Electric potential at the center of two concentric shells

[judas_priest]

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.

 

[SammyS]

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.

 

[judas_priest]

The question doesn't mention whether it's conducting, or non conducting.

 

[SammyS]

The question doesn't mention whether it's conducting, or non conducting.

Does it mention charge distribution ?

 

[judas_priest]

Does it mention charge distribution ?

No. I've written question as it is. Copied it. Doesn't mention anything.

 

[SammyS]

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?