how current density, j = nqv _d

explain this relation to me.

Hi Virender,

 

 

Let us consider a part of a conductor of cross-sectional area A, which is in the influence of an electric field as shown in the diagram below.

V_d is the drift velocity, and Δt is the time taken by the electrons to cross the section. So the length of the taken part of the conductor is V_d Δt. The volume of this part of the conductor is AV_dΔt.

 

Suppose n is the number of electrons per unit volume of the conductor. So, the number of electrons crossing the part of the conductor in time Δt is = n Х  AV_dΔt  = nAV_dΔt. Hence, the net charge flowing through this part of the conductor in time Δt is,

Q = (nAV_dΔt) Х e

In the lesson the unit charge is taken as q, and here I’ve derived the equation using ‘e’ as the smallest charge.

So, we get a general equation, j = nqV_d.

 

Hope this helps you.

Keep posting and good luck!