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ELECTROMAGNETIC FIELDS AND THEORY: FIELDS AND VECTORS:
Rotational/Laplacian
1.6.3 Rotational.



(45) Using the concept of the line integral, we can define the component in direction û of the rotational, the following way, (46) This expression tells us: in a particular point the component in direction û of the rotational of function E is equal to the limit of the circuitation of E along the closed path of C (C is in a perpendicular plane to û) divided by area Su (Su is the area enclosed by C) when Su tends to zero. 

Must be stated that the orientation to solve the line integral on curve C, and the positive direction of û; must obey the rule of the right hand (or the screw). This is, if we were to put our or right index finger along C in the positive direction, our right thumb would tell us which was the positive direction in û for the component of the rotational.
Lets
again take as an example, the vector field constituted by the speed of water
that moves throughout a canal. Only that this time, we will suppose that
speed varies lineally with and only with depth; lets suppose that it is zero
in the bottom of the canal and maximum at the surface. Without getting into
much details, lets suppose that the force water can apply to an obstacle is
proportional to the velocity.
Rectangular:





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