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Vector calculus

  • #1
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is it true that if [itex]\nabla \cdot \vec{F}=0 , \nabla \times \vec{F}=0[/itex] then [itex]\vec{F}=0[/itex]???
 

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  • #2
robphy
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is it true that if [itex]\nabla \cdot \vec{F}=0 , \nabla \times \vec{F}=0[/itex] then [itex]\vec{F}=0[/itex]???
Suppose [tex]\vec F=3\hat x \ldots[/tex]
 
  • #3
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the divergence of 3x is 3 not 0 though?
 
  • #4
robphy
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the divergence of 3x is 3 not 0 though?
By [tex]\hat x[/tex], I mean what you might have seen as [tex]\hat \imath[/tex]....
that is,
[tex]\vec F= (3) \hat \imath [/tex]
or
[tex]\vec F= (3,0,0) [/tex]
...that is, a nonzero constant vector field.
 

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