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Homework Help: Magnetic field and formulating an equation for a particle

  1. Feb 15, 2012 #1
    1. The problem statement, all variables and given/known data
    Consider a general point on the line joining the two wires and a distance d
    away from the mid-point O.
    By summing the magnetic field due to currents of magnitude i flowing in both the wires in the senses you found in (c), show that, on the line joining the two wires, the magnetic field strength is given by:

    B= μ0iD / π(D2 −d2)

    2. Relevant equations
    B= μ0 i / π r

    3. The attempt at a solution
    My diagram is attached.

    Remembering that B(r) = μ0i / 2π r

    From the diagram above then the position r of the arbitrary particle A from the right hand conductor would be the distance to the mid point D plus the distance to A and could be expressed as (D+d). whereas its position from the left hand conductor is the distance to the mid point minus the distance to A as (D - d). The vector cross product of the fields since they point in the same direction and at right angles to O would mean that the resultant is the product. Putting this together then r = (D + d)(D - d) which then equates to r = (D2 - d2).

    The distance between the two conductors is then (D+D) = 2D. Putting this together then the distance r can be expressed as the ratio: r = (D2 - d2) / 2D.

    I have a way to substitute r into the original equation... does this make sense?
     

    Attached Files:

  2. jcsd
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