Electromagnetism

Calculate the mean free time and mean free path between the collisions for the free electrons in copper with number density of the electron $8.5\times10^{28}\,\mathrm{m^{-3}}$ and resistivity $1.7\times10^{-8}\,\mathrm{\Omega\text{-}m}$.($e=1.6\times10^{-19}\,\mathrm{C}$, $m_{e}=9.1\times10^{-31}\,\mathrm{kg}$ and effective speed of the electron = $1.6\times10^{6}\,\mathrm{m/s}$)

Discuss microscopic view of conduction. Show that resistivity and conductivity are independent of applied field and depends on nature of material.

A typical copper wire of household wiring has cross- sectional area $3.31\times10^{-6}\,\mathrm{m^{2}}$ and carries a current of $5\,\mathrm{A}$. What is the drift speed of the electrons? Given, density of copper $8.95\,\mathrm{gcm^{-3}}$, Avogadro's number $6.02\times10^{23}\,\mathrm{mol^{-1}}$, molar mass of copper $63.5\,\mathrm{gm}$.