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Flux in vector field question 
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#1
Feb310, 05:11 PM

P: 84

1. The problem statement, all variables and given/known data
Consider the vector field: F = r/r^{3} 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
Feb310, 05:13 PM

P: 1,084

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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