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Homework Help: Flux in vector field question

  1. Feb 3, 2010 #1
    1. The problem statement, all variables and given/known data
    Consider the vector field:
    F = r/r3

    where r = xi + yj + zk

    Compute the flux of F out of a sphere of radius a centred at the origin.

    2. Relevant equations



    3. The attempt at a solution
    Hi everyone,

    I have: flux = [tex]\int[/tex]F.dA

    I can't use Gauss' Law, because the field will not be defined at the origin.

    Instead, I want to use F.n, where n is the normal vector to the sphere.

    Is it correct that the normal vector is the div of the equation of the sphere?

    ie. n = div (x^2 + y^2 + z^2 = a^2)

    = 2x i + 2y j + 2z k

    and then F.n = 2/r

    Is this correct so far?
    Thanks for any help
     
  2. jcsd
  3. Feb 3, 2010 #2
    Looks good. the divergence is how fast the field falls off, so it has to be in the direction of the normal vector.
     
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