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Homework Help: Calculate the x-component of the electric field

  1. Jan 31, 2009 #1

    Positive charge Q is distributed uniformly along the x-axis from x=0 to x=a. A positive point charge q is located on the positive x-axis at x=a+r, a distance r to the right of the end of Q.

    1. The problem statement, all variables and given/known data
    Calculate the x-component of the electric field produced by the charge distribution Q at points on the positive x-axis where x>a (i.e., r>0) in terms of some or all of the variables k, q, Q, a, and r, where k=\\frac{1}{4\\pi\\epsilon_0}.

    3. The attempt at a solution
    I'm having a problem visualizing the distance between the charge and the point. I understand that e=KQ/R^2. However, I have no idea how to get R.
    I would do: (k*dQ)/(r+a-x)...
    (kQ/a) [integral]1/(r+a-x)dx

    But I don't think that looks right. Can anyone give me a few pointers?
    Last edited: Jan 31, 2009
  2. jcsd
  3. Jan 31, 2009 #2


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    Homework Helper

    Looks great! Except you forgot to square the distance (r+a-x) in the integral.
    Also, something must be done about dq to express it in terms of dx so it will be possible to integrate. The charge on a segment dx would be dq = (q/a)dx because the charge per unit length is q/a.
    Finally, the integral is awkward with the r and a in there. You can get it with math techniques of course (let R= r+a-x), but it might be better to think of the distance as R and integrate it from R = a+r to r. Of course dR = dx.
  4. Jan 31, 2009 #3
    Thank you for your help. I needed someone to confirm the distance for me since I was completely lost on that part.
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