# Why Charge Accumulates at Edges/Corners?

1. Aug 28, 2006

### tommyers

Hi,

Could someone help me understand why charge accumulates at the edges / corners of items - such as our fingers.... but more importantly on the edges / corners of plate capacitors!

Thank you in advance.

Regards

Tom

2. Aug 28, 2006

### chroot

Staff Emeritus
Because like charges repel. If you don't mind the anthropomorphism, charges "try" to get as far as possible from other like charges.

- Warren

3. Aug 28, 2006

### ZapperZ

Staff Emeritus
What you are asking about is what is known as the "field enhancement". When you put a metallic object in an electric field, the strength of the field is enhanced at the sharp corners. To be able to show this, one has to solve the electrostatic Poisson's equation with the appropriate boundary condition reflecting the geometry of the metallic surface.

When you solve this, you'll notice that the electric field "lines" tend to be "bunched up" at sharp edges and corners. This means that the external field that has been applied to the object is enhanced at these locations. The amount of enhancement depends on the degree of sharpness.

Hence, since the electric field is stronger at these locations, there will be more charges accumulating there.

This is also true, somewhat, for dielectric and insulators, but the field enhancement isn't as pronounced as metals under the same field amplitude.

Zz.

4. Aug 28, 2006

### Meir Achuz

You can calculate the surface charge density at a corner of a conductor.
Near the edge of a conducting sheet, it goes like
\sigma~1/\sqrt{r}.

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