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

In the attached image.

2. Relevant equations

Gradient(x, y, z) * <f, g, h> = <fx, gy, hz>

3. The attempt at a solution

Because the cylinder's not capped, I know that all the flux will be in the radial direction. So, I can find a normal vector by finding the gradient of the cylinder:n= <2x, 0, 2z>/(2sqrt(x^2+z^2)) = <x, 0, z>/sqrt(x^2+z^2)

Now, I want to put this in terms of t (the angle) and h (y):

r(t, y) = <acos(t), h, asin(t)>

Where: y: (-2, 2) and t: [0, 2pi)

Now we can rewrite the integrand:

<acos(t)/sqrt(a), 0, asin(t)/sqrt(a)> * <acos(t)/sqrt(a), 0, asin(t)/sqrt(a)> dS

=(a^2cos^2(t) + a^2sin^2(t))/a dS

=a dS

Now, the only thing I'm confused by (assuming everything else is right), is what to do with dS. I know it needs to be put in terms of dt and dh (where I already have the limits of integration), but I am unsure of how to perform this conversion.

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# Homework Help: Flux Through a Cylinder

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