1. Limited time only! Sign up for a free 30min personal 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!

A question that uses divergence thm

  1. Apr 18, 2012 #1
    1. The problem statement, all variables and given/known data


    show that the volume enclosed by a closed surface S is given by

    ## \frac{1}{3} \int_{S} \vec{x} \cdot d\vec{A} ##

    2. Relevant equations


    divergence theorem

    3. The attempt at a solution

    using divergence theorem

    I get that ##V =\frac{1}{3} \int_{V} \nabla \cdot \vec{x} dV ##

    but I want

    ## V = \int_{V} dV ## don't I? how does it simplify?
     
  2. jcsd
  3. Apr 18, 2012 #2
    Unless

    ## \vec{x} = (x,y,z) ##

    Then:

    ## V = \frac{1}{3} \int_{V} (1+1+1) dV = \int_{V}dV ##

    It's because x is just the position vector whose divergence is 3 isnt it? i.e. x is not a vector field?
     
  4. Apr 18, 2012 #3

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Sure, that's it. But the position vector (x,y,z) IS a vector field. It's just a particular one.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: A question that uses divergence thm
Loading...