(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A point charge q_1 = 3.45 nC is located on the x-axis at x = 1.90 m, and a second point charge q_2 = -6.95 nC is on the y-axis at y = 1.20 m.

What is the total electric flux due to these two point charges through a spherical surface centered at the origin and with radius r_2 = 1.65 m?

2. Relevant equations

[tex]\Phi=\oint E_\bot dA[/tex]

[tex]A=4\pi r^2[/tex]

[tex]E=\frac{kq}{r^2}[/tex]

3. The attempt at a solution

I started with:

[tex]\Phi=\oint \frac{kq}{r^2} dA[/tex]

[tex]\Phi=A \oint \frac{kq}{r^2} dy[/tex]

[tex]\Phi=4\pi r^2 \oint \frac{kq}{r^2} dy[/tex]

To get r I did:

[tex]x^2+y^2=r^2[/tex]

[tex]x^2+y^2=1.65^2[/tex]

[tex]x=\sqrt{1.65^2-y^2}[/tex]

[tex]r=\sqrt{(\sqrt{1.65^2-y^2})^2+(y-1.20)^2}[/tex]

So:

[tex]\Phi=4\pi r^2 \oint \frac{kq}{1.65^2-y^2+(y-1.20)^2} dy[/tex]

Evaluating this integral from -1.65 to 1.65 gives -1992.28 Nm^2/C

I'm pretty sure I'm setting up this integral completely wrong. Any help on how to do it correctly would be greatly appreciated. Thanks in advanced for your help.

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# Homework Help: Flux due to a point charge

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