# Potential at the center of a sphere between two long rods

• FS98
In summary: The potential of the shell is zero because it is symmetrical about the center of the sphere. The potential of a just a charged sphere is also zero.
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

[/B]
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.

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FS98 said:
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
kuruman said:
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.

Last edited:
FS98 said:
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.
FS98 said:
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.

## What is the potential at the center of a sphere between two long rods?

The potential at the center of a sphere between two long rods is the electric potential energy per unit charge at that point. It is a measure of how much work is required to move a positive charge from infinity to the center of the sphere in the presence of the two long rods.

## How is the potential at the center of a sphere between two long rods calculated?

The potential at the center of a sphere between two long rods can be calculated using the formula V = kQ/r, where V is the potential, k is the Coulomb constant, Q is the charge of the two long rods, and r is the distance between the center of the sphere and the two long rods.

## What factors affect the potential at the center of a sphere between two long rods?

The two main factors that affect the potential at the center of a sphere between two long rods are the charge of the two rods and the distance between the center of the sphere and the rods. The potential also depends on the medium between the rods and the sphere, as well as the presence of any other nearby charges.

## How does the potential at the center of a sphere between two long rods change with distance?

The potential at the center of a sphere between two long rods follows an inverse relationship with distance. This means that as the distance between the center of the sphere and the rods increases, the potential decreases. Similarly, as the distance decreases, the potential increases.

## What is the significance of studying the potential at the center of a sphere between two long rods?

Studying the potential at the center of a sphere between two long rods helps us understand the behavior of electric charges and how they interact with each other in an electric field. It also has practical applications in various fields such as electronics, electromagnetism, and energy generation.

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