Two hollow long and thin coaxial conducting cylinders have radii a and b for inner and outer conductors respectively as shown in figure. The electric field between the two conductors has a maximum value $E_{\max }$  . Breakdown occurs when the electric field reaches the value $E_{\max }$   (Inner cylinder is positively charged).

The breakdown voltage in terms of maximum electric field $E_{\max }$  is   $V_b-V_a=-E_{\max }a\ln \frac{b}{a}$

The breakdown voltage in terms of maximum electric field  $E_{\max }$ is   $V_b-V_a=E_{\max }a\ln \frac{b}{a}$

The maximum value of breakdown voltage occurs (keeping b fixed) when  $\frac{b}{a}=e$

The maximum value of breakdown voltage occurs (keeping b fixed) when  $\left(\frac{b}{a}\right)=e^2$