Question

A cylindrical capacitor is filled with two cylindrical layers of dielectric with permittivities ε₁ and ε₂. The inside radii of the layers are equal to R₁ and R₂ > R₁. The maximum permissible values of electric field strength are equal to E_1m and E_2m for these dielectrics. At what relationship between ε, R, and E_m, will the voltage increase result in the field strength reaching the breakdown value for both dielectrics simultaneously?

Answer 1

Let λ be the linear charge density then,

The breakdown in either case will occur at the smaller value of r for a simultaneous breakdown of both dielectrics. From (1) and (2)