# Potential inside a sphere with two regions

Tags:
1. Nov 3, 2015

### shinobi20

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
Poisson Equation?

3. 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?

2. Nov 3, 2015

### Staff: Mentor

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

3. Nov 6, 2015

### shinobi20

It just said that a charge Q is distributed uniformly in the lower hemisphere. Find the potential inside and outside.

4. Nov 6, 2015

### Staff: Mentor

"uniformly" is the important keyword here.

5. Nov 6, 2015

### TSny

Are you meant to find the potential at all points inside, or just on the axis of the hemisphere?

6. Nov 8, 2015

### shinobi20

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???

7. Nov 8, 2015

### Staff: Mentor

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