1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Vector Analysis - Determining whether a vector field is conservative

  1. Apr 8, 2013 #1
    1. The problem statement, all variables and given/known data

    n/a

    2. Relevant equations

    ∇ x F = 0

    ∂Q/∂x = ∂P/∂y

    3. The attempt at a solution

    n/a

    Given that no sketch of the vector field is given;

    Is determining the curl of a vector field the most fail proof of determining whether it is conservative?

    I'm just wondering whether or not determining ∂Q/∂x = ∂P/∂y is just as fail proof (Given that: F=Pi + Qj + Rk) because it seems like a faster method within the boundary of this course.
     
  2. jcsd
  3. Apr 8, 2013 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    What if ∂Q/∂x = ∂P/∂y, but ∂Q/∂z ≠ ∂R/∂y ?
     
  4. Apr 8, 2013 #3
    Then the partials of Q and P will only be effective with i + j vector fields?
     
  5. Apr 8, 2013 #4
    Also, the answer to your question would be that the field would only be conservative in the XY plane but not in the XZ or YZ.
     
  6. Apr 8, 2013 #5

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    I've not aware of that sort of distinction.

    If ∂Q/∂z ≠ ∂R/∂y, then ∇ x F ≠ 0 , so the field, F is not conservative.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Vector Analysis - Determining whether a vector field is conservative
Loading...