# Drift velocity and its relation with current –

In this topic we will discuss about drift velocity and how it is related with electric current flowing through a conductor.

Drift velocity and its relation with current

As we know a metal contains large numbers of free electrons . At room temperature these electrons moves randomly into the conductors , and its average velocity becomes zero . But when some potential difference is applied across the ends of the conductor the electric field setup inside it and due to which  electrons drifted from one end to other ( low to high against the direction of electric field ), and drifted electrons suffers several collisions but at the end  reaches to the positive terminal .  So new can define drift velocity is the average velocity with which free electrons drifted from negative to positive terminal under the influence of the external electric field .

Let V is the potential difference across the end of the conductor , l is the length of the conductor , then , electric field setup E = V/l

As we know electric field E = F/q = F/e .  Therefore , F= e E = ma , and hence  a= eE /m ;

SO, drift velocity  Vd = ( v1+v2+v3+………vn)/n ;

As we know V = u+at  so we can write v1 = u1+at1 , v2 = u2+at2 , v3 = u3+at3 ………………..

So , Vd= u1+at1 + u2+at2 + u3+at3 ………../n

=  ( u1+u2+u3…../n ) + a(t1 +t2 +t3 ………../n) ;

But ( u1+u2+u3…../n ) = 0

So, Vd = a(t1 +t2 +t3 ………../n) = eE (t1 +t2 +t3 ………..)/mn  .

But we can write,    a(t1 +t2 +t3 ………../n)=Ʈ

So, Vd = EeƮ/m ……………………………..eq.

Relation between current and drift velocity  –

Suppose a conductor is of length ‘l’ and area of crossection ‘A’ . Let n is the number density of electron . Then total number of electrons in the conductor = Volume x electron density = A.l.n .

Total charge  q= A.l.n.e

Let , V is the potential difference setup across the conductor.

then , electric field E = V/l

as we know time Ʈ (t) = l/Vd

and as we know current I = q/t = Alne/t  = Alne/ (l/Vd) = neAVd

I = neAVd …………….eq. this is the relation between drift velocity and current.