# Video: Describing Electric Fields

Figure 1 shows a polythene rod and a cloth duster. At first, neither object has a net electric charge. If the cloth duster is rubbed against the polythene rod, the polythene rod will accumulate a net negative electric charge and the cloth duster will become positively charged. Explain how an uncharged object may become negatively charged. Figure 2 shows a metal sphere that has a net negative electric charge. Draw the lines of the electric field around the metal sphere when it is isolated from its surroundings. Use arrows to show the direction of the electric field. Another negatively charged object is placed in the electric field. Look at Figure 3. In which position would the object experience the greatest force? [A] P [B] R [C] S [D] T.

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### Video Transcript

Figure one shows a polythene rod and a cloth duster. At first, neither object has a net electric charge. If the cloth duster is rubbed against the polythene rod, the polythene rod will accumulate a net negative electric charge and the cloth duster will become positively charged. Explain how an uncharged object may become negatively charged.

Okay, so the question is talking about a generic object here. We’ve been asked to explain how an uncharged object may become negatively charged. The question doesn’t actually tell us what object we’re talking about specifically. But we can use the example of the polythene rod and the cloth duster to help us answer the question, because, in this case, we’ve been told that if the cloth duster is rubbed against the polythene rod, then the polythene rod will accumulate a net negative electric charge and the cloth duster will become positively charged.

This happens even though, at first, neither object has a net electric charge. In other words, initially, both of these objects are neutral. They’re neither positively charged nor negatively charged. But then when we rub them together, one has a net negative electric charge and the other has a net positive charge.

So let’s consider the situation before we rub these objects together. Well, both of these objects are made up of atoms. Now specifically, these atoms can be thought of as a whole bunch of positively charged ions that cannot move around and a sea of negatively charged electrons that are free to move around.

Now when these objects are neutral — they’re not positively charged or negatively charged — then the total negative charge on all of the electrons cancels out the total positive charge on all of the ions. And remember, this is true for both the polythene rod and the cloth duster. In each item, the positive charges cancel out the negative charges.

However, when we rub the two objects together, there is a transfer of negatively charged electrons from one object to the other. In this case, we’ve been told that the polythene rod accumulates a net negative electric charge. Therefore, what’s happening here is when we rub the two objects together, some of the electrons from the cloth duster are transferred to the polythene rod. This means that the cloth duster is now left with fewer electrons than it had before. And conversely, the polythene rod now has more electrons than it had before.

In other words, in the cloth duster, the total charge on the positive ions is now larger than the total negative charge on the electrons that remain, because there are fewer electrons remaining, whereas in the polythene rod, the situation is the opposite. The polythene rod now has a lot more electrons than it had before, which means that it has a net negative charge.

Now it’s important to remember that this transfer of charge is because of the movement of electrons. The positively charged ions cannot move anywhere. They’re stuck in place. And so when it comes to explaining how an uncharged object may become negatively charged, we can say that negatively charged electrons are transferred to the object, resulting in an accumulation of a net negative charge. This is how an uncharged object, in this case the polythene rod, becomes negatively charged.

Figure two shows a metal sphere that has a net negative electric charge. Draw the lines of the electric field around the metal sphere when it is isolated from its surroundings. Use arrows to show the direction of the electric field.

Okay, so in this part of the question, we’ve been told that we’ve got a negatively charged metal sphere. And we’ve been asked to draw the electric field around this metal sphere when it is isolated from its surroundings. In other words, we don’t need to worry about any other electric fields. If it’s isolated from its surroundings, then only the sphere’s electric field is what we’re going to have to worry about.

So first things first, let’s give ourselves a little bit of space to work with. And let’s start considering what we need to think about in order to draw the electric field that we’ve been asked to draw.

So first of all, we’ve been told that the sphere that we have is negatively charged. This is important because we can recall that electric field lines start on positive charges and end on negative charges. This means that electric field lines point away from positive charges and point towards negative charges. So whatever our field pattern is going to look like, we now know that the field lines are going to be pointing towards the negatively charged metal sphere, because it’s negatively charged.

Secondly, we can recall that a charged sphere has the same electric field as a point charge outside the sphere. What this means is that if we have a point charge — well, let’s say, in this case, it’s a negative point charge because we’ve got a negatively charged sphere that we’re talking about — then this negative point charge has the same electric field lines as this negatively charged sphere, except this is only true on the outside of the sphere, not inside the sphere.

