Why does charge accumulate at the sharpest point?

In summary, at a corner in a conductor, the electric field is discontinuous. This suggests that the charge density is higher on the smaller sphere.
  • #1
jdstokes
523
1
I'm sure I used to have a really simple answer to this. But I've long since forgotten.

BTW This is not my homework.

James
 
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  • #2
I believe the idea is that at least for a conductor, the charge exists evenly on the surface. So when you have a sharp point, you may have charges that are very close to each other in space, even though they may be equally spaced on the surface.
 
  • #3
The local charge density varies inversely as the square of the radius of curvature.
 
  • #4
maverick280857 said:
The local charge density varies inversely as the square of the radius of curvature.

Yes, of course. But why??
 
  • #5
jdstokes said:
Yes, of course. But why??
So that the potential may satisfy the Laplacian outside the conductor.
 
  • #6
Here's a simple model.
Consider two conducting spheres, with unequal radii A and B, connected by a long thin conducting wire... so the spheres are at the same potential. How do free charges distribute themselves on the two spheres?
 
  • #7
robphy said:
Here's a simple model.
Consider two conducting spheres, with unequal radii A and B, connected by a long thin conducting wire... so the spheres are at the same potential. How do free charges distribute themselves on the two spheres?

[itex]
\begin{align*}
V_A & = \frac{\sigma_A 4\pi A^2}{4\pi\epsilon_0 A} \\
& = \frac{\sigma_A A}{\epsilon_0} \\
V_B & = \frac{\sigma_B B}{\epsilon_0} \\
\sigma_A A & = \sigma_B B
\end{align*}
[/itex]

This suggests that the charge density is higher on the smaller sphere. Quite nice, but I think there is probably a simpler explanation.
 
  • #8
jdstokes, have you thought about what would happen at a true corner in a conductor? You know the electric field is always normal to the surface of a conductor and continuous outside the conductor, but what happens at a corner? Imagine you sit just outside the corner: if you move a little to the left you get a field parallel to one surface normal, move a little to the right you get a field parallel to the other surface normal (the surfaces meet at an edge so imagine two planes intersecting). The field seems discontinuous just outside the corner. Of course there are physical limits, but the point is that the electric field is varying really fast, so what does this tell you about the charge density?
 
Last edited:

1. Why does charge accumulate at the sharpest point?

The accumulation of charge at sharp points is due to a phenomenon known as "corona discharge". This occurs when an electric field is strong enough to ionize the surrounding air molecules, causing them to become charged particles. Due to the curvature of a sharp point, the electric field is concentrated, leading to a higher chance of ionization and therefore, charge accumulation.

2. Does the material of the sharp point affect the accumulation of charge?

Yes, the material of the sharp point can affect the accumulation of charge. Materials with a higher dielectric strength, such as metals, are more likely to accumulate charge at a sharp point compared to materials with a lower dielectric strength, such as plastics.

3. Can the accumulation of charge at sharp points be harmful?

Yes, the accumulation of charge at sharp points can be harmful. If the charge buildup is high enough, it can lead to a spark or electrical discharge, which can damage electronic equipment or cause electric shocks to individuals.

4. How can the accumulation of charge at sharp points be controlled?

The accumulation of charge at sharp points can be controlled by using a process called "corona suppression". This involves applying a conductive material or coating to the sharp point, which helps to dissipate the electric field and prevent charge buildup.

5. Can the accumulation of charge at sharp points be beneficial?

Yes, in certain applications, the accumulation of charge at sharp points can be beneficial. For example, in electrostatic precipitators, the sharp points are intentionally used to attract and collect charged particles from the air. In this case, the charge accumulation is controlled and used for a specific purpose.

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