Electric flow

  1. http://t2.technion.ac.il/~snoop/Q.gif
    Q is at one point
    R is the radius of this cylinder, it's height is 2h
    the cylinder is without the bases.
    how can i calculate the electric flow through it?
    the final answer is Q/[epsilon0*sqrt(1+R^2/h^2)]
     
    Last edited: Oct 30, 2004
  2. jcsd
  3. Tide

    Tide 3,143
    Science Advisor
    Homework Helper

    Why don't you try calculating the flux through the flat top and bottom of the cylinder? Then you could subtract it from the total flux given by Gauss' Law.
     
  4. where is my mistake:

    we take ball with radius sqrt(R^2+h^2) and look on the rounded bases: the area of this ball inside the cylinder.

    flow through bases / flow through all ball = bases area / all ball area

    gaus: all ball flow is Q/epsilon0

    all ball area is 4pi(R^2+h^2)

    base area = circumference of projection of the base on y=2h * height of base
    =(2pi*R)*[sqrt(R^2+h^2)-h]

    2 bases area = base area * 2 = 4pi*R[sqrt(R^2+h^2)-h]

    flow through bases=bases area*flow through all ball / all ball area=
    = 4pi(R^2+h^2)Q/(epsilon0 4pi*R[sqrt(R^2+h^2)-h])=
    Q(R^2+h^2)/(epsilon0 *R[sqrt(R^2+h^2)-h])

    now that's not like that right answer, coz we can assign r=1 h=1
    my answer qives 2/(sqrt(2)-1) * Q/epsilon0 = 2(1+sqrt(2)) * Q/epsilon0
    right answer gives 1/sqrt(2) * Q/epsilon0
     
    Last edited: Oct 30, 2004
  5. we get too hard integral at that case:
    S r^2/(r^2+h^2)^(3/2) dr
    or something like that
     
    Last edited: Oct 30, 2004
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