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Gradient Field/ Line integral

  1. Nov 21, 2008 #1
    Greetings,
    I'm having trouble deciding what to do, and in what order for this question:

    Suppose F = F( x, y, z ) is a gradient field with F = [tex]\nabla[/tex]f, S is a level surface of f, and C is a curve on S. What is the value of the line integral (over C) of F.dr ?

    I think I'm a little confused since there are no values to work with... I'm assuming the level surface of f is referring to [tex]\nabla[/tex]f, meaning that S is a surface of the gradients?

    Any help would be appreciated, I'm mighty confused. :)
     
  2. jcsd
  3. Nov 21, 2008 #2

    Dick

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    They mean that C is contained in a level surface of f. I.e. f(c) is constant for c in C. Dotting grad(f) with a direction vector tells you how fast f is changing in that direction, doesn't it?
     
  4. Nov 21, 2008 #3
    Ok, someone just explained to me that it is 0, since it's a conservative force.

    I was having trouble interpreting S being a level surface of a gradient field, I'm still trying to figure that part out.
     
  5. Nov 21, 2008 #4

    Dick

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    S is NOT a level surface of the gradient, it's a level surface of f. That's what the question SAID. And there's an even easier reason to say that it's zero (and it's zero even if C isn't closed). What the dot of the gradient vector and the tangent vector to C?
     
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