Question:
A current of $5 \mathrm{~A}$ passes through a copper conductor (resistivity) $=1.7 \times 10^{-8} \Omega \mathrm{m}$ ) of radius of cross-section $5 \mathrm{~mm}$. Find the mobility of the charges if their drift velocity is $1.1 \times 10^{-3} \mathrm{~m} / \mathrm{s}$.
Correct Option: , 4
Solution:
(4) Charge mobility
$(\mu)=\frac{V_{d}}{E}\left[\right.$ Where $V_{d}=$ drift velocity $]$
and resistivity $(\rho)=\frac{E}{j}=\frac{E A}{I} \Rightarrow E=\frac{I(\rho)}{A}$
$\Rightarrow \mu=\frac{V_{\mathrm{d}}}{E}=\frac{V_{\mathrm{d}} \mathrm{A}}{\mathrm{I}_{\rho}}$
$=\frac{1.1 \times 10^{-3} \times \pi \times\left(5 \times 10^{-3}\right)^{2}}{5 \times 1.7 \times 10^{-8}}$
$\mu=1.0 \frac{\mathrm{m}^{2}}{\mathrm{~V}_{\mathrm{s}}}$