k¥6 Orientation :
. Stokes'
theorem C 16.8 ) walk along C,
head in direction of It
Recall : If E =D , Q , R ) ,then
.no Surface to your left
.
dirt E) =D . E' = Pat Qyt Rz
cancer .one :p:Iaf
P Q R -
= ( Ry - Qz,Pz - Ra
,Qa - Py ) Right - hand rule :
-
Nxt
stokesltheorem
- y .
IfcF. de =ffscurlCEJ.DE/ n
-
NL
E'
vector field NIF points intos surface with the surface .
C boundary curve}compatible -
orientations
÷:÷i¥
Example : E
=Hz
, yz , xy > RelationshipwithGreen'stheorem_
T YS
zaS flat ,
c,
YEZZG /.
,g=zin xy - plane .
it.
--
-
.
l I yiii.-- -
-it÷ 1¥\
-- -
-
-
-
Ky 't^
>
-- -
- -
-
-
-
ffsoxE.ds.fr?dp=ofcEidF=ffsEELkdAQa-Py#
On C : x±yft2-2=4
FdvelocityI
⇒ z=VI dz=O
×= cost ) dx= - sin # Idf µ✓ ONE .D= 2W
y-
- sink ) dy -
- cosltldt
,-
-
-
-- -
- -
-
-
f. E . DF -
-
fccxziyzixys.sdxidy.dz
) ¥,=f ! cost
, B Sint ,sint . cost > . E
-
C- sint , cost , o >
dtffsoxf.Nds-fcf.fdshdfhdf-f.TV#tsinttr3sint-cos
0xFiN=2w+ o ) It =2( normal component of
=O¢ angular velocity)E. F = tangential component of
velocity .
surfaceindepencei-n.tk :
SAE¥7s
ffs,
-
II
Another way to get that IFIZ :
Ii - Ia =ff WE'
. DdsSi - Sz
= fffeo.CO/lE)dV-- OT Forfar any
E'
Divergence theorem
E- solid region enclosed by She Sz.