Electric Fields in Conductors: Study with Video Lessons, Practice Problems & Examples

In a conductor, the net electric field is always zero due to the free movement of electrons, which repel each other and distribute themselves on the surface. When an external electric field is applied, charges polarize, but the internal electric field cancels out, maintaining a net field of zero. Outside the conductor, the electric field behaves as if all charge is concentrated at the center, following the equation K(Q) / r2. Understanding these principles is crucial for grasping electrostatics.

Electric Fields in Conductors

Alright, guys. So in this video, I want to talk about conductors and electric fields. We've talked about them separately. So now I want to talk about what the electric field inside of a conductor is. Let's check it out. Just remember, when we're talking about electric conductors, these are things that allow electrons to move inside of them, all right. And when you have electrons, I'm going to be using electrons for this video. By the way, these electrons, when they're inside of a conductor, are freely able to move around. But they want to get as far away as possible from each other because they repel, right like charges repel. Now, one of the consequences of this fact and this is the key part of this video, is that the net electric field inside of a conductor is always going to be equal to zero. Basically, what happens is that the electrons move around in such a way that they cancel out the electric fields inside of them. We're going to see two specific examples of how that happens right down here. So two specific charge arrangements that you might see in your textbook or in tests or when you have a net charge conductor without an electric field anywhere outside of it. So, if I imagine, I take this neutral conductor that has the same amount of positive charges and negative charges and I start throwing some electrons at it, right? So I put some electrons on it, whether it's conduction or induction. Well, these things are allowed to move inside the conductor, and so because they're like charges, they want to move away from each other. So, what they're going to do is they're going to distribute themselves on the surface, right, because that's as far apart as they could get from each other. Well, imagine I put two more electrons on this thing. Well, these electrons also want to repel each other, but they also want to repel the charges that exist on the outside right here. So in other words, they have to get equally far away from each other in such a way where they sort of balance each other out. So these two electrons will appear right over here. This is the farthest distance that each one of these electrons can end up from the other on. So that's where they want to go. So now, let's say, I add four more electrons over here, so I've got four more now these four electrons again could move inside of the conductor and then want to separate as far as possible. Now, the only place that they could go is basically out to the diagonal points right here. They basically want to maximize the distance away from all of the other electrons as far as possible, so these electrons will distribute themselves on the surface right here. Now, what is the result of this? Well, what happens is that if you were to take a look at this point right here and try to calculate the electric field, you'd have to sum up what the electric fields, which, by the way, point towards the negative charges. They would point all the way. This way they would point towards each one of the respective charges. But what happens is that if the center of this conductor, all the electric field lines will end up canceling each other out. So, you have all of these charges here. So if you have a net charge, Q, but the electric field inside is just equal to zero as we said before. So there's another kind of example that we can see. It's when you actually have an uncharged conductor, which means the same number of positive and negative charges. But now you have an external electric field that is on the outside. Let's take a look at what happens here. We know that there's going to be an equal number of positive and negative charges. But what happens is that positive charges want to go with the flow and negative charges, like electrons, want to go against the flow. So what ends up happening is these positive charges will start to pile up here on the right hand side,Eoutside, and these negative charges will start to pile up on the left-hand side. You start to get this sort of polarization similar to how we talked about polarization before. So you basically have these negative charges and these positive charges. They're just split apart from one another, and the result of this is we know that electric field lines will always point from positive charges to negative charges. So the electric field is basically going to get set up inside of this conductor because you're polarizing all of these charges. You're moving them from one side to the other. So what ends up happening is that you end up with a new electric field that's inside the conductor. Now you might be looking at me like I'm crazy because I said that electric fields have to be zero inside of conductors. But what ends up happening is that this electric field that's inside, Einside, gets set up inside of the conductor and cancels out with one that's outside, Eoutside. So what ends up happening is that the net electric field is equal to zero, as we said before. Now, there's one last thing I want to talk about. We've talked about the electric fields inside. Conductors have to be has to be zero. But what happens if you were to go outside of this electric conductor? Well, outside of a conducting charged sphere with Q. So, for instance, if you were to be outside like this and try to calculate the electric field, that's just going to be K Times Q Divided by R Squared, which is just the same exact thing as if it were basically just a point charge. So even large objects, if you're outside of them, will just act as if all of their charge was concentrated at the center right here. So with that being said, let's go ahead and take a look at an example. We've got a spherical conductor and it has a radius of 0.5m, so I've got this little actually let me go ahead and let's do that. So you've got a spherical conductor and I'm told that the radius of this conductor. So I'm going to call that big R is equal to 0.5m. I'm also told that this spherical conductor has a net charge of two microcoulombs. Now, I know that this net charge, whether it's positive or negative, so I'm just going to call them positives, have to distribute themselves evenly on the surface. So now I have to figure out what happens to the electric field at certain distances from this conductor. So in part A, we're going to be looking at 0.8m, so let's go ahead and draw this out in the diagram. Well, 0.8m is going to be a point that's going to be outside of the conductor, right? Because the Radius 0.5m. So I'm going to call this little are, and that's equal to 0.8m. So I know that the electric field, right, the electric field is going to be outside of a conductor with some charge. It's gonna be K times Q divided by r squared. So I've got 8.99109 times the two microcoulombs by the way that's times 10-6, right, because this is equal to 10-6. And then I've got divided by the distance between them. That's going to be point. Oops, I've got 0.8 and I've got to square that so the electric field over here ends up being 281104 Newtons Per Coulomb, all right, so that's the answer to part a. Part B is now asking us to look at the electric field at 0.4m from the center of the conductor. So now, 0.4m. Well, let's check that out in the diagram. At what point is 0.4 correspond to will? The radius of this thing is 0.5m. So anywhere from the center of this conductor right here, that's 0.4m away. You're going to be inside of the conductor. And what do we say? The electric field inside of a conductor is equal to zero. So this is a very important fact that you need to know. And it's also the answer to our problem. Alright, guys, so this is a very, very important thing. You'll definitely need to know for future sections and chapters. So let me know if you guys have any questions. Watch the video a couple of times if you didn't understand anything and just let me know in the comments if you want to explain, alright.

