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Energy flux vector field problem is the isotherms are circles

  1. Oct 21, 2007 #1
    1. The problem statement, all variables and given/known data
    Suppose that the isotherms in a region are all concentric spheres centered at the origin. Prove that the energy flux vector field points either toward or away from the origin.


    2. Relevant equations
    J = - k (del)T


    3. The attempt at a solution
    so I know that -(del)T is perpendicular to the surface T, which is constant, but I'm not really sure how to finish off the proof from there...
     
  2. jcsd
  3. Oct 22, 2007 #2

    HallsofIvy

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    You are given that " isotherms in a region are all concentric spheres centered at the origin." Suppose you are at a point (x,y,z) on such a sphere. At what angle does the line from (0,0,0) through (x,y,z) cross the sphere?
     
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