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Magnetic field at a point due to a curved wire.

  1. Apr 20, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the magnetic field at the point (the big dot in the picture)
    xhDXl.png
    The curve is supposed to be a quarter circle and both wires are parallel and radius is R
    the wires are infinitely long


    2. Relevant equations
    Biot-Savart Law d[itex]\vec{\textit{B}}[/itex]=[itex]\frac{\mu_{0}}{4\pi}[/itex][itex]\frac{Id\vec{l} \times \hat{r}}{\vec{r}^{2}}[/itex]

    3. The attempt at a solution
    I know that the magnetic field is inward due to both field of the wire and field of the quarter circle the quarter circles magnetic field is [itex]\frac{\mu_{0}\textit{I}}{8R}[/itex] and the piece of wire in line with the point does not affect the magnetic field. How would you find the magnetic field from the other wire on the point? Would it be just taking into account the wire therefore being [itex]\frac{\mu_{0}\textit{I}}{2\pi R}[/itex]? or would you have to use amperes law somehow like you do in a hairpin loop
     
    Last edited: Apr 20, 2012
  2. jcsd
  3. Apr 20, 2012 #2
    This seems like a very contrived problem to me. I guess if you take the problem at it's word then yeah, just add in the the infinite wire contribution. Make sure you get the right vector directions and all though.
     
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