Here’s what students ask on this topic:

Why is the electric field inside a conductor zero?

The electric field inside a conductor is zero because the free electrons within the conductor move in response to any external electric field. These electrons rearrange themselves on the surface of the conductor in such a way that they cancel out any internal electric field. This redistribution continues until the internal electric field is completely neutralized, resulting in a net electric field of zero inside the conductor. This principle is crucial for understanding electrostatics and is a direct consequence of the repulsive forces between like charges.

How do charges distribute themselves on the surface of a conductor?

Charges distribute themselves on the surface of a conductor to minimize repulsive forces between like charges. When excess charges are introduced to a conductor, they move freely and repel each other, seeking the maximum distance from one another. This results in the charges spreading out uniformly on the surface of the conductor. This surface distribution ensures that the electric field inside the conductor remains zero, as the internal fields generated by these surface charges cancel each other out.

What happens to the electric field outside a charged conductor?

Outside a charged conductor, the electric field behaves as if all the charge were concentrated at the center of the conductor. This is described by the equation:

$E=\frac{kQ}{r^2}$

where $k$ is Coulomb's constant, $Q$ is the total charge, and $r$ is the distance from the center of the conductor. This means that the electric field outside a spherical conductor with charge $Q$ is identical to the field produced by a point charge $Q$ located at the center of the sphere.

How does an external electric field affect a conductor?

When an external electric field is applied to a conductor, it causes the free electrons within the conductor to move. Positive charges (protons) align with the direction of the field, while negative charges (electrons) move against it. This movement creates a polarization within the conductor, with positive charges accumulating on one side and negative charges on the opposite side. This induced internal electric field opposes the external field, and the net electric field inside the conductor remains zero. This phenomenon is essential for understanding how conductors behave in external electric fields.

What is the significance of the electric field being zero inside a conductor?

The significance of the electric field being zero inside a conductor lies in its implications for electrostatic equilibrium and shielding. In electrostatic equilibrium, the charges within a conductor have redistributed themselves such that there is no net movement of charge, resulting in a zero internal electric field. This property is also the basis for electrostatic shielding, where a conductor can protect sensitive electronic equipment from external electric fields by ensuring that the field inside the conductor remains zero. This principle is widely used in designing Faraday cages and other shielding devices.