Current density at a point in a conductor is defined as 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.
Let I be the current distributed uniformly across a conductor of cross-sectional area A. The magnitude of the current density for all points on that cross-section of the conductor is
Current density is a vector quantity. Its direction is the direction of motion of positive charge.
As I=Anevd (refer article of relation between current and drift velocity)
The unit of current density is:
Ampere(metre)-2 or Am-2
For a particular surface of conductor, the current is the flux of J over the surface S and is given by
Where ds is elementary surface area vctor of an element taken over the particular surface S and integral is taken over the surface in question.
Conductance(G). The inverse of resistance (R) is called conductance of a conductor, that is,
The unit of conductance is mho or siemen(symbol S). Its unit is inverse of Resistance that we have discussed in Ohm’s law.
Electrical conductivity. The inverse of resistivity (ρ) of a conductor is called its electrical conductivity(σ) i.e.
σ =1/ ρ
the unit of electrical conductivity is mho m-1 or siemens/m.