I need help on this vector calculus question...

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AFraggers
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#1
Report Thread starter 4 years ago
#1
Prove that if f is a (smooth) scalar field and G is an irrotational vector field, then
(∇f × G )f is solenoidal

Ive got the identities in front of me but i dont know how to apply them to this question.

Any help will be appreciated
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AFraggers
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(Original post by TeeEm)
Irrotational means curl is zero
solenoidal means divergence is zero

Take the divergence of
(f× G )f
and see what happens
would taking the divergance mean that
(f× G )f =0 and work from there??
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(Original post by TeeEm)
Yes
I do not remember right now all the vector identities, but there would be curlG also appearing in the proof which of course they would be zero
∇ · (fG ) = (∇f) · G + f∇ · G

∇ · (F×G ) = (∇ × F )·G − F· (∇ × G )
Ive gone through all of my identities and picked these 2 out that can solve this. Are these 2 suitable for this question??
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