As current  is related with drift velocity by relation

I=n Aev_d

I = n Ae(eE/m)              ( because v_d=eE/m)

I   = nAe²E/m

Or                  I/A=ne² E/m                            (1)

As current density is given by J=I/A (Refer article of Current Density, Conductance and Electrical Conductivity)

and  resistivity is given by  ρ=m/ne²t

By putting above values of J and ρ in equation (1), we get

J=E/ρ

Or                                               J=σ E                                      (where conductivity σ =1/p)

Alternate Method:

According to Ohm’s law, the potential difference between ends of a conductor is directly proportional to the current, that is

V α I

Or                                      V=IR                                             (2)

Where  R is resistance (that is obstruction offered to flow of changes)

Also, when a current I flows in a uniform cross-section area normally to it, then

I=∫J.ds

= ∫JdS cos 0⁰

=J∫dS

I=JA          (3)     (where ∫dS = A)

Also, resistance                                            R= ρl/A                                                 (4)

Equation (3) can also be written as

R=l/σA                                             (5)

Where σ=1/ ρ is conductivity.

Substituting equations (3) and (5) in equation (2) we get

V=JA*l/σA

V=Jl/σ

Or                                J=σV/l                                       (6)

But electric field intensity E=V/l

By putting above value of E in equation (6),we get

J= σ E

This is also known as point form of Ohm’s Law.

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