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Cross product magnitude

  1. Feb 4, 2015 #1
    If I choose the positive y direction to be vertically downwards, and the positive x direction to be to the right, and take the cross product y cross x, then the direction of the resultant is out of the page (if I draw x and y as lines on paper). The magnitude is yx sin(φ), where φ is the angle between them.
    I do understand that, but it's been put in a context where I can't find φ. An infinite wire carrying current I in the positive y direction generates a field at P, which is a distance a along the x axis. I want to cross y, which is infinite, with x, which is finite but changing. x is the position vector of point P, relative to the infinite wire. I don't know what to use as the angle between them. Is φ=90°? Is sinφ x/(x2+y2)1/2, by Pythagoras theorem and the geometry of the situation, or should that be a y on the numerator?

    My textbook explains this poorly, and I think it's still more maths than physics, but I'm sorry if I posted in the wrong place.
  2. jcsd
  3. Feb 4, 2015 #2


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    Homework Helper

    Yes your angle would be 90 degrees. In terms of vectors

    I = y k

    x = x i
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