# Stokes Theorum

• Apr 9th 2008, 06:15 AM
joker_900
Stokes Theorum
I'm not sure if this is the right place to put this?

Show that: curl(fu) = fcurlu + (gradf) x u

By using this in relation to Stoke's theorum, show that for a simple closed curve C,

(Line integral) fdS = -(surface integral) (gradf) x dS

Firstly, is this a typo? I've never heard of a line integral of a function wrt to surface element?

I think Stoke's Theorum is:
(Line integral)(A.dl) = (surface integral)((curlA).dS)

I did the first part fine. I then tried to do

(surface integral) (gradf)xdS = (surface integral) (curl(fdS) - fcurldS)

• Apr 9th 2008, 06:58 AM
Oli
I think it is a typo.

I put fu=fdS.
Stick it into the identity you made up to find a value to curl(fdS).

Re-arrange to find an identity for (gradf)xdS.

Then stick (gradf)xdS into an integral sign, use your second identity and Stokes theorem, and note that curl(dS) = 0 (I think).

Then the solution should pop out.
• Apr 9th 2008, 07:23 AM
Oli
Sorry, I was wrong, it is harder than that.
• Apr 26th 2008, 01:44 AM