Drift Velocity | Electron Mobility | Drift Velocity Formula

Definition of drift velocity  

When an electric field is applied across a conductor, its free electrons starts accelerating towards battery’s positive terminal , as they accelerate they collide with atoms and ions thus loosing almost all of their kinetic energy. But, due to present electric field they again accelerate but again they collide  with atoms and ions thus velocity again becoming zero and this continues. In this way the electrons manage to gain only a small  average velocity called drift velocity.

Also, the time for which an electron moves freely between two successive collisions is called relaxation time of electrons.

Drift velocity derivation  

Consider a section of conductor as shown in figure below. Let

   n=number of free electrons per unit volume of the conductor 

   V_d=axial drift velocity of free electrons (in m/s)

   A=area of cross-section of conductor (in m² )

   I = current (in Ampere)                                                                         

Then, in small time dt the distance moved by electrons is

dx= V_d×dt

and the volume swept is  A×dx  and therefore the total number of electrons that cross area A in time dt is number of electrons per unit volume × volume swept  i.e  n × (A × dx)  or n × (A × V_d×dt)

If e is the charge of an electron , the total amount of charge that crosses cross-section A in time dt is  

dq= e×n ×A × V_d×dt

But by definition of electric current, current is the amount of charge passing through conductor cross-section per unit time,  therefore

                                      I=dq/dt 

               = (e×n × (A × V_d×dt))/dt   

 =  n × e × A × V_d  

 Formula for Drift Velocity   

The above expression can be rearranged as      V_d=I/ (n × e × A)                                                   

    

               

Common mistaken view about drift velocity :- It is a common misconception that drift velocity must be very high. No its  not. In fact it is very small. Lets take an example to demonstrate it.

Let us take normal current density , J =1.55 × 10⁶     A/m²

                                     

 n =10²⁹ /m³   , for copper at room temperature

 e =1.6 × 10^-19   Coulomb

                                                                                          

Putting these values in drift velocity formula we get V_d = 0.58  cm/min  , shows electron drift velocity is very small. 

TRY IT YOURSELF :-

1. A conductor material has a free-electron density of 10²⁴ electrons per m³. When a voltage is applied a constant drift velocity of 1.5 × 10^-2 m/s is attained by the electrons. If the cross-section area of the material is 1cm² .Calculate the current.                                                                                 ( Ans= 0.24A )       



Ohm's Law