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Biot-Savart law and Ampere's law

  1. Mar 19, 2014 #1
    1. An electric circuit consists of two long straight sections connecting a loop of radius r. The gap in the loop where the straight sections are connected subtends an angle of theta=60d, as shown in this figure (http://imgur.com/tseDHL6). Determine the magnetic field B at the point P in the centre of the loop, if a current I is flowing through the circuit.

    See the diagram here - http://imgur.com/tseDHL6

    2. Biot-Savart Law



    3. The attempt at a solution - http://imgur.com/QFrlSn7

    I have found the equation relating to the full loop but don't know how to do it for the missing segment.
     

    Attached Files:

  2. jcsd
  3. Mar 19, 2014 #2

    BvU

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    What's wrong with integrating ##d l\over r^2## ?
     
  4. Mar 19, 2014 #3

    maajdl

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    You need to use the Biot-Savart law:

    7463d12e92a79b39f6b3ac7d44dfe1be.png
     
  5. Mar 19, 2014 #4

    BvU

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    Ma is right, but the next step is to convert to integrating ##d l\over r^2## because there is only one component left over; the others cancel.
     
  6. Mar 19, 2014 #5
    [itex]\int rd θ/r^2/[/itex]
     
  7. Mar 21, 2014 #6

    rude man

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    Consider finding the field as though the circular section wasn't there, but the wire was continuous from -infinity to +infinity: B1. Can use ampere's law.

    Then, use Biot-Savart to compute the field due to a short section of wire connecting the loose ends of the loop: B2.

    Then, use Biot-Savart to compute the field due to the loop: B3.

    B = B1 - B2 + B3.
     
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