
#1
Nov709, 11:33 AM

P: 8

Hello!
Can you tell me the sufficient condition for the existence of the vector potential? Thank you very much! 



#2
Nov709, 01:57 PM

P: 707





#3
Nov709, 02:21 PM

P: 8

That is a necessary condition, but I do not think is enough!
Are you sure? Thank you. 



#4
Nov709, 02:51 PM

P: 707

Vector PotentialFor 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. 



#5
Nov709, 07:19 PM

P: 8

Thank you very much!



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