All Problems

Electric Capacitance, Energy of an Electric Field

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?

Reveal Answer
 When ε1R1E1m=ε2R2E2m\text { When } \varepsilon_{1} R_{1} E_{1 m}=\varepsilon_{2} R_{2} E_{2 m}
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