Use the divergence (= Gauss’s) theorem to compute the flux of the vector field?
- Steve4PhysicsLv 71 month agoFavorite Answer
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.