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Homework Help: Electric Force of two hemispheres

  1. Mar 3, 2005 #1
    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. jcsd
  3. Mar 3, 2005 #2
    use maxwell stress tensor approach this problem
     
  4. Mar 4, 2005 #3
    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.
     
  5. Mar 5, 2005 #4
    Anyone...?
     
  6. Mar 6, 2005 #5
    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
  7. Mar 6, 2005 #6
    forget it... the integral will go crazy.....
     
  8. Mar 6, 2005 #7
    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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