Finding Vector Fields that Satisfy Certain Curls

[EngageEngage]

Homework Statement

Is it possible to find a vector field whose curl is yi? xi?

Homework Equations

The Attempt at a Solution

I found that if F = <0,0,y^2/2>, its curl will be yi. However, I cannot figure out a vector field whose curl will be xi. I tried using exponentials and just different combination of x's, y's and z's as components of F, and just building my function as I go through the 'curl determinant', but haven't been able to find anything. If someone could please help me out that would be greatly appreciated. Thank you

 

[PingPong]

Take the divergence of the vector field you're interested. If it's zero, then you can find the "vector potential" for the vector field you're interested in (for more info, see http://en.wikipedia.org/wiki/Vector_potential).

Since the divergence of xi is 1, you cannot find a vector field whose curl is xi.

Hope that helps!

 

[EngageEngage]

Thanks for the help!