Refer image $1.$

$q \rightarrow$ change of electron.

Four due to electric field $=q E$

$\therefore \frac{m v_{0} {^2}}{R_{e}}=q E$

where $R_{e}$ is radius of curvature,

$\therefore \frac{1}{R_{e}}=\frac{q E}{m v_{0} {^{2}}}$

$\therefore=\frac{m v_{0} {^{2}}}{q E}=r_{1}$

In magnetic field,

Focus on electron $=q V_{0} B$

Refer image $2 .$

Balancing of centripetal and centrifugal focuses,

$\frac{m V_{0} {^{2}}}{R b}=q V_{0} B$

$\therefore R_{b}=\frac{m V_{0}}{q B}=r_{2}$

$\therefore \frac{r_{1}}{r_{2}}=\frac{R_{c}}{R_{b}}=\frac{\frac{m V_{0^{2}}}{q E}}{\frac{m V_{0}}{q B}}$

$\therefore \frac{r_{1}}{r_{2}}=\frac{B V_{0}}{E}$