The discussion revolves around the application of the divergence theorem in the context of calculating the flux of a vector field, specifically F(x,y,z)=4x i - 2y^2 j +z^2 k, through various surfaces of a cylinder defined by the inequalities x^2+y^2<=4 and 0<=z<=3. Participants are exploring the implications of using inequalities versus equalities in defining the surfaces for flux calculation.
There is an ongoing exploration of how to express the surfaces in terms of inequalities and what that means for the flux calculations. Some participants have provided specific parameterizations for the surfaces, while others are seeking clarification on the concept of the "tangent surface." The discussion is active, with modifications to questions being made as participants refine their understanding.
Participants have noted previous mistakes in their questions and are working to clarify their understanding of the problem setup. There is a focus on ensuring that the definitions used align with the requirements of the divergence theorem.
kelvin56484984 said:Homework Statement
F(x,y,z)=4x i - 2y^2 j +z^2 k
S is the cylinder x^2+y^2=4, 0<=z<=3
Homework Equations
The Attempt at a Solution
[/B]
I find that the answer is 84 pi
What is the difference after if I change the equation to inequality?
For example :
x^2+y^2<=4, z=3
x^2+y^2<=4 , z=0
X^2+y^2=4, z=3
thanks!
kelvin56484984 said:Homework Statement
F(x,y,z)=4x i - 2y^2 j +z^2 k
S is the cylinder x^2+y^2=4, 0<=z<=3
Homework Equations
The Attempt at a Solution
[/B]
I find that the answer is 84 pi
What is the difference after if I change the equation to inequality?
For example :
x^2+y^2<=4, z=3
x^2+y^2<=4 , z=0
X^2+y^2=4, z=3
thanks!
Bottom: ##\vec R(x,y) = \langle x,y,0\rangle,~0\le x^2+y^2\le 4##kelvin56484984 said:Sorry, I made some mistake previously and I modified the question.
If I want to find the flux of the bottom face, top face, side surface of cylinder and the tangent surface of the cylinder,
How can I express it in inequality?