The Curl in Curvilinear Coordinates

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Section 12.11 The Curl in Curvilinear Coordinates

Just as with the divergence, similar computations to those in rectangular coordinates can be done using boxes adapted to other coordinate systems. Not surprisingly, this introduces some additional factors of $r$ or $s$ (and $\sin\theta$). You can find expressions for curl in both cylindrical and spherical coordinates in Appendix B.1.

Such formulas for vector derivatives in rectangular, cylindrical, and spherical coordinates, are sufficiently important to the study of electromagnetism that they can, for instance, be found on the inside front cover of Griffiths' textbook, Introduction to Electrodynamics.