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 calculus proof

  1. Mar 30, 2014 #1
    The following is used as part of a proof I'm trying to understand:

    Vf(.A)dV=∫SfA.dS-∫VA.(f)dV
    where f is a scalar field, and the surface integral is taken over a closed surface (which presumably encloses the volume).

    I'm not sure how to go about proving this. I can see the divergence theorem will come into play at some stage, but the scalar field seems to be in the way to start with. This is probably really simple, I'm a little rusty with my vector calculus.

    Clues would be helpful, thanks :)
     
  2. jcsd
  3. Mar 30, 2014 #2

    CAF123

    User Avatar
    Gold Member

    Hi physiks,
    Rewrite your expression like $$\int_V f(\nabla \cdot \mathbf{A}) + \mathbf{A} \cdot (\nabla f)\, dV = \int_S f\mathbf{A} \cdot \mathbf{dS}$$ and work with the left hand side to show the right hand side.
     
  4. Mar 30, 2014 #3
    Got it, thanks!
     
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 calculus proof
  1. Vector Calculus Proof (Replies: 0)

  2. Vector calculus proof (Replies: 7)

  3. Vector Calculus proof (Replies: 4)

Loading...