric Fields

In this lesson, we will learn how to interpret diagrams of electric field lines and relate how the field lines are drawn to the strength and direction of the electric field.

14:35

Video Transcript

In this video, we’re going to learn about electric fields. We’ll see what these fields are, how they work, and how they interact with electric charges.

The first thing to know about electric fields is that they’re created by electric charges. Any charge — whether the positive one we have here or a negative charge — creates an electric field around itself. At this particular moment though, if we were to say that this positive charge was the only electric charge in the universe, we couldn’t find evidence for its electric field. It takes some other electric charge — say this one over here — to respond to the field created by this charge in the first place. And by the way, this second charge we’ve drawn in also would create a field itself and the first charge would then respond to that.

In order to make sure we know which charge we’re referring to, let’s take this original charge and we’ll put it on a stand. We’ll fix it in place and we’ll call this the source charge. It’s the electric field created by this charge that we’ll consider specifically. We can give a name to this other charge. We can call this a test charge. We call it that because we’re gonna move this charge around and test the electric field created by our source charge. And remember this is all with the idea of better understanding this invisible phenomenon that we’re calling an electric field.

One way to start getting a sense for this field is to see in what direction it either pushes or pulls our test charge. When it comes to electric charge interaction, we know that two like charges — like the two positive charges we have here — will mutually repel one another. They’ll push one another away. That means if we were to sketch in an arrow representing the direction of the electric force on our test charge, that arrow would point on a line directly away from the source charge.

Now, if we stopped here and based our understanding of the electric field just on this single piece of information we’ve found, we might get the idea that the field is pointing all in this direction, maybe looking something like this. But let’s keep moving our test charge around. Let’s say we put our test charge here. In this case, the test charge would experience a force up in this direction again directly away from the source.

Notice also that the arrow representing this force is shorter than the one we had before. In other words, the magnitude of the push is smaller than when the test charge was closer and towards the source. If we put our test charge here, then we would see a force direction on that charge like this. If we put it here down below the source, we would see this positive test charge move in this direction. And if we tried this spot for our test charge, now we would see that charge move this way.

We’re starting to see a map of what the electric field created by our positive source charge looks like. The field seems to always act along this radio lines pointing outward from the center of the source charge. This is an important realisation about electric fields. So let’s stop for a moment and record some of what we’ve learned about these fields so far.

We’ve learned that all electric charges whether positive or negative create electric fields. Just now, we saw that electric fields point radially from a point charge. In other words, if the point charge is like the center of a wheel, then the electric field points like the spokes of the wheel. We could draw it this way. We could show our source charge and then the electric field lines — that’s what these yellow lines are called — pointing out from that source. Now as we said, electric fields are invisible. And of course, if they had no physical effect, then we wouldn’t be very interested in them or know much about them.

But let’s return to the arrows that we drew in representing the force acting on our test charge as we moved it around our positive source charge. These five arrows we’ve drawn in represent the magnitude and direction of the electric force acting on the test charge. Notice that that force is a force at a distance. After all, the source charge and the test charge aren’t touching one another. They aren’t in physical contact. We say that the electric force is mediated or transmitted by the electric field. And that’s why we’re so interested in the electric field because it’s responsible for the force that pushes and pulls electric charge.

Okay, at this point, we might start to think that electric fields are only created by positive charges. After all, we have a positive source charge and we’ve been working with a positive test charge. But that would go against our rule that all electric charges create electric fields. And indeed, if we switched out our positive source charge with a negative one and if we then used a test charge that was also negative, we could create a similar mapping of the electric field created by our now negative source. But in a way, we don’t need to do that because we’ve already discovered that electric fields in general whether they’re created by positive or negative sources point radially from a point charge.

So instead of doing that, let’s switch things up a bit. Let’s turn our negative test charge back into a positive charge. When we do this of course, we now have a positive charge interacting with a negative charge, opposites. When we do have a case of two oppositely charged particles interacting, we know the force between them is attractive, not repulsive. That would mean if we sketch in the force acting on our positive test charge, it will look something like this, straight towards the center of the negative source.

