Physics Question from JEE Main 2026 · 22 January, Shift 2

A cylindrical conductor of length $2 \, m$ and area of cross-section $0.2 \, mm^2$ carries an electric current of $1.6 \, A$ when its ends are connected to a $2 \, V$ battery. Mobility of electrons in the conductor is $\alpha \times 10^{-3} \, m^2/V\, s.$ The value of $\alpha$ is _____.

(Electron concentration $= 5 \times 10^{28} \, m^{-3}$, electron charge $= 1.6 \times 10^{-19} \, C$)