We will obtain an expression for the curl in the cartesian coordinates. Let us consider a rectangular contour ABCD in the y-z plane having dimensions . The rectangle is oriented with its edges parallel to the axes and one of the corners is located at . We will calculate the line integral of a vector field along this contour. We assume the field to vary slowly over the length (or the bredth) so that we may retain only the first term in a Taylor expansion in computing the field variation.
. The rectangle is oriented with its edges parallel to the axes and one of the corners is located at 
. We will calculate the line integral of a vector field 
along this contour. We assume the field to vary slowly over the length (or the bredth) so that we may retain only the first term in a Taylor expansion in computing the field variation. 
