Why Charge Accumulates at Edges/Corners?

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In summary, the accumulation of charge at the edges and corners of items such as fingers and plate capacitors is due to the field enhancement effect. This occurs because the electric field is stronger at sharp edges and corners, causing more charges to accumulate there. This effect is more pronounced in metallic objects due to their conductive properties.
  • #1
tommyers
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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
 
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  • #2
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
tommyers said:
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

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
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}.
 

1. Why does charge accumulate at edges/corners?

Charge accumulates at edges/corners due to the phenomenon known as the "edge effect." When an object has sharp edges or corners, the electric field lines tend to become more concentrated at these points, resulting in a higher charge density. This is because the electric field lines are closer together, making it easier for charges to accumulate at these locations.

2. How does the shape of an object affect charge accumulation at edges/corners?

The shape of an object plays a crucial role in charge accumulation at edges/corners. Objects with sharp edges or corners have a higher charge density compared to those with smoother surfaces. This is because the electric field lines are more concentrated at sharp points, resulting in a higher charge accumulation.

3. Can charge accumulate at edges/corners in all materials?

Yes, charge can accumulate at edges/corners in all materials. However, the extent of charge accumulation may vary depending on the material's conductivity. For example, conductors tend to have a higher charge accumulation compared to insulators because electrons can flow more freely in conductors, making it easier for charge to accumulate at edges/corners.

4. How does the surrounding environment affect charge accumulation at edges/corners?

The surrounding environment can affect charge accumulation at edges/corners in several ways. For instance, humidity and temperature can impact the conductivity of a material, thereby affecting the charge accumulation. Additionally, the presence of other objects or materials in the vicinity can also influence the distribution of electric field lines, resulting in a different charge accumulation pattern.

5. What are the practical applications of understanding charge accumulation at edges/corners?

Understanding charge accumulation at edges/corners is crucial for various practical applications. For example, it plays a significant role in electrostatics, which is essential in designing electronic devices. It is also essential in understanding the behavior of lightning and air pollution, as charge accumulation at edges/corners can affect the distribution of electric fields in the atmosphere. Furthermore, understanding this phenomenon is crucial in designing efficient power transmission systems and preventing electric shocks.

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