Define Mobility it's S.I unit and Dimensions and Its Relation with Electric Current :

Define Mobility it's S.I unit and Dimensions and Its Relation with Electric Current : 

Conductivity in materials arises due to the motion of charge carriers. In metals, the charge carriers are electrons, while in electrolytes and ionised gases both positive and negative ions may contribute.

Mobility : 

Mobility ($\mu$) is defined as the drift velocity acquired per unit electric field.

$\mu = \frac{[v_d]}{E}$

Where:

$\mu$= mobility

$v_d$= drift velocity

E = electric field

SI Unit : 

$\mu = \frac{m/s}{V/m}$

$\mu =\text{m}^2 \text{V}^{-1}\text{s}^{-1}$

Mobility is always positive.

From drift velocity relation,

$v_d = \frac{e\tau E}{m}$

Therefore,

$\mu = \frac{ \frac{e\tau E}{m}}{E}$

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

Where:

 e= charge of electron

$\tau$ = relaxation time

m = mass of electron

Relation Between Mobility and Electric Current : 

Electric current in a conductor is:

$I = n e A v_d$

Since,

$v_d = \mu E$

Therefore,

$I = n e A \mu E$

Thus, electric current is directly proportional to mobility.

Dimensions of Mobility : 

Using,

$\mu = \frac{v_d}{E}$

Dimensions of drift velocity:

$[v_d] = [LT^{-1}]$

Dimensions of electric field:

$[E] = [MLT^{-2}] \div [A T]$

$[E]= [MLT^{-3}A^{-1}]$

Therefore,

$[\mu] = \frac{[LT^{-1}]}{[MLT^{-3}A^{-1}]} = [M^{-1}T^{2}A]$

Dimensional Formula of Mobility

$[M^{-1}L^{0}T^{2}A^{1}]$