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!

Curl of a gradient and the anti Curl

  1. May 7, 2017 #1
    1. The problem statement, all variables and given/known data
    Is there a vector field D that produces The position vector <x,y,z> if we take the curl of vector field D?

    2. Relevant equations
    Curl of gradient f = 0

    Curl of Vector D = <x,y,z>


    3. The attempt at a solution

    Curl of vector D
    Where vector D=<A,B,C>

    Cy - Bz = x
    Az - Cx = y
    Bx - Ay = z

    I can't solve what component functions A, B, C are.

    HELP
     
  2. jcsd
  3. May 7, 2017 #2
    You are asked to determine if a vector exists s.t. $$ \vec \nabla \times \vec D = \vec r$$
    I suggest you expand the cross product in it's components. For example, the x component would be:$$\partial_y D_z -\partial_z D_y=x$$
    Clearly ##D_z## must be of the form ##a_zyx##, where ##a_z## is a constant. Do the same for the other two components.
     
    Last edited: May 7, 2017
  4. May 7, 2017 #3

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Think about what you know about the divergence of a curl...
     
  5. May 7, 2017 #4
    Divergence of a curl is zero
     
  6. May 7, 2017 #5

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Yes. So....?
     
  7. May 8, 2017 #6
    So... divergence of a curl measures how much the vector diverges outward after measuring how much that vector was curling. Thus, it is always zero.
     
  8. May 8, 2017 #7

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    But what does that observation have to do with your problem?
     
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: Curl of a gradient and the anti Curl
  1. Curl of the curl? (Replies: 1)

  2. Curl of a gradient (Replies: 3)

  3. Curl Operator (Replies: 1)

  4. The curl of a vector (Replies: 9)

Loading...