(a) Definition and SI unit of conductivity
(b) Derivation of the expression for conductivity
Relation between current density and electric field
(a) The conductivity of a material equals to the reciprocal of the resistance of its wire of unit length and unit area of cross section.
Alternatively :
The conductivity ( s ) of a material is the reciprocal of its resistivity (ρ) ]
(Also accept s=‌

1

ρ

)
Its SI unit is
(‌

1

‌ ohm - metre ‌

)∕ ohm −1m−1∕(. mho m−1)∕ siemen m−1
(b) The acceleration,

→

a

=−‌

e

m

→

E

The average drift velocity, vd is given by
vd=−‌

eE

m

τ
( τ= average time between collisions/ relaxation time)
If n is the number of free electrons per unit volume, the current I is given by
I‌=neA|vd|
‌=‌

e2A

m

τn|E|
But ‌‌I=|j|A(j= current‌density)
We, therefore, get
|j|=‌

ne2

m

τ|E|,
The term ‌

ne2

m

τ is conductivity
∴‌σ=‌

ne2τ

m

⇒J=σE