• Electromagnetics I
  • Ch 10: Appendices
  • Loc 10.5
  • Electromagnetics I
  • Ch 10
  • Loc 10.5

Mathematical Formulas - Vector Operators

This section contains a summary of vector operators expressed in each of the three major coordinate systems:

  • Cartesian (,,)
  • cylindrical (,,)
  • spherical (,,)

Associated basis vectors are identified using a caret (

) over the symbol. The vector operand

is expressed in terms of components in the basis directions as follows:

  • Cartesian:
  • cylindrical:
  • spherical:

Gradient

Gradient in Cartesian coordinates:

(10.5.1)

Gradient in cylindrical coordinates:

(10.5.2)

Gradient in spherical coordinates:

(10.5.3)

Divergence

Divergence in Cartesian coordinates:

(10.5.4)

Divergence in cylindrical coordinates:

Divergence in spherical coordinates:

Curl

Curl in Cartesian coordinates:

Curl in cylindrical coordinates:

Curl in spherical coordinates:

Laplacian

Laplacian in Cartesian coordinates:

(10.5.5)

Laplacian in cylindrical coordinates:

(10.5.6)

Laplacian in spherical coordinates:

 

Ellingson, Steven W. (2018) Electromagnetics, Vol. 1. Blacksburg, VA: VT Publishing. https://doi.org/10.21061/electromagnetics-vol-1 CC BY-SA 4.0

 
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