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Electrodynamics and vector calculus question

  1. Oct 23, 2012 #1
    1. The problem statement, all variables and given/known data

    1) The magnetic field everywhere is tangential to the magnetic field lines, [itex]\vec{B}[/itex]=B[[itex]\hat{e}t[/itex]], where [[itex]\hat{e}[/itex]][/t] is the tangential unit vector. We know [itex]\frac{d\hat{e}t}{ds}[/itex]=(1/ρ)[[itex]\hat{e}[/itex]][/n]
    , where ρ is the radius of curvature, s is the distance measured along a field line and [[itex]\hat{e}[/itex]][/n] is the normal unit vector to the field line.

    Show the radius of curvature at any point on a magnetic field line is given by ρ=[itex]\frac{B^3}{abs(\vec{B}X(\vec{B}\bullet\vec{B})\vec{B}) }[/itex]



    2. Relevant equations
    [itex]\vec{B}[/itex]=B[[itex]\hat{e}[/itex]][/t]
    [itex]\frac{d\hat{e}t}{ds}[/itex]=(1/ρ)[[itex]\hat{e}[/itex]][/n]
    ρ=[itex]\frac{B^3}{abs(\vec{B}X(\vec{B}\bullet\vec{B})\vec{B}) }[/itex]


    3. The attempt at a solution
    solved the vector equation, and would then use some form of stokes theorem to equate it and find the value of ρ
     
    Last edited: Oct 23, 2012
  2. jcsd
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