The free–electron number density in a certain metallic conductor is and the electron…

PHYSICS · Multi-part · A Level · Physics · Electricity · Electricity

Problem

The free–electron number density in a certain metallic conductor is

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

and the electron mobility at

300\,\text{K}

4.3\times10^{-3}\,\text{m}^2\,\text{V}^{-1}\,\text{s}^{-1}

. A straight piece of this metal is drawn into a uniform cylindrical wire

1.5\,\text{m}

long and

0.50\,\text{mm}

in diameter. (i) Starting from the definitions of current density and mobility, derive an expression for the resistivity

\rho

of the conductor in terms of

n

e

and

\mu

only. (ii) Using the data given, calculate the numerical value of

\rho

and hence find the resistance of the wire. (iii) The accepted resistivity of copper at

300\,\text{K}

is about

1.7\times10^{-8}\,\Omega\,\text{m}

. Comment on whether the unknown metal may reasonably be copper.