1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

E field of a long charged rod

  1. Jun 21, 2017 #1
    1. The problem statement, all variables and given/known data

    A line of charge with a uniform density of 34.2 nC/m lies along the line y = -14.9 cm, between the points with coordinates x = 0 and x = 42.8 cm. Calculate the electric field it creates at the origin, entering first the x component then the y component
    2. Relevant equations

    3. The attempt at a solution
    E_x = 1/(4πε₀) ∫ λ dx * 1/ (Y² + x²) * x/((Y² + x²)^½

    where Y is the vertical distance 14.9 cm.
    λ dx is the charge element dq, 1/ (Y² + x²) is the " 1/r^2 " and x/((Y² + x²)^½ is the geometric factor for the x-component ("sin(α)" ).

    Then the integral gives

    E_x = λ/(8πε₀) ∫ du * 1/ u^(3/2)
    = λ/(8πε₀) [-2/√u]
    = λ/(4πε₀) (1/Y - 1/√(Y² + X²)) [where X = 42.8 cm]

    Along the same line of reasoning we have for the y-component

    E_y = 1/(4πε₀) ∫ λ dx * 1/ (Y² + x²) * Y/((Y² + x²)^½
    = Yλ/(4πε₀) ∫ dx /(Y² + x²)^(3/2)
    = λ/(4πε₀) X/(Y√(Y² + X²))

    When i substituted λ (34.2*10^-9 C/m), X ( 0.428 m ) and Y ( 0.149 m) and ε₀ ( 8.854 10^-12 F/m) to calculate Ex and Ey I got the following two numbers which were incorrect and I am not sure what I am doing wrong

    Ex = 1385N/C
    Ey = 1948N/C
  2. jcsd
  3. Jun 21, 2017 #2


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    Your approach looks good. I have not checked the numerical evaluation. But do you expect both components of E to be positive?
  4. Jun 21, 2017 #3
    I thought so, do the answers look correct besides one or two of them being negative? Did I need to factor in the negative sign on the y coordinate?
  5. Jun 21, 2017 #4


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    Yes. To determine the signs of the components, choose an arbitrary point along the line of charge and treat the point as a positive point charge. Consider the direction of E at the origin produced by the point charge.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted