Suppose that a parallel-plate capacitor has a dielectric that breaks down if the electric field exceeds K V/m. Thus, the maximum voltage rating of the capacitor is V max =K d, where d is the separation between the plates. In working Problem P3.33, we find that the maximum energy that can be stored is w max = 1 2 ∈ r ∈ 0 K 2 (Vol) in which Vol is the volume of the dielectric. Given that K=32× 10 5 V/m and that ∈ r =1 (the approximate values for air), find the dimensions of a parallel-plate capacitor having square plates if it is desired to store 1 mJ at a voltage of 1000 V in the least possible volume.

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Dielectric Breakdown

A dielectric is a material with low electrical conductivity and so is classified as an insulator. Dielectric materials are used to block the flow of electricity through them, allowing them to behave as an insulators. They can also be used to store electric charge or improve capacitance.Dielectrics have no free electrons for conduction because electrons are tightly bound to the nucleus. Because dielectrics contain a small number of electrons for electrical conductivity, they have a dipole. The two primary roles of dielectrics in electrical devices are insulation and electrical energy storage. An electric field polarizes the dielectric, and the polarization of the molecules allows dielectric materials to store charge.