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Homework Help: Conduing elipsical wire in a magnetic field

  1. Mar 14, 2008 #1
    conduing elipsical wire in a magnetic field :)

    1. The problem statement, all variables and given/known data

    An elipse shaped wire with a major axis a and minor axis b conducts a current I , and is set on the XY plane.
    A const. magnetic field B is present, towards the Y axis (pointing "up")

    I need to caculate the moment of force acting upon the elipse.

    2. Relevant equations

    1) F = ILBsin(alpha) (force acting upon a conduing wire in the presence of a magnetic field)

    2) N = r X F (moment of force)

    3. The attempt at a solution

    The force acts towards "inside the page" - spinning the elipse.
    Since the force acting upon each element of the eplise is different (and depends on the angle between the wire and the magnetic field), I figured I should somehow sum the cross-products (rXF) of each element throughout the elipse, with integration on "theta", which is the angle between the radius and the major axis as I progress...
    The problem I encountred was calculating this angle, of each element, and express it using "theta".
    I have reached a very far-fetched expression, using some Wiki help and some friends help, and reached a pretty complex relation. I shall reffer to the wanted angle (again, the angle between the wire element and the magnetic field, which points up) as "alpha":

    note: e = c/a
    alpha = 90 + "theta" - arctg ((e)^2sin(2theta)/sqrt(1-(e^2)(cos(theta))^2).

    No way this thing enters my intergration :).

    I'm really lost... maybe there's a much easier way? some symmetry I cannot see?

    Thank you very much for reading! I'm sorry if it's messy.... but the question I hope is coherent.

  2. jcsd
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