$i=$ constant

Resistance of element $d R=\frac{\rho d x}{\pi r^{2}}$

$d V=i d R=\frac{i \rho d x}{\pi r^{2}}$

$E=\frac{d V}{d x}=\frac{i \rho}{\pi r^{2}}$

$V_{d}=\frac{e E \tau}{m}$

$\therefore V_{d} \propto E$

$\rightarrow E \propto \frac{1}{r^{2}}$

if $r$ decreases, $E$ will increase $: V_{d}$ will increase