So next, we can recall what the electric field of a negatively charged particle looks like. Well, for a negatively charged particle, the electric field lines point towards the particle, because, remember, electric field lines end on negative charges. More specifically, the field lines for a charged particle point towards the particle in a radial direction. What this means is that the field lines look like the following diagram. The field lines are all pointing inwards from outside towards the particle.

Now let’s say that, instead of this particle, we have a negatively charged sphere. Let’s say that this is the sphere. What we know that, outside the sphere, the electric field is exactly the same as for the charged particle. And that’s exactly what this diagram is showing. The electric field lines end at the surface of the sphere. Inside the negatively charged sphere, there is no electric field. And also, rather interestingly, the reason that the electric field lines are known to be radio is because each field line is a continuation of the radius of the sphere.

Now the radius can be measured by starting at the center of the sphere and moving outwards until you get to a point on the surface of the sphere. And this line is the radius of the sphere. Well, these electric field lines that we’ve drawn lie along the same line as each radius of the sphere, at which point we’ve basically answered the question. All that remains is to draw the field lines on figure two.

So here’s the electric field of the negatively charged metal sphere. Each line ends at the surface of the sphere and is a continuation of the shortest line that goes from the surface of the sphere to the center of the sphere, in other words a radius of the sphere. Also, each line is pointing towards the sphere because it’s negatively charged, and so this is the electric field produced by the negatively charged metal sphere.

So having done this, let’s move on to the final part of the question. Another negatively charged object is placed in the electric field. Look at figure three. In which position would the object experience the greatest force? Tick one box: P, R, S, T.

Okay, so here we’ve got the same negatively charged sphere as the previous part of the question. And what we’re doing is we’re placing another negatively charged object in positions P, R, S, or T. We’ve been asked to state the position in which the object would experience the greatest force.

To answer this question, we once again need to look at the electric field from the negatively charged sphere. So here is the electric field from before. Now here’s the reason why we need to consider the electric field in the first place. If we take a charged object and place it into an electric field, then naturally the electric field will exert a force on the charged object.

And here’s the important point. Let’s say we’ve got some other electric field that looks something like this. Here, we can see an electric field where all the field lines are parallel to each other. But in this region of the field, the field lines are far apart from each other, whereas in this region, the field lines are close together. And in fact, as we go from here to here, the field lines are getting closer and closer to each other.

Well, here’s what we need to know. In a region where electric field lines are close together, the force exerted on a charged particle in that electric field is a large force. So in this case, let’s say we’ve placed a negatively charged particle in the electric field. Well, a negatively charged particle moves against the direction of the electric field. So the force on the negatively charged particle due to the electric field is going to be in this direction, against the direction of the electric field.

But the important thing is that the force is going to be a very large force. This is because, in this region, the electric field lines are very close together. However, if we were to take that same charged particle and place it over here, for example, then again it would experience a force in the opposite direction to the electric field. But the strength of that force would be very weak. This is because the electric field lines in this region are very far apart from each other.

So basically, here’s the key point. If we place a charged particle in a region of an electric field where the field lines are far apart from each other, then the force on that particle is going to be small. However, if we place that same charge in a region of the electric field where the field lines are close together, then the force on that particle is going to be large. The closer the field lines are together, the larger the force the electric field exerts on a particle in that field.

So coming back to our question then, we need to find the position out of positions P, R, S, and T where the electric field lines are closest together. Well, we can see that as we come nearer and nearer to the sphere, the electric field lines are getting closer and closer together.

Let’s say, for example, we were in this position here. Well, the electric field lines are quite far apart from each other. However, in this position here, the electric field lines are slightly closer to each other. And in this position here, they’re even closer to each other. This means that the force exerted by the electric field is weakest here, slightly stronger here, and the strongest here. In other words, as we get closer to the sphere, the force exerted gets larger and larger.

So essentially, we just need to find the point that’s closest to the surface of the sphere. And that point happens to be point R. Hence, the answer to our question is position R. When we place a negatively charged object in the electric field of the negatively charged sphere, it will experience the greatest force at position R out of the four positions given to us.