Results 1 to 4 of 4

Math Help - Electromagnetism: Integral

  1. #1
    Member
    Joined
    Nov 2009
    Posts
    177

    Electromagnetism: Integral

    I had this integral pop up that I can't solve:
    \int_C \frac{x}{(x^2+z^2)^{3/2}}dz

    How do you write a base vector in Latex by the way?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,394
    Thanks
    1845
    Quote Originally Posted by Mondreus View Post
    I had this integral pop up that I can't solve:
    \int_C \frac{x}{(x^2+z^2)^{3/2}}dz

    How do you write a base vector in Latex by the way?
    I don't know what you mean by a "base" vector but you can do vectors by \vec{v} : \vec{v}

    That's a contour integral isn't it? I had started doing the integral with the substitution z= x tan(\theta) before I recognized that! The integrand is analytic everywhere except at z= ix and z= -ix which are poles. If the contour does not inclose either of those, then the integral is 0. If it does inclose either or both, then you can look at its residues at those points.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2009
    Posts
    177
    Sorry I meant basis vector. It's a line integral where I'm supposed to calculate the electric field at x\bold{e_x} due to a constant charge density \rho_\ell along the line C: -b \leq z \leq a.

    The original integral looks like this:
    \bold{E} = \int_C \frac{1}{4\pi \epsilon_0}\frac{x\bold{e_x}-z\bold{e_z}}{(x^2+z^2)^{3/2}}\rho_\ell dz
    Last edited by Mondreus; March 27th 2010 at 08:30 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Nov 2009
    Posts
    177
    This is supposely a very common integral since it's in our formula collection, but I don't know how to solve it.
    The answer is:
    \frac{z}{x^2(x^2+z^2)^{1/2}}
    Last edited by Mondreus; March 28th 2010 at 03:27 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: March 25th 2011, 12:12 PM
  2. Replies: 1
    Last Post: June 2nd 2010, 03:25 AM
  3. Replies: 0
    Last Post: September 10th 2008, 08:53 PM
  4. good electromagnetism notes
    Posted in the Math Forum
    Replies: 6
    Last Post: June 20th 2008, 01:17 PM
  5. Physics electromagnetism, please help
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: June 4th 2008, 04:50 AM

Search Tags


/mathhelpforum @mathhelpforum