Hi PF-members.(adsbygoogle = window.adsbygoogle || []).push({});

My intuition tells me that: Given a divergence free vector field [itex] \mathbf{F} [/itex], then the curl of the field will be perpendicular to field.

But I'm having a hard time proving this to my self.

I'know that : [itex] \nabla\cdot\mathbf{F} = 0 \hspace{3mm} \Rightarrow \hspace{3mm} \exists\mathbf{A}: \mathbf{F} = \nabla\times\mathbf{A} [/itex]

Therefore : [itex] \mathbf{F}\cdot(\nabla\times\mathbf{F}) = 0 \hspace{3mm} \Rightarrow \hspace{3mm} [\nabla\times\mathbf{A}]\cdot[\nabla\times(\nabla\times\mathbf{A})] = 0 [/itex]

But I can't prove that this actually equals zero... Please help!!

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Is the curl of a div. free vector field perpendicular to the field?

Loading...

Similar Threads - curl free vector | Date |
---|---|

A Angular Moment Operator Vector Identity Question | Feb 10, 2018 |

A Impossible Curl of a Vector Field | Mar 21, 2017 |

I What will be the 4th axis of a 3d curl? | Oct 15, 2016 |

I Intuitively understand the curl formula? | Aug 19, 2016 |

Divergent free question | Nov 24, 2013 |

**Physics Forums - The Fusion of Science and Community**