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Math Help - Cylinder with uniform charge distribution - algebra block!

  1. #1
    Junior Member froodles01's Avatar
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    Cylinder with uniform charge distribution - algebra block!

    I have a cylinder whose radius, r = a & length = L
    charge distribution through cylinder is
    ρ = C/2 * r3
    where r = radial distance in cylindrical coordinates
    C = constant
    show that the average charge density ρbar = Ca3 / 5

    * * * * * * * * * * * * *

    I have average charge = tot. charge / tot. volume

    aAGH! Amendment
    vol =
    ∏r2L

    i.e. ρ / ∏r2L


    = ((C/2)*r3) / ∏r2L


    = Cr3 / 2∏r2L

    = Cr / 2∏L

    = Cr2 / 6.28L

    Now this should make more sense to me but doesn't.
    Last edited by froodles01; April 8th 2013 at 11:44 AM.
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  2. #2
    Junior Member Mathhead200's Avatar
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    Re: Cylinder with uniform charge distribution - algebra block!

    \rho is not the "tot. charge", it is the charge at a single point. It's been a few years since I took calculus (so maybe someone else can correct me if I'm mistaken), but I believe you need to calculate:
    \int_{r=0}^{r=a}{\int_{\theta=0}^{\theta=2\pi}{ \frac{C}{2} r^3 \,d\theta\,dr\ }} = 2\pi \int_0^a{ \frac{C}{2} r^3 \,dr }
    Last edited by Mathhead200; April 8th 2013 at 12:09 PM.
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  3. #3
    Junior Member froodles01's Avatar
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    Re: Cylinder with uniform charge distribution - algebra block!

    Of course.
    All makes perfect sense.
    Cylinder with uniform charge distribution - algebra block!-smiley-lightbulb.jpg
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