Question regarding charges on a hollow sphere

In summary, for a hollow conducting sphere in a static situation, the charges are located on the surface of the sphere according to Gauss' Law. This is because there is no electric field inside the sphere, so there is no flux and therefore no charge inside. The charge is evenly distributed on the outside surface, as charges on the inside surface would feel repulsion from each other and be pushed to the outside surface. This applies to both a massive and a hollow sphere.
  • #1
Haye
15
2

Homework Statement


I have a hollow conducting sphere with a charge on it, and I'm looking at the static situation. Where are the charges located?

Homework Equations


Gauss' Law


The Attempt at a Solution


A static situation, so no electric field inside the sphere, or charges would move until the field is zero. Gauss' law tells me that no E field also means there is no flux, and therefore the charge inside the sphere is zero, so the charges are on the surface of the sphere.
I get this for a massive sphere, but for the hollow sphere you have a surface on the inside aswell.
My thoughts are that if charges would be on the surface on the inside, they wouldn't feel net repulsion from the charges on the outside surface, but would feel repulsion from other charges on the inside surface, and would therefore be pushed to the outside surface.
So I believe that also for a hollow sphere, all the charge would be on the outside surface.
Is my thinking correct?

Regards, Haye
 
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  • #2
your thinking is spot on
 

1. What is the formula for calculating the electric field inside and outside of a charged hollow sphere?

The formula for calculating the electric field inside a hollow sphere is E = Q/4πεr^2, where Q is the charge on the sphere, ε is the permittivity of free space, and r is the distance from the center of the sphere. Outside the sphere, the formula is E = Qr/4πεR^3, where R is the radius of the sphere.

2. How does the charge distribution on a hollow sphere affect the electric field inside and outside of the sphere?

The charge distribution on a hollow sphere does not affect the electric field inside the sphere. However, it does affect the electric field outside the sphere. If the charge is evenly distributed on the surface of the sphere, the electric field outside will be the same as if all the charge were concentrated at the center of the sphere. If the charge is unevenly distributed, the electric field outside will be affected accordingly.

3. Can a hollow sphere have a net charge of zero?

Yes, a hollow sphere can have a net charge of zero if the total amount of positive charge is equal to the total amount of negative charge. In this case, the electric field both inside and outside the sphere will be zero.

4. How does the radius of a hollow sphere affect the electric field inside and outside the sphere?

The radius of a hollow sphere affects the electric field inside the sphere. As the radius increases, the electric field inside decreases. However, the radius does not affect the electric field outside the sphere.

5. Can a hollow sphere have a non-uniform electric field inside?

No, a hollow sphere cannot have a non-uniform electric field inside. Due to the symmetrical distribution of charge on the surface, the electric field inside the sphere will always be uniform. However, the electric field outside the sphere may be non-uniform depending on the charge distribution on the surface.

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