Microscopic form of Ohm’s Law

(Relation between Current density, Conductivity and Electric field)

 

Microscopic form of Ohm’s Law :- This form of Ohm’s law is a relation between current density J, conductivity σ and the electric field E on microscopic level.

In the previous article “Relation Between Current and Drift Velocity” we proved that the current I = neAv_d

Where

A = area of cross-section of the conductor

n = number of free electrons per unit volume of the conductor

v_d = drift velocity of the electrons

Now we know that current density J at a point in a conductor is the amount of current flowing per unit area of the conductor around that point provided the area is held in a direction normal to the current, i.e.,

J = I/A

As drift velocity,

So,

Now, is called the conductivity and it depends only on the material of the conductor and its temperature.

Hence

J = σE

In vector form,

The relation J = σE is called “Microscopic form of Ohm’s Law”.

 

 

Note :-

If a steady current flows in a metallic conductor of non uniform cross section then current density, drift velocity and electric field intensity depends on area.

Here I₁ = I₂ , A₁ < A₂ , J₁ > J₂ , E₁ > E₂ , V_d1 > V_d2

 

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