Section 2.2 · Examples · 5 of 5
Example 2.2.5: Divergence of a curl
Divergence of a curl
#Find for any given vector field .
Adapted from: D. K. Cheng, Field and Wave Electromagnetics, 2nd ed., Problem P.2-38.
Taking the divergence (2.2.6) of the curl (2.2.8),
where in the second line the six terms have been regrouped by component. With continuous second derivatives each bracket is zero:
Answer
The curl of any vector field is solenoidal: a field of vortex sources has no flux sources.