Now were going to do Del crossed with the vector field. The first form uses the curl of the vector field and is C F dr D curl F k dA C F d r D curl F k d A. Surface S With Closed Boundary S F Could Be The E Or B Fields Again N Is The Unit Normal The Curl Of A Vector Field Equations Vector Calculus Grid Vector The curl of a vector field is the mathematical operation whose answer gives us an idea about the circulation of that field at a given point. Curl of a vector field . The curl of a vector field denoted curlF or del xF the notation used in this work is defined as the vector field having magnitude equal to the maximum circulation at each point and to be oriented perpendicularly to this plane of circulation for each point. Imagine the vectors in a vector field as representing the current of a river. Where k k is the standard unit vector in the positive z z direction. The second operation on a vector field that we examine is the curl which measures the extent of rotation o...