Why does surface charge density change for an inner surface?

In summary, the direction of the surface normal is reversed, leading to a change of sign in the area and resulting in a negative value for the surface charge density. This does not mean that the charge is actually different at that point, but is a result of the coordinate system and the comparison of the surface area and the charge.
  • #1
Ascendant78
328
0
Rather than try to explain what I am talking about, I am going to link to an image of it below. My question is in regards to the negative value I marked in the answer (the one for the surface charge density for the inside of the outer shell). While I get the concept that it would be negative in this type of scenario, I don't know exactly why? I am assuming it has something to do with the positive charge facing outwards and the surface area being analyzed facing inwards, but I am curious about how this pops up in the math so that I will know on more complicated problems that won't be so obvious?

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  • #2
The change in sign arises because the direction of the surface normal is reversed, which is conventionally represented by a change of sign in the area.

Claude.
 
  • #3
Claude Bile said:
The change in sign arises because the direction of the surface normal is reversed, which is conventionally represented by a change of sign in the area.

Claude.

Oh, thank you. What was confusing me was that I thought it meant that the charge was actually different at that point, which was the part that was throwing me off. I wasn't understanding at what point the charge would shift from negative to positive, but now I see that I was looking at it wrong.

So if I understand you correctly, the only reason the sign changes at that point for the charge isn't because the charge itself is changing, but simply because the coordinate system causes it to based off the comparison of the surface area and the charge, right?
 

Related to Why does surface charge density change for an inner surface?

1. Why does the surface charge density change for an inner surface?

Surface charge density changes for an inner surface due to the distribution of charges on the surface. As charges accumulate on the surface, the surface charge density increases. Similarly, when charges are removed from the surface, the surface charge density decreases. This change in surface charge density is also affected by the material and properties of the surface.

2. How does the material of an inner surface affect its surface charge density?

The type of material of an inner surface can greatly impact its surface charge density. Different materials have different abilities to hold or release charges, which can affect the distribution of charges on the surface and therefore the surface charge density. Materials with high electrical conductivity, such as metals, tend to have higher surface charge density compared to insulating materials.

3. Can surface charge density on an inner surface be controlled?

Yes, surface charge density on an inner surface can be controlled by manipulating the distribution of charges on the surface. This can be done through various methods such as applying an external electric field, altering the material of the surface, or introducing charged particles to the surface. By controlling the surface charge density, we can also control the properties and behavior of the surface.

4. What is the relationship between surface charge density and electric field?

The surface charge density on an inner surface is directly proportional to the strength of the electric field. This means that as the electric field increases, the surface charge density also increases. This relationship is described by the Gauss's law, which states that the flux of the electric field passing through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of the material.

5. How does the surface charge density on an inner surface affect the behavior of the surface?

The surface charge density on an inner surface plays a crucial role in determining the behavior and properties of the surface. It affects the electrostatic forces between the surface and other charged particles, the adhesion of the surface to other materials, and the overall stability of the surface. Changes in surface charge density can also lead to changes in the surface potential and surface tension, which can impact the interactions between the surface and its surroundings.

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