Physics

Problem

A conical metallic rod

20\,\text{cm}

long has its radius increasing uniformly from

1.0\,\text{mm}

at the thin end to

3.0\,\text{mm}

at the thick end. The rod carries a steady current of

4.0\,\text{A}

and the number density of free electrons is

8.0\times10^{28}\,\text{m}^{-3}

. (a) Derive an expression for the drift velocity

v_d(x)

of electrons at a distance

x

from the thin end (

0\le x\le0.20\,\text{m}

). (b) Calculate the drift velocity at the midpoint of the rod.