Derive the equation of mobility in terms of electric current.

(A) When $n$ electrons move with drift velocity $v_{d}$ in a conductor of cross-sectional area $A$,the electric current $I$ is given by:
$I = n A v_{d} e$
By definition,mobility $\mu$ is the ratio of drift velocity to the applied electric field $E$:
$\mu = \frac{v_{d}}{E}$
Therefore,the drift velocity can be expressed as:
$v_{d} = \mu E$
Substituting this into the current equation:
$I = n A (\mu E) e$
Rearranging the equation to solve for mobility $\mu$:
$\mu = \frac{I}{n A E e}$
The $SI$ unit of mobility is calculated as:
$\mu = \frac{A}{m^{-3} \times m^{2} \times (V/m) \times C} = \frac{A}{V \cdot C} = m^{2} V^{-1} s^{-1}$