August 9th, 2017, 12:29 AM  #1 
Member Joined: May 2017 From: Slovenia Posts: 52 Thanks: 0  Flux of vector field
I have F(x,y,z)=(z,0,2) and i need to find the flux through the upper side of the paraboloid z=2x^2y^2 1<z<2. When solving this with Gaussian theorem (divergence theorem) I'm not sure whether z will be = to 1 or 2? 
August 9th, 2017, 03:29 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,576 Thanks: 667 
The 'upper side' of the paraboloid is neither z= 1 nor z= 2, it is the paraboloid! The paraboloid has vertex at (0, 0, 2) and opens downward. In order to make it a closed surface, so that you can use the divergence theorem, you would add the plane z= 1.


Tags 
field, flux, vector 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Flux of the vector field through the surface  Vid  Calculus  1  August 5th, 2017 03:23 AM 
Vector field  Uniman  Linear Algebra  2  October 19th, 2012 08:32 AM 
vector field and flux  cummings123  Calculus  3  October 17th, 2012 03:41 PM 
Vector Calculus Divergence of a Vector Field  MasterOfDisaster  Calculus  2  September 26th, 2011 09:17 AM 
Vector Field 2  OSearcy4  Calculus  2  October 27th, 2009 06:39 PM 