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sodaboy7 Nov19-12 05:05 AM

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.
Useful equations:
I=dq/dt=nqvA
R=rho*l/A
Where v is drift velocity

Any suggestion (may be using different equations and parameters)?

K^2 Nov19-12 06:24 AM

Re: Path of current functional
 
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.

sodaboy7 Nov19-12 07:05 AM

Re: Path of current functional
 
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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