Q 12-03-250JEE MainJEE Main 2019 (10 Apr, Shift 1)Medium
A current of $5\ \text{A}$ passes through a copper conductor (resistivity $= 1.7\times10^{-8}\ \Omega\,\text{m}$) of radius of cross-section $5\ \text{mm}$. Find the mobility of the charges if their drift velocity is $1.1\times10^{-3}\ \text{m s}^{-1}$.
Answer: (C) $1.0\ \text{m}^2\text{V}^{-1}\text{s}^{-1}$
Electric field in the wire: $E = \rho J = \rho\dfrac{I}{\pi r^2} = \dfrac{1.7\times10^{-8}\times5}{\pi(5\times10^{-3})^2} = 1.08\times10^{-3}\ \text{V/m}$.
$$\mu = \frac{v_d}{E} = \frac{1.1\times10^{-3}}{1.08\times10^{-3}} \approx 1.0\ \text{m}^2\text{V}^{-1}\text{s}^{-1}$$
Solution by Sreeraj P, M.Sc Physics