Curl of 2 dimensional vector field

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KindofSlow

Junior Member
Joined
Mar 5, 2010
Messages
90
Hello All,
This is from
F = -y/(r^2) î + x/(r^2) ĵ
Page says curl F = 0 and cites a previous example. ....... sp. edited
I cannot find the sited previous example
But I get curl F = 1/(r^2) - -1/(r^2) = 2/(r^2)
I cannot figure out what I'm doing wrong.
Apologies in advance since this seems like I'm missing something really obvious and simple, but I can't figure it out.
Any assistance pointing out what I'm missing greatly appreciated.
Thank you
 
KindofSlow said:
Hello All,
This is from
F = -y/(r^2) î + x/(r^2) ĵ
Page says curl F = 0 and cites a previous example. ....... sp. edited
I cannot find the sited previous example
But I get curl F = 1/(r^2) - -1/(r^2) = 2/(r^2)
I cannot figure out what I'm doing wrong.
Apologies in advance since this seems like I'm missing something really obvious and simple, but I can't figure it out.
Any assistance pointing out what I'm missing greatly appreciated.
Thank you
Click to expand...
"But I get curl F = 1/(r^2) - -1/(r^2) = 2/(r^2)"............incorrect

Curl is a vector - your answer is not in vector form.
 
Romsek, HallsofIvy, topsquark, and Subhotosh Khan,
1. Substituting x^2 + y^2 for r^2 worked perfectly and I got zero so thank you for that hint.
2. Thank you also for pointing out my spelling error which is quite embarrassing as not an error I should have made. Sorry about that.
3. Regarding curl being a vector and my answer not being in vector form.
I actually was aware of this but made my submission not in vector form based on this:

As always, thank you all very much for your assistance.
 
Strictly speaking the "curl" is only defined for a three dimensional vector. For a two dimensional vector we treat it as a three dimensional vector with the third component 0. The curl will then be a vector with first and second components 0 (so perpendicular to the two dimensional plane). Yes, since we are not "strictly speaking" we can treat the curl as being the third component.
 
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