# microscopic form of ohms law

Ashwin Sinha
520 Points
13 years ago

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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