Problem 3.106

A cylindrical capacitor is filled with two cylindrical layers of dielectric with permittivities $\varepsilon_{1}$ and $\varepsilon_{2} .$ The inside radii of the layers are equal to $R_{1}$ and $R_{2}>R_{1} .$ The maximum permissible values of electric field strength are equal to $E_{1 m}$ and $E_{2 m}$ for these dielectrics. At what relationship between $\varepsilon, R,$ and $E_{m}$ will the voltage increase result in the field strength reaching the breakdown value for both dielectrics simultaneously?