Electric potential at the center of two concentric shells

In summary, the question asks for the potential at the center of two concentric shells with given radii and electric potentials. It is assumed that the shells are conducting and there are no isolated charges inside. The result is derived by considering the electric field at the center of a shell, which is zero in the case of a conducting shell with no isolated charges inside. The question does not provide information on the charge distribution on the shells.
  • #1
judas_priest
174
0

Homework Statement



If the electric potential of the inner shell is 10 volts and that of outer shell is 5 volts, then the potential at the center will be?

Homework Equations



The radius of inner shell = a (given)
The radius of outer shell = 2a (given)

The Attempt at a Solution



Having read that electric field at the center of a shell is zero, I assume, the potential is constant throughout like in the case of a conducting sphere, and hence the answer is 10 volts. But I could get this answer only after a lot of manipulation, and I'm still not clear about it.

Also, if someone can help me out with why the electric field inside a shell is zero? Doesn't necessarily have to be a conducting shell.
 
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  • #2
judas_priest said:

Homework Statement



If the electric potential of the inner shell is 10 volts and that of outer shell is 5 volts, then the potential at the center will be?

Homework Equations



The radius of inner shell = a (given)
The radius of outer shell = 2a (given)

The Attempt at a Solution



Having read that electric field at the center of a shell is zero, I assume, the potential is constant throughout like in the case of a conducting sphere, and hence the answer is 10 volts. But I could get this answer only after a lot of manipulation, and I'm still not clear about it.

Also, if someone can help me out with why the electric field inside a shell is zero? Doesn't necessarily have to be a conducting shell.
If it is a conducting shell and there are no isolated charges inside, then the result is quite easy.

If it's not a conducting shell, then we need more information regarding the charge distribution.
 
  • #3
The question doesn't mention whether it's conducting, or non conducting.
 
  • #4
judas_priest said:
The question doesn't mention whether it's conducting, or non conducting.
Does it mention charge distribution ?
 
  • #5
SammyS said:
Does it mention charge distribution ?

No. I've written question as it is. Copied it. Doesn't mention anything.
 
  • #6
After thinking about this for a while, and in consideration of your replies, I'm quite sure that it doesn't matter whether the shells are conducting or not.

In coming up with your answer, did you determine what charges were on the shells?
 

1. What is the formula for calculating the electric potential at the center of two concentric shells?

The formula for electric potential at the center of two concentric shells is V = (kQ1 + kQ2)/R, where k is the Coulomb's constant, Q1 and Q2 are the charges of the shells, and R is the distance between the shells.

2. How does the electric potential at the center of two concentric shells change with the distance between the shells?

The electric potential at the center of two concentric shells is directly proportional to the distance between the shells. This means that as the distance increases, the electric potential also increases, and vice versa.

3. Can the electric potential at the center of two concentric shells be negative?

Yes, the electric potential at the center of two concentric shells can be negative. This happens when the charges on the shells have opposite signs, resulting in a negative value for the potential.

4. What happens to the electric potential at the center of two concentric shells if one of the shells is removed?

If one of the shells is removed, the electric potential at the center will change. The new potential will depend on the remaining shell's charge and the distance between the remaining shell and the center point.

5. Can the electric potential at the center of two concentric shells be zero?

Yes, the electric potential at the center of two concentric shells can be zero. This occurs when the charges on the shells are equal and opposite, canceling each other out and resulting in a net potential of zero at the center.

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