Charge distribution on the surface of a conductor: Examples

We had a steel ball, remember? A spherical conductor... and it was charged up with excess electrons. These electrons became distributed evenly on the surface of the conductor. Now we're going to change the shape of the conductor, like this, to a drop shape.

What will happen to the charged particles -- where will they go? Well, they are sort of crowding up a bit, at the narrow end... Let's adjust the shape a bit more, to see the effect better. Hmmmm. Even more crowding now.

It seems we can state a rule here: The more pointed the conductor is, the more densely the electrons will pack together. Let's look a bit closer, at a cross section, to to see what happens. Look up here first, on the part of the surface that is not so pointed. Here's an electron. It can't move inwards in the conductor, since it's repelled by the electrons on the other side.

And neither can it move out into the air, because air is an insulator. If this electron is to move at all, it's going have to be along the surface of the conductor. But there are many electrons who also want to be on the surface. And they repel each other, as much as they can, to get as far away from each other as possible. Notice that the direction of their repellant force is pretty much along the surface of the conductor.

Now we go over here, and compare the situation of this electron. This one also can only move along the surface of the conductor. But there's a difference here on the curved part of the conductor: Because... notice where the other electrons are - those who are repelling our electron the most. They are in effect, underneath ours, relative to the surface, so their repelling force is directed outward from the conductor, in a direction that our electron can't move.

And if some of the force is directed outwards, then there's less force to be directed sideways, towards the other electrons. So here, in the bent part of the conductor, the electrons push less on each other, and more on the outer wall. That's why more electrons can squeeze together next to each other here. Then of course it's very uncomfortable for our electron, being pressed so hard against the wall. Actually, it's so uncomfortable that we can measure it.

If we measure the electrical field around the conductor, we'll see that it's stronger in precisely this area, where the electrons are so fiercely repelled against the outer wall. Where a conductor is bent, or bulges out, or has a sharp corner, there's going to be a higher concentration of charged particles, and that's also where the electric field is going to be strongest. This is something you can test for yourself. If you charge a conductor with static electricity -- you'll notice that it's much easier to get it to discharge through the air from a sharp point, than from a flat surface.