Which diagram correctly shows the electric field lines of a negative charge that is not moving?
Now, we’ve been given four different diagrams. And we need to find out which one shows the correct set of electric field lines for a negative charge that’s not moving. And to do this, we need to know what electric field lines represent. So electric field lines represent the direction of force exerted on a positive charge in the electric field.
So let’s say we’ve got a positive charge right here. We’ll call it positive capital 𝑄. We won’t use lowercase 𝑞 because we’ve used lowercase 𝑞 in the diagrams already. Now we’ve got this positive charge 𝑄. And let’s place it in an electric field where the field lines, for example, are doing something like this.
Well since the electric field lines represent the direction of force on a positive charge, what that positive charge is going to do is to accelerate in this direction following the field lines. If the field lines do something like this for example and we placed a positive charge in that field, plus 𝑄, then what it will do is it will follow those field lines in that direction.
So how do we generate field lines? What do we need to know in order to be able to draw electric field lines? Well, we’ve just said that the field lines represent the direction of force on a positive charge. What do we know about positive charges? We know that they’re attracted to negative charges and repelled by other positive charges. Therefore, what we can do is to place a positive charge in any of these electric fields and see what would happen.
So let’s say we placed a positive charge capital 𝑄 in the electric field of diagram a, what would happen to it? Well it would follow the field line, and it would be meeting the negative charge here. That makes sense. Positive charges are attracted to negative charges. And this is true wherever we place the positive charge. It will follow the field lines and meet the negative charge.
If we place it here, it will follow the field line and meet the negative charge. So this kind of looks like the correct answer. But let’s go through the other ones just to make sure that they’re all wrong. So let’s look at diagram b. Let’s say we placed a positive charge here. Well what it’s gonna do is just follow the field line and go around in a circle. That makes absolutely no sense at all.
The positive charge needs to be attracted to the negative charge. Moreover, we can realize that electric field lines begin on positive charges and they must end on negative charges. This is because when positive charges and negative charges are placed in close vicinity, the positive charge and negative charge should be attracted to each other. So any small test positive charge placed in the electric field of a negative charge should be attracted to that negative charge.
Looking at diagram c then, let’s say we placed a positive charge here. Well in this case, it sort of comes along to meet the negative charge as expected. But if we had placed it here, it goes away from the negative charge. That doesn’t make sense either. Also another thing to note is that in this case we’ve got alternating field lines that go towards and away from the negative charge.
If that is how field lines worked, which is not, but if that is how they worked, how would we differentiate between positive charges and negative charges? Because the field lines of the positive charges would look exactly the same. Some of them would be going out, and some of them would be going in to the positive charge. So in that case, there would be no difference between positive and negative charges. So clearly this can’t be the answer.
So, very swiftly, we can move on to diagram d. Let’s say we placed a positive charge here. Well it moves away from the charge, same thing if we placed it here, same thing if we placed it here. Now this doesn’t make sense either because this looks more like the electric field of a positive charge. This diagram would be correct if we simply did this; that is, if the charge was a positive charge.
That way our test positive charge, the little orange one here, would be repelled by the big positive charge, this one. But anyway, the question is asking us for the field lines of a negative charge. And so, our final answer is that diagram a correctly shows the electric field lines of a negative charge that’s not moving.