WTW258: LU 3.8: STOKES’S THEOREM Lecture notes

3. 8. Stoke's Theorems
evaluate flux integrals under specific conditions

of field
integrals vector :
line a

"
! Edt must be conservative

2) { f- ( Fcb) ) feria))
'




Fdr
'
-
-




3) ftp.dxeady-DQx-bydA
R

Now JSÉ .dj ( LU 3.7)
↳ surface integral

HE .DE fggdivfdv
143-8 143-9
'




f) curl E. 05=5 Edf -




'
E
S

Right-hand Rule ,
-

$tt•¥F*r¥nTthh - -




i

- "

shows in direction of ñ orientated surface
Thumb -
i. let sbea
arts
'


Curl in direction Ofc
'

let c be the boundary
fingers
'
I
as given by
RHR
-



with direction
I
1 Then
dÉ=jÉjj
.




of surface Crim ) your / E. ,
boundary ,

{ int {
Us
-
orientated surface I int
I

← l
- - - - - - -


-




←
↓ ↓
ñ

Stokes relation → flux int .


+ line int .




overs over a
( Rotation
theorem