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!

Integration involving a physics problem.

  1. May 24, 2013 #1
    1. The problem statement, all variables and given/known data
    Hello all! I'm currently trying to work a problem for my Physics 2 class (for engineering and science majors). The example problem deals with "Field of a charged line segment." I conceptually understand the problem, but I am having trouble with the details involving the integration.

    The problem: "Positive charge Q is distributed uniformly along the y-axis between y= -a and y= +a. Find the electric field at point P on the x-axis at a distance x from the origin."

    I know that [itex]\stackrel{\rightarrow}{E}[/itex]= [itex]\frac{kQ}{r^{2}}[/itex]




    therfore; dE=(k)([itex]\frac{dQ}{r^{2}}[/itex])= (k)([itex]\frac{Q}{2a}[/itex])([itex]\frac{dy}{x^{2}+y^{2}}[/itex])





    simplifying and factoring out constants gives:


    Here is where my problem comes in.... I don't know how to integrate this. The book says "a table of integrals will help."

    The solution is given to be:


    2. Relevant equations

    3. The attempt at a solution

    I do have the latest CRC book which has integral tables in it. I looked at the general forms containing: c2+x2. The one it looked the closest to was: [itex]\frac{dx}{(c^{2}+x^{2})^{n}}[/itex]. But I'm not sure... I believe the x's may be treated as constants since I'm integrating with respect to y, but I'm not exactly sure how to go about working it. I looked a U-substitution but I get bogged down and confused by the fact that I am integrating a function that includes two variables. Any help would greatly be appreciated. Again, I understand the concept, but I'm getting confused on the calculus part of it (the integration/last step). Thank you.
  2. jcsd
  3. May 24, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    It looks like a trig substitution might work. Try ##y = x\tan\theta,\, dy=x\sec^2\theta\,d\theta,\,
    \sqrt{x^2+y^2}=x\sec\theta## and see if that does anything for you.
  4. May 24, 2013 #3


    User Avatar

    Staff: Mentor

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted