What is the Charge Distribution on Concentric Spherical Shells?

In summary, using Gauss's Law, the charge on all four surfaces of the concentric conducting spherical shells can be determined. The inner shell has a net charge of -8C, while the outer shell is neutral. Placing a 2C point charge inside the inner shell, the charge on the inner and outer surfaces of the shells can be determined to be 6C and -6C respectively.
  • #1
veronicak5678
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Homework Statement



You have two concentric conducting sherical shells. the net charge in the inner shell is -8 C and the outer shell is neutral. In the inner hollow is placed a 2C point charge. Using Gauss's Law, find the charge on all 4 surfaces of the shells.

Homework Equations



Econductor = 0

The Attempt at a Solution


Inner radius of inner shell: -2C
Outer radius of inner shell: -6C
Inner radius of outer shell: 0
Outer radius of outer shell: 0

Not sure how to use Gauss's law here, or if the answers for the outer shell are right.
 
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  • #2
Try envisioning a Gaussian sphere that lies outside the inner radius of the inner sphere but inside the outer radius. Do the same for the outer sphere.
 
  • #3
I think this means the inner shell answers are correct, but not the outer. Is the outer shell going to have a -8 charge on the inner radius and a positive 8 charge on the outer?
 
  • #4
Not -8. Think about how much charge there is inside the outer shell.
 
  • #5
Oh! There is -6C inside the outer shell. So 6C on the inner and -6 on the outer.
 

1. What is a conducting spherical shell?

A conducting spherical shell is a hollow sphere made of a material that allows electric charges to move freely. This means that the charges on the surface of the sphere can redistribute themselves to create an electric field inside the shell, but the electric field outside the shell is zero.

2. How is the electric field inside a conducting spherical shell calculated?

The electric field inside a conducting spherical shell is calculated using Gauss's Law, which states that the net electric flux through a closed surface is equal to the enclosed charge divided by the permittivity of free space. In the case of a conducting spherical shell, the enclosed charge is equal to the charge on the shell itself.

3. What is the relationship between the electric field and the potential inside a conducting spherical shell?

The electric field inside a conducting spherical shell is directly proportional to the potential, meaning that as the electric field increases, so does the potential. This relationship is described by the equation E = -dV/dr, where E is the electric field and V is the potential.

4. Can a conducting spherical shell have a non-uniform charge distribution?

No, a conducting spherical shell must have a uniform charge distribution in order for the electric field inside the shell to be zero. This is because any non-uniform charge distribution would result in an electric field inside the shell, which goes against the properties of a conducting shell.

5. How does the electric field inside a conducting spherical shell change if a point charge is placed inside the shell?

If a point charge is placed inside a conducting spherical shell, the electric field inside the shell will still be zero. This is because the charge on the shell will redistribute itself in a way that cancels out the electric field of the point charge. However, the electric field outside the shell will now be non-zero due to the presence of the point charge.

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