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Path of current functional

by sodaboy7
Tags: current, functional, path
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sodaboy7
#1
Nov19-12, 05:05 AM
P: 81
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)?
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K^2
#2
Nov19-12, 06:24 AM
Sci Advisor
P: 2,470
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
#3
Nov19-12, 07:05 AM
P: 81
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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