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Surface Integral HW problem

  1. Sep 14, 2005 #1
    "Find the surface integral of r over a surface of a sphere of radius and center at the origin. Also find the volume integral of Gradient•R and compare your results"


    Do I just integrate r to get (1/2)r^2 and plug some limits in since the r-hats equal one?
     
    Last edited: Sep 14, 2005
  2. jcsd
  3. Sep 14, 2005 #2
    Well, it must give you what the vector r is right?

    [tex]\iint\limits_{S}\mathbf{F}dS[/tex]

    where S is the surface area of the sphere and F=r.
     
  4. Sep 15, 2005 #3
    In xyz, r would equal R = x x^ + y y^ + z z^ but I'm just using R = r r^r to be simpler.
     
  5. Sep 15, 2005 #4

    HallsofIvy

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    Be sure to distinguish the VECTOR r from the variable r. The vector r is the vector from the origin to the point on the sphere (of radius R?). You will actually be integrating that with the unit normal vector. Since the unit normal vector to the surface of the sphere and r are in the same direction, that is just the length of r. Hmmm, for the first part of this problem you don't actually have to do an integral at all!
     
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