Potential inside a sphere with two regions

[shinobi20]

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?

 

[mfb]

I don't think you can avoid an integration over the sphere.
What is the charge distribution?

 

[shinobi20]

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.

 

[mfb]

"uniformly" is the important keyword here.

 

[TSny]

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?

 

[shinobi20]

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?

 

[mfb]

A mathematical sphere is hollow. Filled it would be a ball.