Does the Curl Relationship Exist in Both Directions for Vector Fields?

[hisotaso]

We are studying electrodynamics, more specifically magnetic potential. We are given

B=∇xA

I saw on a certain website here http://www.ittc.ku.edu/~jstiles/220/handouts/The Magnetic Vector Potential.pdf that

A=∇xB

So is it true in general that for a vector field, the curl relationship exists in both directions as shown above?

 

[the_wolfman]

We are studying electrodynamics, more specifically magnetic potential. We are given

B=∇xA

I saw on a certain website here http://www.ittc.ku.edu/~jstiles/220/handouts/The Magnetic Vector Potential.pdf that

A=∇xB

So is it true in general that for a vector field, the curl relationship exists in both directions as shown above?

Where does it say A=∇xB?

This is wrong.

 

[hisotaso]

Looks like I read it wrong. My mistake. Back to my question: the answer is no?

 

[the_wolfman]

Yep. The answer in no.

 

[hisotaso]

Thank you.