Dougy asked in Science & MathematicsMathematics · 1 month ago

# Use the divergence (= Gauss’s) theorem to compute the flux of the vector field?

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• 1 month ago

div(F) = ∂F/∂x + ∂F/∂y + ∂F/∂z = 3x² + 3y² + 3z²

= 3(x² + y² + z²)

In spherical polar coordinates this is: div(F) = 3r²

Using the  divergence theorem, the flux (Φ) out of the sphere is the volume integral of div(F) inside the sphere.  (Sphere is radius R = √2.)

Φ = ∰div(F)dV = ∰3r² r²sinφdrdθdφ

= 3∰r⁴dr sinφdφ  dθ

which you should now be able to complete for yourself.