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Vector Potential

by ManuelF
Tags: potential, vector
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ManuelF
#1
Nov7-09, 11:33 AM
P: 8
Hello!
Can you tell me the sufficient condition for the existence of the vector potential?
Thank you very much!
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wofsy
#2
Nov7-09, 01:57 PM
P: 707
Quote Quote by ManuelF View Post
Hello!
Can you tell me the sufficient condition for the existence of the vector potential?
Thank you very much!
when a field is divergence free it has a vector potential.
ManuelF
#3
Nov7-09, 02:21 PM
P: 8
That is a necessary condition, but I do not think is enough!
Are you sure?
Thank you.

wofsy
#4
Nov7-09, 02:51 PM
P: 707
Vector Potential

Quote Quote by ManuelF View Post
That is a necessary condition, but I do not think is enough!
Are you sure?
Thank you.
It is necessary and sufficient in Euclidean space.

For instance, in magnetostatics a magnetic field always has a vector potential.

If the field is B = (u,v,w) consider the 2 form udy^dz -vdx^dz + wdx^dy

Since B has zero divergence, the 2 form is closed. By Poincare's Lemma it is therefore the exterior derivative of a 1 form adx + bdy + cdx. The curl of (a,b,c) equals B.
ManuelF
#5
Nov7-09, 07:19 PM
P: 8
Thank you very much!


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