# Electrostatics - hollow charged sphere

• JustStudying
In summary, a hollow charged sphere is a conducting sphere with a hollow interior and a uniform charge distribution on its surface. It differs from a solid charged sphere, which has a non-uniform charge distribution. The electric field inside a hollow charged sphere is zero, and the electric potential is constant at all points inside the sphere. However, if there are other nearby charges, the charge distribution on the surface may become non-uniform, leading to a non-constant electric potential inside the sphere.
JustStudying
So we have a cross sectoin of a sphere that is charged with Q (refer to attachment). electrostatics say the electric field within a charged conductor is 0, and the electric field is perpendicular to the surface.

But for a hollow charged sphere (like in the attachment), does the hollow area within the sphere have a electric field of 0 too?

#### Attachments

• physicsforumq.png
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Good question - how would you go about finding out?

No ... seriously... this is a standard exercise in electrostatics.
It is important to your understanding for you to do the calculation (or reason it out) for yourself.

## 1. What is a hollow charged sphere?

A hollow charged sphere is a conducting sphere that has a hollow interior and a net charge on its surface. This means that the charge is spread evenly over the surface of the sphere, rather than being concentrated at a single point. The interior of the sphere is empty, or hollow, which allows the charge to be evenly distributed.

## 2. How is a hollow charged sphere different from a solid charged sphere?

A solid charged sphere has a net charge that is concentrated at a single point, typically at its center. This results in a non-uniform distribution of charge, with the charge density being highest at the center and decreasing as you move towards the surface. In contrast, a hollow charged sphere has a uniform distribution of charge on its surface, resulting in a constant charge density throughout the sphere.

## 3. What is the electric field inside a hollow charged sphere?

The electric field inside a hollow charged sphere is zero. This is because the net charge on the surface of the sphere cancels out the electric field generated by the charge at any point inside the sphere. This is known as the "shell theorem" and is a fundamental concept in electrostatics.

## 4. How is the electric potential related to a hollow charged sphere?

The electric potential at any point inside a hollow charged sphere is constant. This is because the potential is determined by the charge distribution, and since the charge is evenly spread over the surface of the sphere, the potential will be the same at all points inside the sphere. This also means that the potential at the surface of the sphere is equal to the potential inside the sphere.

## 5. Can a hollow charged sphere have a non-uniform charge distribution?

Yes, a hollow charged sphere can have a non-uniform charge distribution if there are other charges present nearby. In this case, the charges will redistribute themselves on the surface of the sphere such that the resulting electric field inside the sphere is zero. However, the charge density on the surface will no longer be uniform, and the potential inside the sphere will also no longer be constant.

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