# Questions tagged [curl]

In vector calculus, the curl is a vector operator that describes the infinitesimal rotation of a vector field in three-dimensional Euclidean space.

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### Getting different answers for same problem on divergence and curl.

Given that $\vec{a}$ is a constant vector and $\vec{r}$ is a position vector. We are asked to prove the following: $$\nabla\times(\vec{a}\times\vec{r})=2\vec{a}$$ I tried two ways. Could prove it ...
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### Is this possible in vector calculus?

$$(\boldsymbol{\nabla}\alpha)\wedge(\boldsymbol{\nabla} \wedge \boldsymbol{x} )$$ In all the examples in lecture, it has always been a $$\boldsymbol{\nabla}$$ on the left hand side. Does this give ...
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### What would the curl of a longitudinal wave mean?

Is the curl of longitudinal waves even defined? Would the curls of a longitudinal wave and a transverse wave be different in any way?
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### Implying continuity from knowing divergence/curl/laplacian of vector function equals zero

my question comes from a physics question but is math related. In an electrodynamics related question I've seen the following declaration: Link to a screenshot . In the problem the author is using ...
suppose that we have a function $F(x,y)=(\frac{-y}{x^2+y^2},\frac{x}{x^2+y^2})$ if we calculate $curlF$ we understand that $curlF=0$ ( computing $curlF$ is not my question). now the book has written ...