|Nov19-12, 05:05 AM||#1|
Path of current functional
Current follows the path of least resistance or shortest path. I just want to prove this or rather reproduce it using calculus of variations. I just want to show it in a fancy way. I want help to form the FUNCTIONAL for it.
Where v is drift velocity
Any suggestion (may be using different equations and parameters)?
|Nov19-12, 06:24 AM||#2|
The current does not actually take the path of least resistance. It takes all available paths. In general:
[tex]J = \sigma E[/tex]
Where J is current density, E is electric field, and σ is the electrical conductivity.
|Nov19-12, 07:05 AM||#3|
It prefers path of least resistance. Or it maximum current follows the path of least resistance upon division at a point.
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