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B Field in Semicircle Conductor

  1. Nov 10, 2008 #1
    1. The problem statement, all variables and given/known data

    Basically there is conductor shell which is in the shape of a semicircle. It extends to infinity. (Think of this as like half of a cylindrical conductor shell). The radius of this shell is A, and it carries a total current of X. The shell extends infinitely into the page. What is B-Field (Magnetic Flux Density) at the center of this conductor? I attached image for clarity.

    3. The attempt at a solution

    I think that this problem should be easy to solve. Basically I find the B field due to a long wire of some current, and then change this to make it dB which I would integrate from 0 to pi to find the total B - Field as the superposition of all of the dB elements. Does this sound like the right approach? I know that the field due to a wire is ([tex]\mu[/tex]* I)/(2*[tex]\pi[/tex]*r) where r is the distance from the wire. For dB, this should be ([tex]\mu[/tex]* dI)/(2*[tex]\pi[/tex]*r). I am not quite sure how to set up this integral as I am not quite sure on how to express dI. Any suggestions?

    Sorry for my bad English I do not speak it natively.

    Attached Files:

  2. jcsd
  3. Nov 10, 2008 #2
    Also I am sorry I am not good at the text formatting for the equation. The mu and the pi should not be superscript.
  4. Nov 11, 2008 #3
    So I think I have made progress. I have dB = ([tex]mu[/tex]dI) / (2[tex]pi[/tex]A) and I have dI as Id[tex]phi[/tex]/[tex]pi[/tex]. The B-Field from each dB is in the [tex]\phi[/tex] directions, and as you integrate dB from 0 to [tex]\pi[/tex] to get the whole B-Field the final field will point to the left because everything else will cancel out. The problem is when I take this integral I get 0. Any help? Please.
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