# Homework Help: Flux Integral

1. Jan 29, 2012

### sandy.bridge

1. The problem statement, all variables and given/known data
Find the flux of $\vec{F}=(x, y, z)$ outward across the sphere $x^2+y^2+z^2=a^2$.

I am able to get it to this point:
$$\int\int_Cadxdy$$ and I then convert it to polar coordinates, and integrate rdr from 0 to a, and theta from zero to 2pi. However, this does not give me the correct result, as the answer is 4a^3*pi, and Im getting a^3*pi.

2. Jan 30, 2012

### tiny-tim

hi sandy.bridge!
it's the surface of a sphere …

what does r have to do with it?

(and why are you integrating? surely you know the surface area of a sphere? )

3. Jan 30, 2012

### sandy.bridge

Okay, well I know that once I get it to this point, it's right:
$$\int\int_CadS=\int\int_Ca(1)dxdy$$

The projection of the sphere on the xy-plane is a circle, no? So why can I not use
$$dxdy=rdrd\theta$$?

4. Jan 30, 2012

### tiny-tim

projection? are you treating F as if it was a parallel field along one of the axes?

in that case, yes, the projection perpendicular to the field would be a circle

but the given F is radial ((x,y,z) = t), and constant in magnitude over the sphere,

so you just need the amount of surface it cuts through, which is 4πa2