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Use of Biot-Savart Law for Square Loop

  1. May 12, 2012 #1
    Hey,

    My question concerns the integration of the biot savart law of a differential magnetic field element to find the magnetic field at the center of a square loop. The question is part (c) (using info from (b)) of the image below:

    electromagnetism3.png

    I want to check if what I did was right, but what I did was to integrate the differential magnetic field element separately for each of the 4 sides, using the fact the angle varies between 45 and -45 degrees for each side. So basically I multiplied the integral of the differential magnetic field by 4 and integrated across the limits of 45 degrees and -45 degrees to attain:

    [tex]B=\frac{\sqrt{2}\mu _{0}I}{\pi a}[/tex]

    Is this right?

    Many thanks for any help/comments!
    SK
     
  2. jcsd
  3. May 12, 2012 #2

    tiny-tim

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    Hey Sekonda! :wink:

    Yup, looks ok. :smile:

    (btw, [3] is the differential form of the usual (µo/4πa)(sinθ1 - sinθ2), = µo/2πa for an infinite straight wire :wink:)
     
  4. May 12, 2012 #3
    Cheers thanks, and so it is; I always miss the ''intricate'' relations between scenario's in electromagnetism.

    Thanks again,
    SK
     
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