- #1
Stef42
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Homework Statement
Use the divergence theorem in three dimensions
[tex]\int\int\int\nabla\bullet V d\tau= \int \int V \bullet n d \sigma[/tex]
to evaluate the flux of the vector field
V= (3x-2y)i + x4zj + (1-2z)k
through the hemisphere bounded by the spherical surface x2+y2+z2=a2 (for z>0) and the x-y plane
Hint: The direct evauation of the flux may not be the easiest way to proceed
Homework Equations
The Attempt at a Solution
I found it pretty simple which means I probably messed up (and I'm not sure what the hint is talking about
ok so the divergence is
[tex]\nabla \bullet V = 3-2=1 [/tex]
and the integral over the volume of the hemisphere (using spherical polar coordinates) is
[tex] \int_{0}^a r^2 d \tau \int_{0}^{2\pi} d\phi \int_{0}^{\pi/2} sin\theta d\theta = \frac{2\pi a^3}{3} [/tex]
So am I doing it completely wrong? I don't know the answer but if anyone could look through it and spot anything I would really appreciate it