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Flux through a sphere given a vector field

  1. Dec 12, 2011 #1
    1. The problem statement, all variables and given/known data

    Vector field F = (2siny-cosz, 2cosx+3sinz, cosy-2sinx)

    Compute the flux of F through a sphere of radius one centered at the origin with respect to the outer unit normal.


    2. Relevant equations

    Divergence theorem/Gauss's Law


    3. The attempt at a solution

    The only way I know how to calculate flux is to look at F and let
    2siny-cosz = M
    2cosx+3sinz = N
    cosy-2sinx = P

    then do dM/dx dN/dy dP/dz

    then use the divF integral to integrate dM/dx + dN/dy + dP/dz with respect to x,y,z


    But I don't understand how else to do it when their derivatives are all 0.

    Thanks a lot for any help
     
  2. jcsd
  3. Dec 12, 2011 #2

    LCKurtz

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    Do you know the saying "Don't look a gift horse in the mouth."? What do you get when you calculate [itex]\iiint_V 0\, dv[/itex]?
     
  4. Dec 12, 2011 #3
    I thought that you couldn't integrate 0
     
  5. Dec 12, 2011 #4

    LCKurtz

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    For example, in one variable[tex]\int_a^b 0\, dx = C|_a^b = C - C = 0[/tex]
     
  6. Dec 12, 2011 #5
    Well the triple integral yields zero then.
    Does this mean that the vector field does not flow through the sphere? There is no flux?
    Can I plot this?

    Thanks, by the way.
     
  7. Dec 12, 2011 #6

    LCKurtz

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    It means that the total outward flow is zero. That doesn't mean no flux flows through the sphere, just that as much goes in as out in total. For example, a constant flux flowing right through the sphere would give a total flux of zero.

    You're welcome.
     
  8. Dec 12, 2011 #7
    So the flux is not zero, it is just out = in. From the information given is there anything else I can know about the flow?
     
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