- #1

RoyalFlush100

- 56

- 2

## Homework Statement

In the attached image.

## Homework Equations

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

## 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.