1. Calculate the flux of the field
![](Self Assesment_clip_image002.gif)
over the surface of a right circular cylinder of radius R and height h in the first octant, i.e. in the region (x>0, y>0, z>0).
2. Evaluate the surface integral of the vector field
over the surface of a unit cube with the origin being at one of the corners.
3. Calculate the flux of
over the surface of a sphere of radius R with its centre at the origin.
This problem is to be attempted similar to the problem 5 of the tutorial, i.e., by closing the cap and subtracting the contribution due to the cap. The divergence being 3, the flux from the closed cone is 3 times the volume of the cone which gives
The contribution from the top face (which is a disk of radius 2 ) is
. Thus the net flux is zero. (You can also try to get this result directly as done in problem 4, where we showed that the flux from the curved surface is zero).