# Advanced Knowledge of Drift Velocity

Physics

## definition

### Relaxation time of electrons

The average value of the time elapsed after the last collision of all the electrons in a perturbed system is known as the relaxation time. It is represented by .

## definition

### Mean free path

The mean free path is the average distance traveled by a moving particle (such as an atom, a molecule, a photon) between successive impacts (collisions), which modify its direction or energy or other particle properties.

Where is the mean free path, is the number of target particles per unit volume, and is the effective cross-sectional area of collision.

## formula

### Relation of drift velocity with electric field

•  An electron will suffer collisions with the heavy fixed ions, but after collision, it will emerge with the same speed but in random directions. If we consider all the electrons, their average velocity will be zero since their directions are random. Hence,
• Now, if an electric field is present. Electrons will be accelerated due to this field by where is the charge and is the mass of electron.
• Consider the electron at a given time . This electron would have had its last collision some time before , and let be the time elapsed after its last collision. If was its velocity immediately after the last collision, then its velocity at time t is .
•  The average velocity of the electrons at time t is the average of all the .
•  Hence
• The average of is zero as seen above.
• The average of is called relaxation time denoted by .
• The average of is called drift velocity
• Hence
• The last result show that electron move with average velocity which is independent of time.