Flux in vector field question


by Pyroadept
Tags: field, flux, vector
Pyroadept
Pyroadept is offline
#1
Feb3-10, 05:11 PM
P: 84
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
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dacruick
dacruick is offline
#2
Feb3-10, 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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