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There is a triangle in the upper right hand corner of the xy plane. You are given θ, and x_{0}.

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(x^{2}y, -xy^{2}) 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+ tan^{2}θ/{12}) x_{0}^{4}tanθt + 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 -∫x_{0}y^{2}dy, as y goes from 0 to x_{0}tanθ. This gives us -x_{0}/3 (tan^{3}θ).

For the last line integral: ∫x^{2}y dx - x∫y^{2}dy. I get ((tanθ)/3)x_{0}^{3}- (x/3)tan^{3}θ. The thought is that for the dx part of this integral we are integrating from 0 to x_{0}. 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.

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# Homework Help: Find Magnetic Flux

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