But remember when we had a positive source charge, the force on the positive test charge was in the opposite direction. This difference in direction tells us that the electric field created by a negative source is not the same as that created by a positive. In other words, to be comprehensive, we would want to draw an electric field coming from a negative source because that field is somehow different from this one, the one coming from a positive source.

So then, just how are these two fields different? Well, looking at the difference in force direction on our positive test charge, we can tell that the fields have opposite directions. They point in opposite ways. The positive source charge pushes this positive test charge away. So we could complete our sketch for the electric field created by a positive source by putting these arrowheads on those lines, while a negative source pulls this positive charge toward it. In this case then for the electric field from a negative source, we’ll draw those field lines pointing in toward the source.

What we’re learning then is something about electric field direction. The direction electric fields point is the same as the direction that a positive charge in the field would move. That’s why all the electric field lines point inward in the case of our negative source and outward in the case of our positive. And now, it’s time to start understanding electric fields at a deeper level. We’ve seen that they have a direction associated with them. And more than that, they even have a magnitude. That is, electric fields are vector quantities. We’ve seen the sense in which electric fields have a direction. But what would their magnitude be? How would we represent that?

To see how we do that, let’s draw in some electric field lines created by our negative source charge. With that done, let’s now consider what will happen to our positive test charge as we slide it up and down — so to speak — this imaginary field line. Always remember by the way that when you see electric field lines drawn in a diagram, they aren’t physically real structures. They just represent electric field properties. But anyway, we’re gonna move our positive test charge up and down this field line and see what happens.

For starters, let’s say that we move it farther away from the negative source. With our test charge farther away from the source, the force vector — that is the electric force acting on it — would still point directly towards the source. But its magnitude will be smaller. That is, the arrow will be shorter. Now, let’s try moving our test charge close to the source. In this case, the force on our test charge would be very strong indeed represented by a longer arrow than the others and in the same direction as before towards the center of the source. So no surprise, as we moved our test charge closer and closer in, the force on it got comparatively stronger.

But notice something about the electric field lines of our source charge. Out here where our test charge was far away from the source, the field lines are fairly far apart from one another. As we moved to the middle position, the field lines got nearer one another, separated by a smaller distance. And close in, they’re separated by an even smaller distance. Here’s what we could say about this. We could say that the density of the electric field lines is increasing as we move towards the source charge.

Now, we may be used to thinking of this term density as a mass per unit volume. And indeed, that’s the definition of density. In our case, we’re using this term in a slightly different way. When we talk about the density of electric field lines, we mean how many field lines fill a certain volume of space. Of course, the field lines don’t have mass. But we can count how many of them are spread out over a certain space. We can think of it this way.

Let’s say that we create a square and the square looks just like this and it has this size. And what we’re gonna do is count how many field lines appear in that square as we move it closer and closer to the source. Right now, as we’re farther away, we can see that there’s just one field line in it. But then, we move this same-size square closer in. Now, there are two electric field lines through it. And we can move it closer still. And now, we count one, two, three, four, five field lines through it.

The point is as we move this same-size square closer and closer in towards the source, we found more field lines moving through it. That is, the density of field lines is increasing. And we can recall that as we moved our test charge closer and closer in towards the source, the magnitude of the force acting on it increased. Here’s the point of all this. We can connect the density of electric field lines with the strength of the field and therefore the strength of the electric force. We can write that out this way. We can say that the electric field line density — that is how many field lines there are over a certain space — indicates electric field strength: the greater the density, the greater the field strength.

So far, we’ve learnt quite a lot about electric fields. Before we try out a couple of examples, let’s cover one more thing. So far, we’ve just talked about the fields created by point charges, a single positive or a single negative charge. But really, any object so long as it has a net electric charge to it will create an electric field. And that field will look different than the fields created by the point charges we’ve studied so far.

