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Vector Field everywhere parallel to

  1. Feb 21, 2010 #1
    1. The problem statement, all variables and given/known data

    The Vector field B(x) is everywhere parallel to the normals to a family of surfaces f(x) = constant. Show that

    [tex] B \bullet ( \nabla \times B ) = 0[/tex]

    2. Relevant equations

    3. The attempt at a solution

    Clearly B(x) is orthogonal to the tangent planes at each points on any of the surfaces. So if curl of B(x) was in the direction of the the tangent planes of the family of surfaces, the result would follow. but I dont see :S

    Thanks for any help :)
  2. jcsd
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