If a current of $80 \ A$ is passing through a straight conductor of length $10 \ m$,then the total momentum of electrons in the conductor is (mass of electron $= 9.1 \times 10^{-31} \ kg$ and charge of electron $= 1.6 \times 10^{-19} \ C$).

Find the mobility of an electron in a wire if its average collision time is $9.1 \times 10^{-15} \,s$. (Charge of electron $= 1.6 \times 10^{-19} \,C$ and mass of electron $= 9.1 \times 10^{-31} \,kg$)

Derive the equation of mobility in terms of electric current.

The electric field $E$,current density $J$ and conductivity $\sigma$ of a conductor are related as

$A$ current of $10 \, A$ is passing through an aluminum wire of cross-sectional area $4 \times 10^{-6} \, m^{2}$. If the density of aluminum is $2.7 \, g/cm^{3}$ and it provides $1$ free electron per atom for conduction,find the drift speed of the electrons in $\times 10^{-4} \, m/s$. (Given: molecular weight of aluminum = $27 \, g/mol$,Avogadro's number $N_{A} = 6.022 \times 10^{23} \, mol^{-1}$)

The drift speed of electrons in a material is found to be $0.3 \ m s^{-1}$ when an electric field of $2 \ V m^{-1}$ is applied across it. The electron mobility (in $m^2 \ V^{-1} \ s^{-1}$) in the material is