For example, imagine that we have a gigantic flat plate. This plate goes on and on as far as the eye can see. And let’s say further that this plate has an overall or a net positive electric charge. Because of that, this plate will create an electric field around itself. And the electric field lines will look something like this. Notice that they point away from the plate because it has a positive charge, but they’re parallel with one another. That is, these lines would never cross.

By the way, that’s actually quite a good thing because electric field lines never should cross. If we ever did have electric field lines that crossed, that would mean that if we put a test charge right at their crossover point, that test charge will tend to move in two different directions. But that doesn’t make sense. Remember electric field lines point in the direction a positive charge in the field would move. If we had overlapping field lines that would seem to say that a positive test charge placed there would move into different directions. But that can’t be.

So anyway, these field lines coming out from our plate don’t get closer together and they don’t move farther apart. That tells us something about the electric field strength. Looking down here, we saw that electric field line density indicates electric field strength. But if the field lines are parallel and they are, that means that density is never changing. If the field line density isn’t changing, the electric field strength isn’t changing either. So that’s interesting.

But then imagine something yet further. Let’s say that we add more positive charge to this large plate. When we did that, we would need to add more electric field lines than we drew previously because now the electric field is stronger than it was before. Once again though, the field lines are parallel. And therefore, the field strength is constant no matter how far where we get from this plate. Alright, all that said, let’s look at an example question involving electric fields.

The diagram shows the electric field created by a pair of parallel charged plates. The red plate represents the positively charged plate and the blue plate represents the negatively charged plate. At which of the points 𝑃, 𝑅, or 𝑆 is the electric field strongest?

Looking at the diagram, we see the red plate which we’re told has a positive charge and the blue plate which we know has a negative charge. Thanks to that charge difference, an electric field is set up between the plates. And we see the field lines represented by these hashed lines. We also see three points between the plates: point 𝑃, point 𝑅, and point 𝑆. And we want to know at which of these three points is the electric field strongest. To figure this out, there’s something we’ll want to recall about electric field lines and how they relate to electric field strength.

Electric field line density indicates relative electric field strength. That means that electric field lines which are spaced closer together indicate a stronger electric field than field lines that are spaced farther apart. For example, if we were to look at the electric field created by a positive point charge, if we put a box far away from this point charge, not many field lines will pass through it. But as we move the box in closer, more field lines would pass through it. That is, field line density would increase. And likewise, electric field strength would increase. And that brings us back to our diagram.

When we look at these electric field lines between the parallel plates, we notice that they run parallel to one another. That is, the spacing between electric field lines is always the same. They don’t get closer together or farther apart. In other words, the electric field line density is constant all throughout this region between the plates. And that tells us that the relative electric field strength is also a constant in this region. It’s not stronger in one place and weaker in another. But it’s the same strength everywhere. This is true whether we’re considering points 𝑃, 𝑅, and 𝑆 or any point in between these plates. That then tells us our answer about where the electric field is strongest. The electric field has the same strength at each point. And as we saw, that includes all points between the parallel plates.

We’re now at a good point to summarise what we’ve learnt about electric fields. Starting off, we learnt all electric charges produce electric fields. It’s the electric fields that mediate or transmit electric force, the pushes and pulls on electric charges. For point charges, the electric fields they produce are aligned like the spokes on the wheel of a bicycle. That is, they point radially from the source charge. We also learnt that the fields created by positive and negative point charges are not the same. They point in opposite directions. The field created by a positive charge points outward and the field created by a negative charge points in toward that charge.

Along with that, we learnt that electric field line density — the number of field lines contained within a space or a volume — indicates the relative electric field strength. And last but not least, we saw that electric field lines never cross one another because that would indicate that at the intersection point, the force on a charged particle will be in two different directions. There’s lots more to learn about electric fields. But these points will help get us started.

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