Electric Force of two hemispheres

  • Thread starter TimNguyen
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  • #1
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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?
 

Answers and Replies

  • #2
609
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use maxwell stress tensor approach this problem
 
  • #3
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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
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Anyone...?
 
  • #5
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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:
  • #6
609
0
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.....
 
  • #7
9
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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.
 

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