# How does the mobility of electrons in a conductor change, if the potential difference applied across the conductor is doubled, keeping the length and temperature of the conductor constant?

Mobility

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

Where vd is the drift velocity and E is the electric field.

Drift velocity

$v_d=\frac{-Ee}{m}\tau$

Substituting this value in the equation of mobility

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

If the temperature and length of the conductor are constant there is no change in the relaxation time $\tau$. And also mobility is independent of potential difference. So there is no change in mobility of electrons if the potential difference is changed keeping the length and temperature constant.

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