Suppose I need to find the flux of vector Field $\vec{F} = <y^2, xz , -1>,$ across the cone $z = 2\sqrt{x^2 + y^2}$ between the planes $z = 0$ and $z = 2$,
As we can see, there will be two surfaces $S_1$ the conical part and $S_2$ the circular part on top of the cone of radius $1$ .
My question is : Do I need to find the flux through each of the surfaces or do I need to just find it acroos $S_1$ ?,
I have solved a number of questions like these , sometimes the problem is solved just by considering it across $S_1$(ie the conical part) , while some time I also have to take care of $S_2$ the circular part.
Can anyone please tell me in detail when Do I have to include both the surfaces and when do I have to exclude one ?
(The given problem is from Thomas Calculus, and the flux is calculated simply by considering $S_1$)
Thank you
If the problem asks for the flux through the surface, I cant imagine why you would calculate it through only part of the surface! Could you give an example in which you "I have solved a number of questions like these , sometimes the problem is solved just by considering it across S1 (ie the conical part)"?