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Find Magnetic Flux

  1. Nov 19, 2011 #1
    1. The problem statement, all variables and given/known data

    There is a triangle in the upper right hand corner of the xy plane. You are given θ, and x0.

    Consider an electric field which does not vary with time or the z direction but which varies in the x and y directions according to E=K(x2y, -xy2) throughout the region of interest (aka the triangle), where K is a constant. Show that the magnitude of the magnetic flux [itex]\phi[/itex]B through the triangle is given by
    [itex]\phi[/itex]B = K(3+ tan2θ/{12}) x04tanθt + c, where c is an arbitrary constant and t represents positive time.

    So I know that ∫E. ds = derivative of the magnetic flux.

    So the first line integral over the x axis is zero b/c y = 0.

    For the second second line intergral: dx = 0. So -∫x0y2dy, as y goes from 0 to x0tanθ. This gives us -x0/3 (tan3θ).

    For the last line integral: ∫x2y dx - x∫y2dy. I get ((tanθ)/3)x03 - (x/3)tan3θ. The thought is that for the dx part of this integral we are integrating from 0 to x0. For the dy part, we are going from 0 to tanθ, since the line is y = tanθ.

    So this doesn't seem right. And even if it were, what do I do next. If I integrate to find the magnetic flux, what do I integrate with respect to.
     
    Last edited: Nov 19, 2011
  2. jcsd
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