Читать книгу RF/Microwave Engineering and Applications in Energy Systems - Abdullah Eroglu - Страница 41

The curl of a vector is used to identify how much the vector v curls around a reference point. The curl of a vector is expressed as

(1.62)

Curl can be given in a cylindrical or spherical coordinate system as

(1.63)

and

(1.64)

It is important to note that curl operation on any vector results in another vector. Curl cannot operate on a scalar quantity. In addition, the following two properties follow for curl operation.

(1.65)

(1.66)

Equation (1.65) implies that the curl of a vector does not diverge and the curl of a gradient of a scalar does not exist as expected.