List questions from curl

Published on 26 Mar 2026 - 7:57

198

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What is $\nabla\wedge\vec{\mathbf F}(x,y,z)$

Published on 09 Apr 2026 - 13:27

36

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Analogue of $(f\cdot\nabla)f=\frac12\nabla|f|^2-f\times\operatorname{curl}f$ in the two-dimensional case

Published on 26 Mar 2026 - 8:02

56

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Show that for all $w$, there is a unique $v$ with $\nabla\cdot v=0$ and $w=\nabla\wedge v$

Published on 26 Mar 2026 - 8:00

78

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Expression for potential vector of a central field

Published on 09 Apr 2026 - 9:29

63

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If $\nabla\cdot u=0$ and $w=\operatorname{curl}u$, then $\int w=0$

Published on 26 Mar 2026 - 8:00

224

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Is the curl of matrix times gradient equal to zero?

Published on 26 Mar 2026 - 8:04

98

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What's the dimension of the image of Curl in ${\rm I\!R}^2$?

Published on 25 Mar 2026 - 14:46

1.4k

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How can I prove that these definitions of curl are equivalent?

Published on 26 Mar 2026 - 9:46

275

Views

Integral definition of curl

Published on 26 Mar 2026 - 9:48

1.9k

Views

Show that $\vec\nabla\times(\vec\nabla\times\vec A )=- \nabla^ 2\vec A + \vec\nabla (\vec\nabla\cdot\vec A )$

Published on 26 Mar 2026 - 8:03

52

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Relation between $|(\nabla\times F)(u)|$ and $|\nabla F(u)|$

Published on 26 Mar 2026 - 7:59

125

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Intuition behind the curl of the curl of a vector field

Published on 26 Mar 2026 - 7:59

280

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Given $G:\mathbb{R}^3\to\mathbb{R}^3$, find $F$ such that $G=\operatorname{curl}(F)$

Published on 26 Mar 2026 - 8:00

327

Views

Potential and Field

Published on 01 May 2026 - 9:29

List Question

Can a vector and its curl be collinear?

What is $\nabla\wedge\vec{\mathbf F}(x,y,z)$

Analogue of $(f\cdot\nabla)f=\frac12\nabla|f|^2-f\times\operatorname{curl}f$ in the two-dimensional case

Show that for all $w$, there is a unique $v$ with $\nabla\cdot v=0$ and $w=\nabla\wedge v$

Expression for potential vector of a central field

If $\nabla\cdot u=0$ and $w=\operatorname{curl}u$, then $\int w=0$

Is the curl of matrix times gradient equal to zero?

What's the dimension of the image of Curl in ${\rm I\!R}^2$?

How can I prove that these definitions of curl are equivalent?

Integral definition of curl

Show that $\vec\nabla\times(\vec\nabla\times\vec A )=- \nabla^ 2\vec A + \vec\nabla (\vec\nabla\cdot\vec A )$

Relation between $|(\nabla\times F)(u)|$ and $|\nabla F(u)|$

Intuition behind the curl of the curl of a vector field

Given $G:\mathbb{R}^3\to\mathbb{R}^3$, find $F$ such that $G=\operatorname{curl}(F)$

Potential and Field

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