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

Use Stokes Theorem to compute

[tex]\int_{L}^{} y dx + z dy + x dx[/tex]

where L is the circle x^{2}+ y^{2}+ z^{2}= a^{2}, x + y + z = 0

3. The attempt at a solution

I feel like this problem shouldn't be that hard but I can't get the right answer: (pi)a^{2}/3.

I calculated the curl of F as: -(i + j + k)

and the normal vector as:

[tex]\frac{i + j + k}{\sqrt{3}}[/tex]

So:

[tex]\int_{L}^{} y dx + z dy + x dx = \int \int -(i + j + k) \cdot (\frac{i + j + k}{\sqrt{3}}) ds = -\frac{3}{\sqrt{3}} \int \int ds[/tex]

Here's where I'm stuck. I think the integral should just be the area of the circle (pi*a^{2}) but maybe I'm thinking about it wrong. Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Stokes Theorem

**Physics Forums | Science Articles, Homework Help, Discussion**