Next: Example
Up: Vector integral calculus
Previous: Example
Consider a closed contour
spanned by an open regular surface , as shown in Fig. A.3. The positive direction along the path
is linked to the positive direction for the unit normal
at any point on by the socalled corkscrew rule: if the handle of a righthanded corkscrew were to rotate in the positive direction along , then the screw would enter the cork in the positive
direction. Another way of linking the positive unit vector
along the path
to the positive
on
is by the socalled right hand rule: hold the thumb, index and middle fingers of your right hand at right angles to one another, as shown in Fig. ; if the index finger rotates to move parallel to the middle finger, and if in so doing its tip follows the contour
in the positive direction, then the thumb is pointed in the
direction.
Figure A.3:
Geometry for Stokes' theorem.

Stokes' theorem equates the flux of the curl of a vector field
across the open surface
to the integral of
along the closed path
which bounds :

(2.16) 
Next: Example
Up: Vector integral calculus
Previous: Example
19990701