Arrive at an expression for drift velocity.

Explanation

In a conductor, the free electrons have thermal motion. They collide with atoms and travel in random directions. There is no net transfer of charges in any directions. The average velocity of electron is zero.
i.e., `(1)/(N)underset(i=1)overset(N)Sigma barV_(1)=0` N-Total number of electrons
`barV_(i)` =Velocity of electron
When the potential difference is applied across the conductor the free electrons experience electrostatic force
Where `vecF=-evecE`
Where `vecE` is the electric field in the conductor The -vesign indicates that the force on the electron is opposite to the direction of `vecE`
`vecF=-evecE=mveca`
`veca=(-evecE)/(m)` where `veca` is the acceleration of the electron
The electron will drift opposite to the direction of electric field and constiture the current 1.
The accelerationg electron collides with the vibrating atoms and time between two successive collision of electron is called the relaxation time (`tau`)The drift velocity of the electron is
`barV_(d)=u+at`
`vecV_(d)=0+((-evecE)/(m))tau(because u=0,t=tau)`
`vecV_(d)=(-evecE)/(m)tau`
In magnitude =`V_(d)=(-eE)/(m)tau`