microscopic form of ohms law

2 years ago

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Dear Harpreet Singh,


Ohm's Law is the linear proportionality between current and voltage that occurs for most conductors of electricity. A graph of voltage against current is a straight line. The gradient is the resistance.


The most well known form of Ohm's law is V=IR, where V is the voltage, I is the current and R is the resistance. However there is another form of Ohm's law which often used by physicists that operates on a microscopic level, relating the current density J to the conductivity σ and the electric field, E.


To see how consider, the volume of material with faces of area A a distance l apart. With an e.m.f. V across the faces of the material



  • the current is proportional to the voltage V

  • the current is proportional to the surface area A

  • and the current is inversely proportional to the distance l.


The current is therefore,


I = VAσ/l.


R = l/Aσ


The proportionality constant σ is the conductivity of the material.


V/l = |E|, and J = I/A in the direction of E so in general we have the constitutive relation.


J = σE


 


                      Good Luck!!!!!!


 


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2 years ago

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