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Magnet field of a solenoid

  1. May 31, 2012 #1
    1. The problem statement, all variables and given/known data
    Attached file shows the problem statement.

    3. The attempt at a solution
    I can do this problem easily. Problem is that there's just one step in my book's derivation that I don't understand. It sets ρ equal to the hypotenuse in the triangle and then says that:

    dl = ρ/sinθ dθ (1)

    For some reason I can't get this result. If we look at the cosine of θ then:
    cosθ = l/ρ
    =>
    l = ρcosθ
    =>
    dl/dθ = -ρsinθ
    =>dl = -ρsinθdθ

    Incosistent with (1). What am I doing wrong?
     
  2. jcsd
  3. May 31, 2012 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    hi zezima1! :smile:
    ah, but ρ isn't constant, h is …

    differentiate cotθ = l/h :wink:
     
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