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Magnetic field from a conductor using Law of Biot-Savart

  1. Jun 1, 2014 #1
    1. The problem statement, all variables and given/known data
    An electric current I flows in a straight conductor of length L. Use the law of
    Biot-Savart to find the magnetic field at a point lying on an axis going through the
    centre of the conductor and perpendicular to the conductor.

    2. Relevant equations
    Law of Biot-Savart: [itex] B=\frac{\mu _{0}}{4\pi }\int \frac{Idl \times \widehat{r}}{r^{2}} [/itex]


    3. The attempt at a solution
    Ok so this will be quite hard to explain my attempt so far without my diagram but here goes:
    [itex] r=\sqrt{x^{2} + y^{2}} [/itex] where y is the height up the conductor (the 'position' of dl), x is the distance from the conductor along the x-axis

    Let L go from -a to +a,
    then [itex] B=\frac{I \mu _{0}}{4\pi }\int^{+a}_{-a} \frac{dl \times \widehat{r}}{(x^{2} + y^{2})^{3/2}} [/itex]
    which is the same as
    [itex] B=\frac{I \mu _{0}}{4\pi }\int^{2a}_{0} \frac{dl \times \widehat{r}}{(x^{2} + y^{2})^{3/2}} [/itex]

    Then it's the whole dl x r bit that gets me. I'm sure I have to change this into dy, and then Iknow how to integrate that.

    but I can't figure out how to bring dy into the equation :(
     
  2. jcsd
  3. Jun 1, 2014 #2

    George Jones

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    Where is the origin of your ##\left( x,y,z \right)## coordinates?
     
    Last edited: Jun 1, 2014
  4. Jun 1, 2014 #3
    Isn't dl = jdy?
     
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