$A$ cylindrical wire of radius $0.5 \, mm$ and conductivity $5 \times 10^{7} \, S/m$ is subjected to an electric field of $10 \, mV/m$. The expected value of current in the wire will be $x^{3} \, \pi \, mA$. The value of $x$ is ......

$A$ 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 velocity of the electrons in a copper wire of length $2\ m$ under the application of a potential difference of $200\ V$ is $0.5\ m/s$. Their mobility (in $m^2 V^{-1} s^{-1}$) is

Cross-sectional area of a copper wire is equal to the area of a square of length $2 \ mm$. If this copper wire draws $8 \ A$ electric current,then find the drift velocity of free electrons. The number density of electrons in the copper wire is $8 \times 10^{28} \ m^{-3}$.

$A$ metal has $9 \times 10^{28}$ conduction electrons per $m^3$ and its resistivity is $1 \times 10^{-8} \Omega \cdot m$. If the drift speed of an electron in the metal is $1.6 \times 10^6 \ m/s$, then its mean free path is (mass of electron $= 9 \times 10^{-31} \ kg$ and charge of electron $= 1.6 \times 10^{-19} \ C$). (in $nm$)

An electric cell of emf $E$ is connected across a copper wire of diameter $d$ and length $l$. The drift velocity of electrons in the wire is $v_{d}$. If the length of the wire is changed to $2l$, the new drift velocity of electrons in the copper wire will be