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Biot-Savart Law Difficult Problem

  1. Dec 13, 2009 #1
    1. The problem statement, all variables and given/known data
    A short, straight wire segment of length l carries current I and is oriented so that it makes an angle of 30° with the horizontal. Point P is a distance r below the wire segment.

    Which expression below is the best approximation for the magnetic field caused by the wire segment at point P?

    http://online.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys212/oldexams/exam2/fa09/fig15.gif [Broken]

    (a) (μoIlcos30°) / (4π^2)
    (b) (μoIlsin30°) / (4π^2)
    (c) (μoIl) / (4π^2)


    2. Relevant equations

    dB = (μo Idl x r(unit vector)) / (4πr^2)

    3. The attempt at a solution

    It seems I have to integrate to get the answer, however the geometry behind this problem is really confusing me. I believe I have to integrate r from when it touches the begining of the wire segment to the end of the wire segment, however I can't figure out how to manipulate the Biot-Svart law to do that. This is what I have so far:

    (μo I)/(4π) = S sin(theta)ds/r^2 (S = integral :p)

    Now, what do I do with ds?
    Can anyone help me out, help would be greatly appreciated :]!

    Btw π = pi and μo = mu(0), dont know if you can tell.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Dec 13, 2009 #2

    rl.bhat

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    You can keep r fixed. Resolve current element I*l into two components, I*l*cos(theta) and I*l*sin(theta). The point P lies on equatorial line to I*l*cos(theta). So it contributes to magnetic field.
    The point P lies on axial line to I*l*sin(theta). So it does contributes to magnetic field.
     
  4. Dec 13, 2009 #3
    Ok, but then where does the pi^2 term come from in the denominator?
    Also, the answer is (a) which makes since for the cos, but the pi^2 is what I dont get...
     
    Last edited: Dec 13, 2009
  5. Dec 13, 2009 #4

    kuruman

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    There is no integral involved. Just think it through. Which of the three choices gives what you expect when the angle between the wire and the doted line is zero instead of 30o? What about if it is 90o instead of 30o?
     
  6. Dec 13, 2009 #5
    Ok, I know the answer just by looking at the choices. What I am trying to figure out is where part of that answer comes from. I don't see where that pi^2 in the denominator comes from.
     
  7. Dec 13, 2009 #6

    kuruman

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    I don't see where it comes from either. The posted set of possible answers is dimensionally incorrect. Compare with the law of Biot-Savart equation that you posted. The dimensions should be dimensions of μ0 times dimensions of current divided by Length.
     
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