PhD., University of Maryland
Jonathan is a published author and recently completed a book on physics and applied mathematics.
Conductors have a flow of charge through the conduction band. Metals are extremely good conductors. In general, charge congregates at sharp points. Conductivity is related to electric fields by the equation charge flow = conductivity x electric field.
So what are conductors? A conductor is a material that allows charge to flow freely through it. Now, by charge I really mean electrons. So most of these conductors are metals. So what is, what's going on with metals that allows charge to flow freely through them? Well, most metals look like this. We've got nuclei down here. Each nucleus has a bunch of electrons that are associated with it.
Now, with conductors with metals, we've got some of these where the electrons are held very close to the nucleus. so this blue one, we know which electron belongs with which nucleus. But then we've got something called a conduction band, where the electrons can move form one nucleus to the next, to the next, to the next and it's okay. So it's this conduction band that allows metals to conduct electricity. Alright. How do we characterize this electricity flow. How do we characterize how good of a conductor a certain metal is?
Well, we've got an equation that tells us j, j measures the charge flow, is equal to sigma times e. Sigma is called the conductivity and it characterizes the metal that we're talking about and e is the electric field that we apply. We need to apply an electric field because there's no reason for charge to move unless there's electric field trying to push them. So this sigma tells us the response of charge inside of a metal to an applied electric field. Now for most good metals, we've got sigma, the conductivity of the order of 10 to the 8, 100 million in SI units. Now I'm not going to talk about what those units are yet because we need a little bit more to do that, but, just so you know, it's a pretty big number for the good conductors.
Alright. Now an electric field makes charge flow. So if I apply an electric field to a conductor, then the charge is going to flow. Now, as that charge flows, if the electric field doesn't go away then it will just keep flowing and flowing and flowing and flowing. So if I've got a slab of good conductor, and I apply an electric field to it, then the charges are going to move until there's no more electric field. So that means that if it's a good conductor, then I can take the electric field as zero inside of it. Alright.
Let's look a little bit at what this means. So the electric field is zero inside and what that means is that all the charges inside don't want to go anywhere. They're just sitting there. There's no electric field. So why are they going to go anywhere? So that means that the entire surface of the conductor is at the same potential because if there was a potential difference, if it was a higher potential over here than over here, then the electrons would move. But that would mean there had to be an electric field. There is no electric field. So that means that the surface of a good conductor is an equipotential region. Equi, meaning equal and potential meaning potential. Alright.
So, when I have an equipotential surface, the electric field must be perpendicular to that surface. So, if I've got a conductor right here and I've got an electric field coming in, well, it's got to stop at negative charges because that's where electric fields stop. So, it's got to be perpendicular, so I'm going to draw my electric field lines so that they hit the surface of the conductor perpendicular and that gives us this nice little diagram. No electric field inside, and then because there's negative charge on this side, there must be positive charge on this side or else the conductor is charged. Now, I don't want the conductor to be charged, I want it to have zero net charge. So what happens is, these positive charges over here generate the electric field lines again perpendicular to the surface so that if I were to take the conductor away, then the electric field lines would just go straight across. Like that.
Now, you may be wondering, how is it that the electric field is zero inside. Here's the idea. When we have got this positive and negative, the electric field associated with this positive charges will push this way toward the negative charges. And what that does is it cancels out the electric field from outside. So those two, the contribution from both of those electric fields cancels and we get zero inside, when we take the whole electric field. And that's generally the way that it works. When you apply an electric field to a conductor, the positive charges will move further downstream of that electric field and then they generate their own electric field which opposes the electric field that I first put on the conductor.
Alright. Now let's look at a slightly different situation. Suppose that I've got a conductor like this with a sharp point. Again, it's a conductor. And that means the electric field lines got to end perpendicular to the conductor. Now over here that's fine, get nice spread out charges. But over at the sharp point, look what happens. I've got these electric field lines that got to come out in this very strange way. So that means that I've got a congregation of charge over here. So charge congregates at sharp points. You may be familiar with that from Vandegraff generators where you touch the top and then people's hair goes way up. That's because people behave kind of like conductors and then when you're taking all that charge in, that charge is going to go congregate at sharp points. Well, where are the sharpest points on the human body? In the hair So that's the way that that works and that's why you got hair that stands all out when you touch a vandegraff generator.