Why Does Vector Potential Align with Current in Infinite Distributions?

AI Thread Summary
The discussion centers on the alignment of vector potential with current direction in both finite and infinite current distributions. It highlights that while the formula for vector potential A typically applies to finite distributions, examples from Griffiths show that the alignment holds true even for infinite distributions. Participants note that this phenomenon may be influenced by gauge dependence, particularly in the context of the Coulomb gauge. The conversation seeks to reconcile the apparent contradiction between the standard understanding and the behavior observed in specific examples. Ultimately, the alignment of vector potential and current direction remains consistent across different scenarios.
Kolahal Bhattacharya
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We know in all ordinary cases the direction of vector potential will be mimic to the direction of current.As it is evident from the expression of A=(mu/4*pi) int{J /(r-r')}dV which is valid only for finite current distributions.
But in example 5.12 and in exercise 5.25 Griffiths has given situations where current distributions extend upto infinity.But,still the direction of A is the same as direction of J .Can you help me to reconcile these two apparently contrasting views?
 
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Kolahal Bhattacharya said:
We know in all ordinary cases the direction of vector potential will be mimic to the direction of current.
You do know it is gauge dependent, right (The formula you brought works for Coulomb)? I don't know about the example you talked about.
 
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