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

Derive the equation of mobility in terms of relaxation time $(\tau)$. Write its unit.

Consider a conductor of length $40 \ cm$,where a potential difference of $10 \ V$ is maintained between the ends of the conductor. Find out the mobility of the electrons,provided the drift velocity of the electrons is $5 \times 10^{-6} \ m/s$.

$A$ current of $5\, A$ passes through a copper conductor (resistivity $= 1.7 \times 10^{-8}\, \Omega \, m$) of radius of cross-section $5\, mm$. Find the mobility of the charges if their drift velocity is $1.1 \times 10^{-3}\, m/s$.

$A$ 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 ......

The mechanism of the heat produced in a conductor when an electric current flows through it can be explained on the basis of