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Magnetic Field above a Rectangular Circuit

  1. Jan 11, 2013 #1
    1. The problem statement, all variables and given/known data
    On the XY there lies a conducting wire-rectangle with sides parallel to the axis.
    The current is given and constant.
    What is the magnitude of the magnetic field along an axis parallel to the z axis, going through the intersection of the rectangle's diagonals?

    2. Relevant equations
    [tex] \vec { dB } =\frac { I }{ c{ \left| \vec { r } \right| }^{ 3 } } \vec { dl } \times \vec { r } [/tex]

    3. The attempt at a solution
    Due to symmetry, I can expect the field along this axis to be in the z direction. I can integrate along just one of each pair of the circuit's sides and double the result.
    What i'm having trouble with is the cross product in Biot-Savart's Law - it seems to me that the angle [itex] { \theta }_{ \vec { dl } ,\vec { r } } [/itex]changes throughout the integral. If this is true then it seems the calculation of the field is not too easy..
    I'd just like to make sure i'm correct before I get into it - does [itex] { \theta }_{ \vec { dl } ,\vec { r } } [/itex]change throughout the integral?
    Last edited: Jan 11, 2013
  2. jcsd
  3. Jan 11, 2013 #2
    Remind yourself how the calculation goes for an infinite line of current using the Biot-Savart law. The same calculation will apply to each piece of the loop, just with finite integration bounds.
  4. Jan 11, 2013 #3
    I haven't calculated that field with Biot-Savart.. But I presume the implied answer is that the angle changes and this is not negligible.. Right?
  5. Jan 12, 2013 #4
    Yes, the angle changes. It is usually one of the first calculations done in any EM text after introducing the Biot-Savart law. You can take at look at "Introduction to Electrodynamics" by Griffiths, for instance.
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