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Biot and Savart Integral using Vectors

  1. Jul 17, 2015 #1
    How would I go about setting up a Biot and Savart Integral using Vectors?

    Here is an exercise we had in class:
    I tried to set it up using Vectors, and figured dl to be <-L,L> and r to be <½L, -½L>. After the cross product, I am not sure how to handle the integration, since r can vary. Would it be a double integral, or am I overthinking it?

    The instructor gave me the answer, and I have been trying to figure out a way to use Vectors to solve it, since I am fairly comfortable with them. Any help would be appreciated!
     
  2. jcsd
  3. Jul 17, 2015 #2
    Not a double integral. The sum of two line integrals.
     
  4. Jul 19, 2015 #3
    Alright, so I split it up into two parts, r1 and r2.

    Both have a magnitude of L / sqrt(2).
    r1 has a direction vector of <√2 / 2, √2 / 2, 0>,
    r2 has a direction vector of <√2 / 2, -√2 / 2, 0>.

    Then, dl1 is <-L, 0, 0> and dl2 is <0, L, 0>.

    Both cross products are L * (√2 / 2) in (-k) direction.

    Do I integrate from L to 0 for the horizontal part, and 0 to L for the vertical part?

    The answer he supplied is (μ0 / 4π) * (I * (√2 / L)) in (-k) direction, but I am not getting the same answer.
     
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