Current Electricity: JEE Main 2026 Physics question

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 $\alpha\times10^{-3}$ m$^2$/V s. The value of $\alpha$ is : (electron concentration $=5\times10^{28}$/m$^3$ and electron charge $=1.6\times10^{-19}$ C)