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Homework Help: Force Between Cylindrical Capacitor Plates

  1. Sep 15, 2008 #1
    1. The problem statement, all variables and given/known data

    Capacitor plates are length L with radii a,b a<b are co-axial and intially covering eachother with line charge density of the inner plate Q/L.

    determine the force between plates as the inner plate is partially withdrawn along the axis.

    i) if cylinders charged to voltage V and then discnnected
    ii) if cylinders remain connected and maintained at voltage V

    2. Relevant equations

    u=(1/2)cv^2=(1/2)qv F=-du/dL

    voltage between plates = Qln(b/a)/2Lpi*e0

    capacitance between plates = 2Lpi*e0/ln(b/a)


    3. The attempt at a solution

    using partial derivitives. for

    i) hold q constant differentiate for V

    du=(1/2)qdv

    -du/dl=(-1/2)Q(d/dL)(Qln(b/a)/2Lpi*e0)

    = (1/4)(Q^2)ln(b/a)/2(L^2)pi*e0)

    and is directed same direction to one being removed..


    using partial derivitives. for

    i) hold v constant differentiate for q

    du=(1/2)(v^2)dc

    -du/dl=(-1/2)(v^2)(d/dL)(2Lpi*e0/ln(b/a))

    = (-1/2)(v^2)(2pi*e0/ln(b/a))


    and is directed in opposite direction to one being removed



    Are this working OK?

    Many thanks!
     
  2. jcsd
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