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 = neAvd
A = area of cross-section of the conductor
n = number of free electrons per unit volume of the conductor
vd = 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,
Now, is called the conductivity and it depends only on the material of the conductor and its temperature.
J = σE
In vector form,
The relation J = σE is called “Microscopic form of Ohm’s Law”.
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 , Vd1 > Vd2
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