Electric Force of two hemispheres

[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?

 

[vincentchan]

use maxwell stress tensor approach this problem

 

[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.

 

[TimNguyen]

Anyone...?

 

[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)

 

[vincentchan]

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

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

 

[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.