Evaluate flux through a surface

[cobolt]

Hi,

Im asked to evaluate the flux through a surface s2.

The overall region R is a half ball bounded by disc s1 with y=0 and $$x^{2}$$+z$$^{2}$$=4 and the hemispherical shell s2 with y>=0 and $$x^{2}$$+z$$^{2}$$+y$$^{2}$$=4.

In the region there exists a force with field F = -zi+y$$^{2}$$j+xk.

I have tried evaluating the integral of F.n where n is the unit normal to R but am stuck of how to do this entirely.

Thanks.

 

[lanedance]

there may be an easier way to do this... do you know about conservative vectors fields?

 

[cobolt]

I am aware of these but the question ask for it in this fashion. :\

 

[lanedance]

which fashion - does it explictly ask for a surface inetgral to be performed as the reulst of the surface integral can be deduced from just the form of the vector field

 

[cobolt]

integral of the field dotted with the unit normal to the surface S2.