Drift Velocity and Mobility

Drift Velocity

“Drift velocity is defined as the average velocity with which the free electrons get drifted towards the positive end of the conductor under the influence of an external electric field applied”.

The drift velocity of electrons is of the order of m/s .

If V is the potential difference applied across the ends of the conductor of length l, the magnitude of electric field set up is

Each free electrons in the conductor experience a force,

.

The acceleration of each electron is

Average Drift Velocity,

as (v=at)

where, τ is the relaxation time

Relation between Drift Velocity and Current

Drift velocity:-The velocity with which the free electrons are drifted towards the positive terminal, under the action of the applied field, is called the drift velocity of the free electrons.

V = (eV/ml)

Here, e is the charge of electron, V is the potential difference, m is the mass and  is the relaxation time.

Electric current and Drift velocity:-  I= q/t = nAve

Consider a conductor (say a copper wire) of length l and of uniform area of cross-section

Volume of the conductor = A × l.

If n is the number density of electrons, i.e., the number of free electrons per unit volume of the conductor, then total number of free electrons in the conductor

= A × l × n.

Then total charge on all the free electrons in the conductor,

q = A × l × n × e

The electric field set up across the conductor is given by E = (in magnitude)

5. Due to this field, the free electrons present in the conductor will begin to move with a drift velocity vd towards the left hand side as shown in figure

Time taken by the free electrons to cross the conductors,

hence, Current

Therefore,

Putting value of , we have

Relaxation Time (τ)

The time interval between two successive collisions of electrons with the positive ions in the metallic lattice is defined as relaxation time

Mobility

Drift velocity per unit electric field is called mobility of electron i.e.

Mobility of charge carrier (µ), responsible for current is defined as the magnitude of drift velocity of charge per unit electric filed applied, i.e.,

Therefore, Mobility of electrons