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

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Discussion Overview

The discussion revolves around the relationship between the curl of vector fields in the context of electrodynamics, specifically regarding magnetic potential. Participants explore whether the curl relationship, represented as B=∇xA, implies that A can also be expressed as A=∇xB.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant states that for a vector field, the curl relationship exists in both directions, questioning if A=∇xB is valid.
  • Another participant challenges this assertion, indicating that A=∇xB is incorrect.
  • A later reply acknowledges a misunderstanding regarding the source of the claim about A=∇xB and seeks clarification on whether the answer is no.
  • Another participant confirms that the answer is no, reinforcing the previous challenge.

Areas of Agreement / Disagreement

There is disagreement regarding the validity of the statement A=∇xB, with some participants asserting it is incorrect while others seek clarification on the matter.

hisotaso
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hisotaso said:
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.
 
Looks like I read it wrong. My mistake. Back to my question: the answer is no?
 
Yep. The answer in no.
 
Thank you.
 

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