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Voltage change away from long line of uniform charge

  1. Dec 6, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the voltage change going from 5.0cm to 10.0cm along the radius away from a long line of uniform charge density 5.0 μC/m


    2. Relevant equations

    V = (kq) / r (I believe... I'm very lost)



    3. The attempt at a solution

    ΔV = ∫.05 to .1 2∏rLdL = 2∏r((L^2) / 2 | from .05 to .1) = 2∏r ( .1^2 / 2 - .05^2 / 2) = 0.0235r

    Obviously I'm doing this wrong... I'm struggling with the topic of electricity so I apologize if this is too elementary...
     
  2. jcsd
  3. Dec 6, 2012 #2

    gneill

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    Staff: Mentor

    Hi Pyuruku, Welcome to Physics Forums.

    Why not start with the expression for the electric field strength at a distance r from an infinite line of charge? Then integrate along the path between the two radial distances.
     
  4. Dec 6, 2012 #3
    Would that be [itex]E = \frac{\lambda}{2\pi r\epsilon}[/itex]?

    If so...

    [itex]\frac{\lambda}{2\pi\epsilon}\int_{0.05}^{0.1} \! \frac{dr}{r} = \frac{\lambda}{2\pi\epsilon} ( ln(r) \bigr|_{0.05}^{0.1}) = \frac{\lambda}{2\pi\epsilon}ln(\frac{0.1}{0.05}) = \frac{5.0}{2\pi(8.85x10^{-12}}ln(\frac{0.1}{0.05}) = 6.23x10^{10}[/itex]

    Does that seem correct? I can't check the answer for myself (practice worksheet)
     
  5. Dec 6, 2012 #4

    gneill

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    Staff: Mentor

    Fine, except that the charge density is not 5 coulombs per meter, it's 5 microcoulombs per meter. So your result is off by only six orders of magnitude :smile:
     
  6. Dec 6, 2012 #5
    [itex]\frac{\lambda}{2\pi\epsilon}\int_{0.05}^{0.1} \! \frac{dr}{r} = \frac{\lambda}{2\pi\epsilon} ( ln(r) \bigr|_{0.05}^{0.1}) = \frac{\lambda}{2\pi\epsilon}ln(\frac{0.1}{0.05}) = \frac{5.0x10^{-6}}{2\pi(8.85x10^{-12})}ln(\frac{0.1}{0.05}) = 6.232 x 10^{4} V[/itex]

    (I believe this is now correct)
     
  7. Dec 6, 2012 #6

    gneill

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    Staff: Mentor

    Yup, looks okay now. Be sure to make your final result match the given data in terms of significant figures.
     
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