Potential inside a sphere with two regions

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Homework Help Overview

The discussion revolves around determining the electric potential inside a sphere with a charge distributed in the lower half, while the upper half is uncharged. The problem involves concepts from electrostatics and potential theory.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants explore the appropriate equations to use, questioning whether to apply Poisson's or Laplace's equation. There is discussion about the necessity of integration over the sphere and the implications of uniform charge distribution.

Discussion Status

The conversation is ongoing, with participants raising questions about the specifics of the charge distribution and the potential to be calculated. Some guidance has been offered regarding the importance of uniformity in charge distribution, but no consensus has been reached on the method to proceed.

Contextual Notes

There is mention of the need to clarify whether the potential should be found at all points inside the sphere or just along the axis. The distinction between a hollow sphere and a filled sphere is also noted, which may affect the approach taken.

shinobi20
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Homework Statement


Suppose a charge is distributed in a lower half region of a sphere and the upper half has zero charge. What is the potential inside?

Homework Equations


Poisson Equation?

The Attempt at a Solution


My problem here is I don't know how to start, I think laplace equation can't be used because there is charge inside, so it should be poisson's equation. But what exactly should I do?
 
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I don't think you can avoid an integration over the sphere.
What is the charge distribution?
 
mfb said:
I don't think you can avoid an integration over the sphere.
What is the charge distribution?
It just said that a charge Q is distributed uniformly in the lower hemisphere. Find the potential inside and outside.
 
"uniformly" is the important keyword here.
 
shinobi20 said:

Homework Statement


Suppose a charge is distributed in a lower half region of a sphere and the upper half has zero charge. What is the potential inside?

Are you meant to find the potential at all points inside, or just on the axis of the hemisphere?
 
TSny said:
Are you meant to find the potential at all points inside, or just on the axis of the hemisphere?
All points inside the sphere. If it were a hollow sphere, laplace equation will do but for this case, I think it should be poisson equation?
 
A mathematical sphere is hollow. Filled it would be a ball.
 

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