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

AI Thread Summary
The discussion centers on the relationship between vector fields and their curls in electrodynamics, specifically regarding magnetic potential. The initial claim suggested that if B is the curl of A, then A could also be expressed as the curl of B. However, it was clarified that this is incorrect, and the relationship does not exist in both directions. The final consensus is that the curl relationship is not reversible. This conclusion emphasizes the importance of understanding the properties of vector fields in electrodynamics.
hisotaso
Messages
26
Reaction score
0
Physics news on Phys.org
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.
 
Thread 'Motional EMF in Faraday disc, co-rotating magnet axial mean flux'

Thread 'Motional EMF in Faraday disc, co-rotating magnet axial mean flux'

So here is the motional EMF formula. Now I understand the standard Faraday paradox that an axis symmetric field source (like a speaker motor ring magnet) has a magnetic field that is frame invariant under rotation around axis of symmetry. The field is static whether you rotate the magnet or not. So far so good. What puzzles me is this , there is a term average magnetic flux or "azimuthal mean" , this term describes the average magnetic field through the area swept by the rotating Faraday...
View full post »

Similar threads

Vector field equality Curl Proof of Moving Magnet & Conductor Problem
2
Replies
54
Views
4K
A Relationship between magnetic potential and current density in Maxwell
Replies
2
Views
2K
Conceptual origin of the magnetic vector potential....?
Replies
3
Views
3K
Magnetic Dipole Field from a Loop of Wire
Replies
5
Views
3K
Vector potential and constant magnetic flux density
Replies
3
Views
4K
How to find the potential of a field that has regions of non-zero curl
Replies
3
Views
929
Apparent ambiguity in the E field direction in Faraday's Law
Replies
16
Views
2K
Electric potential energy between charge and moving magnet
Replies
7
Views
2K
I'm not getting the curl of vector potential equal to magnetic field
Replies
3
Views
2K
Magnetic Field of Uniformly Magnetized Infinite Slab
Replies
6
Views
1K

Hot Threads

Recent Insights

Back
Top