# Why does the charge uniformly distributed on the surface of the sphere only?

• cdymdcool
Because the electrons are free to move within the conductor and will repel each other, spreading out evenly on the surface. In summary, the charge on a solid conducting sphere is uniformly distributed on the surface because the electric field inside must be zero, and the free electrons will repel each other to evenly distribute on the surface.
cdymdcool
1. A solid conducting sphere is given a positive charge Q. Why is the charge uniformly distributed on the surface of the sphere only?

## Homework Equations

3. I know there are electron clous where electrons hang out, but what happen when the sphere is given a postive charge? I don't think protons comes to the surface or anything like that...

cdymdcool said:
1. A solid conducting sphere is given a positive charge Q. Why is the charge uniformly distributed on the surface of the sphere only?

## Homework Equations

3. I know there are electron clous where electrons hang out, but what happen when the sphere is given a postive charge? I don't think protons comes to the surface or anything like that...

The electric field inside a conductor must be zero, so there can be no charge inside the sphere. The remaining charges array themselves on the surface until there is no field inside the sphere, and the only way that can work is if they are concentrated uniformly on that surface.

But why aren't the charges uniformly distributed throughout the sphere?

## 1. Why does the charge uniformly distributed on the surface of the sphere only?

This is due to the principles of electrostatics, specifically Gauss's Law. According to Gauss's Law, the electric field at any point on a closed surface is proportional to the enclosed charge. In the case of a sphere, the electric field is the same at every point on the surface because the charge is uniformly distributed, resulting in a symmetrical electric field.

## 2. How does the charge distribute itself uniformly on the surface of a sphere?

The charge distributes itself uniformly due to the repulsive forces between the like charges. When charges are placed on a conducting surface, they will spread out evenly in order to minimize the repulsive forces between them. This results in a uniform distribution of charge on the surface of the sphere.

## 3. What happens if the charge is not uniformly distributed on the surface of a sphere?

If the charge is not uniformly distributed on the surface of a sphere, the electric field at different points on the surface will not be the same. This will result in an uneven distribution of charge, causing non-uniformity in the electric field and potentially leading to unpredictable behavior.

## 4. Can the charge on a sphere be non-uniformly distributed?

Yes, it is possible for the charge on a sphere to be non-uniformly distributed. This can occur if the sphere is not a perfect conductor or if there are external electric fields present that disrupt the uniform distribution of charge. In this case, the electric field at different points on the surface will vary and the charge will not be uniformly distributed.

## 5. Is the charge on a sphere always uniformly distributed?

No, the charge on a sphere is not always uniformly distributed. As mentioned before, external factors such as the material of the sphere or external electric fields can affect the distribution of charge. However, in ideal conditions, a conducting sphere will have a uniform distribution of charge on its surface due to the principles of electrostatics.

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