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How can gradient be zero if its a normal vector?

  1. Jul 5, 2009 #1
    Physical interpretation of gradient says that its a vector normal to equipotential (or level) surface [tex]\phi(x,y,z) = 0[/tex]
    but what about other surfaces, say the surface which are not equipotential?
    This is my first question.

    ok, now
    as [tex]grad \phi[/tex] is a vector normal to surface it cant be 0. Because that would mean that surface have no normal vector, or say a normal vector of indeterminate direction (as 0 vector is of indeterminate direction). how can it be possible that a surface has no normal vector, more specifically a 0 vector as its normal vector?
    But I have seen many examples in which [tex]grad \phi[/tex] is 0.
    So doesn't that contradicts the assumption that [tex]grad \phi[/tex] is a normal vector?
  2. jcsd
  3. Jul 5, 2009 #2
    Equipotential surfaces are defined by the eqution:
    [tex]\phi(x,y,z) = C[/tex] (C is constant)
    But consider the contant potential field ,say [tex]\phi(x,y,z) = 2[/tex],can you find a unique equipotential surface for it?
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