Consider a cylindrical conductor of length \(l\) and area of cross-section \(A\). Current \(I\) is maintained in the conductor and electrons drift with velocity \(v_d\). Show that the conductivity \(\sigma\) of the material of the conductor is given by
\[
\sigma=\frac{ne^2\tau}{m}.
\]
Show Hint
Important microscopic relation:
\[
\sigma=\frac{ne^2\tau}{m}
\]
and
\[
\rho=\frac{1}{\sigma}.
\]
For metals, resistance increases approximately linearly with temperature.