ABSTRACT
Let C be a closed, smooth curve bounding a planar surface , placed on the x-y plane. After orienting C counter clockwise, the unit normal n to points in the same direction as k, i.e., n = k, and
Z
n curl vd = Z
k @Q
@x @P @y
k d =
Z
@Q
@x @P @y
d: (D.2)
Consider a cylindrical body of unit height and cross-section , and an auxiliary three-dimensional vector eld w = Qi P j+ 0k. (See Figure D.1.)
Figure D.1: An arbitrary clockwise oriented curve C and its related cylindrical body .
