Editing Curl (mathematics) (section)

=== Example 2 ===
{{Multiple image
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| image1            = Uniform curl.svg
| image2            = Curl of uniform curl.png
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| footer            = Vector field {{math|1='''F'''(''x'',''y'')=[''y'',−''x'']}} (left) and its curl (right).
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The [[vector field]]
<math display="block">\mathbf{F}(x,y,z)=y\boldsymbol{\hat{\imath}}-x\boldsymbol{\hat{\jmath}}</math>
can be decomposed as
<math display="block">F_x =y, F_y = -x, F_z =0.</math>

Upon visual inspection, the field can be described as "rotating". If the vectors of the field were to represent a linear [[force]] acting on objects present at that point, and an object were to be placed inside the field, the object would start to rotate clockwise around itself. This is true regardless of where the object is placed.

Calculating the curl:
<math display="block">\nabla \times \mathbf{F} =0\boldsymbol{\hat{\imath}}+0\boldsymbol{\hat{\jmath}}+ \left({\frac{\partial}{\partial x}}(-x) -{\frac{\partial}{\partial y}} y\right)\boldsymbol{\hat{k}}=-2\boldsymbol{\hat{k}}
</math>

The resulting vector field describing the curl would at all points be pointing in the negative {{Math|''z''}} direction. The results of this equation align with what could have been predicted using the [[Right-hand rule#A rotating body|right-hand rule]] using a [[Cartesian coordinate system#In three dimensions|right-handed coordinate system]]. Being a uniform vector field, the object described before would have the same rotational intensity regardless of where it was placed.

{{clear}}