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zhiyuan3yu5

  • 3 years ago

a plate occupies an elliptic region G: x^2/4 + y^2/9 less than or equal to 1. the surface density of electric charge is G(x,y)=sin^5(xy^2). Find the total electric charge Q.

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  1. zhiyuan3yu5
    • 3 years ago
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    |dw:1353266741808:dw|

  2. henpen
    • 3 years ago
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    x^2/4 + y^2/4<=1 That's a circle, not an ellipse

  3. zhiyuan3yu5
    • 3 years ago
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    o oops it's supposed to be y^2/9

  4. Rezz5
    • 3 years ago
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    are you trying to work ou the area of the plate?

  5. zhiyuan3yu5
    • 3 years ago
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    so how do i apply G(x,y)=sin^5(xy^2) ?

  6. henpen
    • 3 years ago
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    Apologies, I misread the boundary function as the density function. \[\large \int\limits_{x=-2}^{x=2}\int\limits_{y=0}^{y=\sqrt{9(1-\frac{x^2}{4})}}\sin^5(xy^2)dydx+\int\limits_{x=-2}^{x=2}\int\limits_{y=-\sqrt{9(1-\frac{x^2}{4}}}^{y=0}\sin^5(xy^2)dxdy\] I'm less sure about this one

  7. henpen
    • 3 years ago
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    Swap the last dxdy for dydx

  8. henpen
    • 3 years ago
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    I think that's OK, what do you think about the x-bounds?

  9. zhiyuan3yu5
    • 3 years ago
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    i think this is correct. thank you!

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