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.

Vd 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 Vd Δt. The volume of this part of the conductor is AVdΔt.
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  AVdΔt  = nAVdΔt. Hence, the net charge flowing through this part of the conductor in time Δt is,
Q = (nAVdΔt) 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 = nqVd.
Hope this helps you.
Keep posting and good luck!

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thank u very much

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