The flux of the vector field F ( x , y , z ) = 3 z k across the closed rectangular box with opposing vertices at ( 0 , 0 , 0 ) and ( 6 , 5 , 7 ) is:

Question

Using Surface Integrals, not divergence theorem, find The flux of the vector field F ( x , y , z ) = 3 z k across the closed rectangular box with opposing vertices at ( 0 , 0 , 0 ) and ( 6 , 5 , 7 ) .

Answer 1

Total flex is equel flux throuh upper rectangele (others rectungles flex 0 because at the bottom z = 0 and F= 0

and sides rectangles are parralle with field f = 3zk. So we have flux is 3·7·(6·5) = 630 becouse z = 7 and area = 6·5 and F = 3zk perpendicular to this surface(upper rectangle)

Answer: flex is 630