Thread: divergence

Hi guys, any help with this would be greatly appreciated!


Illustrate (verify) the Divergence Theorem with the force function
F (x,y,z) = <1, 2, z^3> where the surface S is the cylinder x^2 + y^2 = 16, 0z6.

left side of Gauss's Th =

right side of Gauss's Th =

Originally Posted by boousaf

Hi guys, any help with this would be greatly appreciated!


Illustrate (verify) the Divergence Theorem with the force function
F (x,y,z) = <1, 2, z^3> where the surface S is the cylinder x^2 + y^2 = 16, 0z6.

left side of Gauss's Th =

right side of Gauss's Th =

since and is a circle of radius 4.


By symmetry the only non-zero contribution of the flux of F through S is through the top of the cylinder ...... (You can check this - using cylindrical coordinates for the flux through the curved part of the cylinder is probably easiest but it can be done using cartesian coordinates too). Note that [tex]\vec{dS} = k dx dy on the ends of the cylinder.

Then the flux integral becomes .

thanks again mr. fantastic!!