Define the term ‘Mobility’ of charge carries in a conductor. Write its SI unit. What is its relation with relaxation time?

Mobility of charge carriers in a conductor refers to the ability of charged particles (such as electrons or holes) to move through the material when an electric field is applied. It is a measure of how quickly charge carriers can respond to the applied electric field, which affects the conductivity of the material.

The SI unit of mobility ($\mu$) is meter squared per volt-second ($m^2/V \cdot s$).

The relation between mobility and relaxation time ($\tau$) can be expressed by the formula:

$\mu = \frac{q \tau}{m}$

where:

• $\mu$ is the mobility of the charge carriers,
• $q$ is the charge of the carriers,
• $\tau$ is the average relaxation time between collisions, and
• $m$ is the effective mass of the carriers.

This relationship indicates that the mobility is directly proportional to the relaxation time. A longer relaxation time means that charge carriers experience fewer collisions, allowing them to move more freely, thus increasing their mobility.