## 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/metre ^{2}**.

We know, I = nAeν_{d}⇒ I/A = neν _{d} ⇒ J = neν _{d} |

**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 = nAeν_{d} ————(I)But, ν _{d} = Eeτ/m —————–(II)Put (II) in (I) ⇒ I = nAe (Eeτ/m) ⇒ I = nAe ^{2}Eτ/m ⇒ I/A = ne ^{2}τ/m x E⇒ J = ne ^{2}τ/m x E But, ne ^{2}τ/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. |