Write relation between conductivity and mobility of metal. - Vidyadip

Question

Write relation between conductivity and mobility of metal.

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Answer

Ratio of drift velocity and electric field inside the conductor is constant at a given temperature. This constant quantity is known as mobility ( $\mu$ ) of charge carrier (electron)
Mobility $(\mu)=\frac{\text { Drift velocity }}{\text { Electric field }}$
$=\frac{v_d}{ E }=\frac{\left(\frac{e E }{m}\right) \tau}{ E }=\frac{e \tau}{m}$
$\mu=\frac{e \tau}{m}$
Conductivity of the substance
$\sigma=\frac{n e^2 \tau}{m}$
$\sigma=n e\left[\frac{e \tau}{m}\right]$
On putting the value from equation (1) in (2)
$\sigma=n e(\mu)$
Hence, conductivity of metal $\sigma=n e \mu $

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