MathLiveCurl of a vector field
Gives the curl of a three-dimensional vector field, a vector measuring the local rotation of the field at each point. It is used in electromagnetism, fluid dynamics and vector calculus wherever circulation per unit area is needed.
\nabla \times \boldsymbol{F} = \begin{pmatrix} \frac{\partial F_z}{\partial y} - \frac{\partial F_y}{\partial z} \\ \frac{\partial F_x}{\partial z} - \frac{\partial F_z}{\partial x} \\ \frac{\partial F_y}{\partial x} - \frac{\partial F_x}{\partial y} \end{pmatrix}What the symbols mean
| vector field with components F_x, F_y, F_z | |
| curl operator (del cross product) | |
| Cartesian components of the vector field | |
| Cartesian coordinates |
About this formula
- FieldMathematics
- TopicVector calculus
- LevelUniversity
- Also calledcurl, rotation of a vector field, curl operator, nabla cross F, curl in Cartesian coordinates, vector field rotation formula
- SourceWikidata Q206310
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