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Velocity of charge orbiting infinite line of negative charg

  1. Sep 7, 2016 #1
    Sorry I couldn't finish the title. I ran out of space. Anyway, here's the question:

    A uniformly charged, infinitely long line of negative charge has a linear charge density of -λ and is located on the z axis. A small positively charged particle that has a mass m and a charge q is in circular orbit of radius R in the xy plane centered on the line of charge. (Use the following as necessary: k, q, m, R, and λ.)

    (a) Derive an expression for the speed of the particle.

    (b) Obtain an expression for the period of the particle's orbit.

    Relevant Equations:

    E = λ/(2πrε0) for an infinite line of charge. In the case of this problem I used -λ instead of just λ.

    F = Eq = mv2/r

    T = (2π)/ω = (2π)/(v/r) = (2πr)/v



    I tried using the first equation I listed above in order to derive E. This led to:

    E = -λ/(2πRε0)
    F = Eq = mv2/R , so this leads to:

    F = -λq/(2πRε0) = mv2/R

    solving algebraically for v yields:

    v = sqrt(-λq/(2πmε0)) = sqrt(-λkq / (2m) )

    Here I thought I had derived v, but webassign said that this was wrong. I tried taking out the negative sign since having an imaginary velocity makes no sense, but it was still wrong. I can't do (b) until I solve (a). Please help.
     
  2. jcsd
  3. Sep 7, 2016 #2

    Simon Bridge

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    you expression for centripetal acceleratio should have a minus sign, since it points inwards.
    remember: vectors.

    note: $$\frac{1}{2\pi\epsilon_0} = 2k$$
     
  4. Sep 7, 2016 #3
    Thanks! I solved it now.
     
  5. Sep 8, 2016 #4

    Simon Bridge

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    Well done.
     
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