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Calculate the electric potential and field

  1. Sep 25, 2007 #1
    Here is the question. a hollow, thin walled insulating cylinder of radius b and height h has charge Q uniformly distributed over its surface. Calculate the electric potential and field at all points along the z axis of the tube.

    Outside the tube
    Inside the tube.

    I know how to find the field, its just -"del" V, but my problem is finding V...

    I know you have to take into account the area of the surface and the radius b...

    here is what I have for the integral, which i don't know is right or not. Any help would be outstanding...If someone could help me set it up, I think i could get it from there.

    (Q*k )/h * int (1/R), dz, limit from 0 to h, where R is equal to sqrt(b^2+(p-z)^2)

    after integration

    I get a

    (Q*k )/h ln [(sqrt(b^2+(p-z)^2)+h-p)/(sqrt(b^2+p^2)-p)}


    If I can get it set up, I know I can do the integral. Please help.
     
  2. jcsd
  3. Sep 26, 2007 #2
    I think you should divide your cylinder into elementary circular slabs. Find the expression for the potential at a point above the centre for one slab and integrate it for the entire length of the cylinder. Try and see if this works...
     
    Last edited: Sep 26, 2007
  4. Sep 26, 2007 #3
    I tried it with no success..

    I attempted to treat it like a ring of charge...finding E then integrating to find V.
    Still no success.

    I think I am getting lost in the "point any where on the axis inside or outside the tube".
    any suggestions how to solve this?
     
  5. Sep 27, 2007 #4
    The charge is distributed over the surface, so by Gauss's law the electric field inside the cylinder is zero. Find the value of the surface charge density [itex]\sigma[/itex] using Gauss's law for field outside the cylinder.
    [​IMG]
    The electric potential of a charged ring will be given by:
    [tex]V = \frac{1}{4\pi \epsilon_0}\int_{ring} {dq \over r} = \frac{1}{4\pi \epsilon_0}\left(\frac{1}{\sqrt{a^2 + x^2}}\int dq\right)[/tex]
    a = h in your case.
    Now write dq in terms of [itex]\sigma[/itex] and integrate along the z-axis.
     
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