# Electric Force of two hemispheres

1. Mar 3, 2005

### TimNguyen

Hello.

I'm having trouble with this problem.

Suppose there is a sphere of uniform charge (Q). What is the electric force of the top hemisphere due to the bottom hemisphere?

2. Mar 3, 2005

### vincentchan

use maxwell stress tensor approach this problem

3. Mar 4, 2005

### TimNguyen

I apologize, I have no idea what a tensor is at all.

All I know is that the electric force equals (QE), therefore the only solution I could think of is of the form F = (1/4 Pi PermitivityConstant)(???). I'm trying to picture a way to find the electric field of the system but I just don't see it.

4. Mar 5, 2005

Anyone...?

5. Mar 6, 2005

### davidY

if you are good at maths, here is one option:
use gauss laws to find equation E field at every point
integrate the F=Eq over the entire sphere
long integration, not really that hard if it is a hollow sphere. seems quite hard if it is solid, not sure

(i hope this method works)

Last edited: Mar 6, 2005
6. Mar 6, 2005

### vincentchan

forget it... the integral will go crazy.....

7. Mar 6, 2005

### davidY

for hollow sphere:

well, the e field is constant over the surface of the sphere. so all you have to do is to use a polar integration with two cosines in the function. to find the component in the away from centre direction. because by symmetry the force is outwards radially.

for solid sphere:

well, you are totally right.