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## Stokes' theorem

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 so-called corkscrew rule: if the handle of a right-handed 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 so-called 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.

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

1999-07-01