Voltage, electric field and potential energy for concentric shells

In summary, the problem involves two concentric shells, one with a charge of Va=120V and the other grounded with Vb=0V. The questions ask for the voltage (Vo), electric field (Eo), and potential energy (U) at the center of the shells. The problem does not specify the shape of the shells, so it is unclear if they are spherical or cylindrical. The solution may involve an integral, but the exact form is not given.
  • #1
tinesi
2
0
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1. Homework Statement

the a shell is charged Va=120v
shell b is grounded, Vb=0V

What is the voltage in the center of shells (vo)?
The electric field in the center of shells?
The potential energy in the center of shells?

Homework Equations


Vr=Va+(1/r-1/a)/(1/a-1/b)Vab (from integrals)
though I am not sure

The Attempt at a Solution


I assume that V0=Va=120V but I don't think so
I assume the field inside is 0

1/ro=1/0=0(?)
Vab=120v?
vo=-120v?
Eo=0?
U=0?
 

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  • #2
You have not reproduced a proper problem statement. Please spell out the problem exactly as given and give your detailed attempt.
 
  • #3
Sorry, my first time here. I have written more details.
 
  • #4
Welcome to the PF. :smile:
tinesi said:

Homework Statement


the a shell is charged Va=120v
shell b is grounded, Vb=0V

What is the voltage in the center of shells (vo)?
The electric field in the center of shells?
The potential energy in the center of shells?
Are the concentric shells spherical or cylindrical? Can you show the integral that is used to calculate the E-field for this geometry?
 

1. What is the relationship between voltage and electric field for concentric shells?

The voltage between two concentric shells is directly proportional to the electric field. This means that as the voltage increases, the electric field also increases.

2. How does the potential energy differ between concentric shells compared to parallel plates?

The potential energy between concentric shells is inversely proportional to the distance between them, while the potential energy between parallel plates is directly proportional to the distance between them. This means that as the distance between concentric shells decreases, the potential energy increases, while the opposite is true for parallel plates.

3. Can you have a negative potential energy between concentric shells?

Yes, it is possible to have a negative potential energy between concentric shells. This occurs when the charge on the inner shell is negative, causing an attractive force between the two shells.

4. How does the voltage change if the distance between the concentric shells is increased?

If the distance between the concentric shells is increased, the voltage will decrease. This is because the voltage is inversely proportional to the distance between the shells.

5. What is the equation for calculating the electric field between concentric shells?

The equation for calculating the electric field between concentric shells is E = Q/(4πεr^2), where Q is the charge on the inner shell, ε is the permittivity of the medium, and r is the distance between the shells.

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