Cross product magnitude

In summary, the cross product of y and x, in the context of an infinite wire generating a field at point P along the x-axis, is out of the page with a magnitude of yx sin(φ), where φ is the angle between them. In this scenario, φ is equal to 90 degrees.
  • #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.
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  • #2
Yes your angle would be 90 degrees. In terms of vectors

I = y k

x = x i

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