# How to find whether the electric field between capacitor plates is above or below the electrical breakdown limit of the insulator between the plates?

Let's say the two plates of a capacitor have charges $q_1$ and $q_2$. The separation between these plates is $d$. I know that I can calculate the electric field by dividing the voltage that is applied to the capacitor by the separation distance and comparing the answer with the electrical breakdown limit to see whether it is above or below the electrical breakdown limit. However, what should I do if I know the charges on the plates rather than the voltage? Sould I use $E=kq/d^2$ where d is the separation distance? If I should use it then which q should I use in the equation, $q_1$ or $q_2$? Because the electric fields calculated with $q_1$ and $q_2$ are different which makes me confused.

• Are you really asking about two capacitors, or are you just getting the terminology confused? One capacitor consists of two conductors separated by a dielectric. Are you really asking about two capacitors, in which case the question involves four conductors? Or are you really meaning to ask about one capacitor, whose two conductors hold charges of $q_1$ and $q_2$? Aug 24 '14 at 14:35
• @RedAct I'm sorry I meant one capacitor which contains 2 conductors. Aug 24 '14 at 16:31
• So that others can understand your question, I took the liberty of tweaking your question so that it says what you intended it to mean. Aug 25 '14 at 2:52
• It's really not that complicated as you think. If you know the charges on the plates, that's enough. Find the field [hyperphysics.phy-astr.gsu.edu/hbase/electric/elesht.html] due to each plate induvidually at a point as a function of the distance from one of them, then vectorially add them to get the net field. Oct 1 '14 at 11:44

The total amount of charge on the two plates is 0, i.e. $q_1=-q_2$, in the case of a plate capacitor, the field is twice that of a field produced by an infinite charged plate, so $E=\frac{q}{A\epsilon}$ where q is the charge on the plate, A is the area of the plate, and $\epsilon$ the relative dielectric constant of the material between the plates.