Potential at the center of a sphere between two long rods

[FS98]

Homework Statement

A spherical shell with radius R and surface charge density σ is sandwiched between two infinite sheets with surface charge den- sities −σ and σ , as shown in Fig. 2.46. If the potential far to the right at x = +∞ is taken to be zero, what is the potential at the center of the sphere? At x = −∞?

Homework Equations

P = kQ/R (where p is being used as electrical potential)

The Attempt at a Solution

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P = kQ/R

For the sphere:

The electrical potential should be 0 because of symmetry.

So shouldn’t the electrical potential just be from the *sheets?

I’m not quite sure how to find that.

 

[kuruman]

So shouldn’t the electrical potential just be from the rods?

You mean sheets.

Are the sheets and the shell conducting or not? It makes a difference.

 

[FS98]

You mean sheets.

Are the sheets and the shell conducting or not? It makes a difference.

Yes, I meant sheets, sorry about that.

I’m not sure what you mean by conducting, but all of the information I have is in the post.

 

[kuruman]

I’m not sure what you mean by conducting, but all of the information I have is in the post.

I mean they are made of some conducting material like metal that has electrons free to move in response to external electric fields. When you place a charged conductor near a charge, the original charge distribution on the conductor will change to make it an equipotential. Since the problem does not specify that we have conductors here, we will assume that the charges are not free to move and imagine them being pasted on the surfaces of the sheets and shell.

The electrical potential should be 0 because of symmetry.

What kind of symmetry is this that requires the potential of the shell to be zero? What is the potential (relative to infinity) of just a charged sphere? Forget the sheets for the time being.