Current Density Conductance and Conductivity:
Current Density (J)- It is defined as the amount of current flowing per unit area of the conductor at a particular point, provided the area is held perpendicular to the direction of the current.
Let ‘I’ be the current distributed uniformly over the cross-sectional area A of the conductor, then
|J = I/A|
Current density, J is a vector quantity. Its direction is the direction of motion of the positive charge. The S.I. unit of current density if ampere/metre2.
|We know, I = nAeνd|
⇒ I/A = neνd
⇒ J = neνd
Conductance (G)- The inverse of resistance is called conductance of the conductor i.e.
|G = 1/R|
The S.I. unit of conductance is mho or siemen (S).
Conductivity (σ)- The inverse of resistivity is called the conductivity of the conductor i.e.
|σ = 1/ρ|
The S.I. unit of conductivity is mho-m-1 or siemen-m-1.
Relation between Current Density Conductance and Conductivity:
|We know, I = nAeνd ————(I)|
But, νd = Eeτ/m —————–(II)
Put (II) in (I)
⇒ I = nAe (Eeτ/m)
⇒ I = nAe2Eτ/m
⇒ I/A = ne2τ/m x E
⇒ J = ne2τ/m x E
But, ne2τ/m = 1/ρ
⇒ J = 1/ρ x E
But, 1/ρ = σ = conductivity of the conductor
⇒ J = σE
It is microscopic form of Ohm’s Law.