# Capacitors and dielectrics

1. Feb 25, 2015

### vysero

1. The problem statement, all variables and given/known data

You are building a parallel plate capacitor out of two square metal plates with side lengths of L and a thin piece of dielectric of thickness d and dielectric strength of Eb. The piece of dielectric will act as a means of separating the two metal plates. In terms of l, Eo(epsilon knot), k, d, Eb how much charge can the capacitor hold before it fails? With l = 10cm, d = .1mm and paper as a dielectric what is the capacitance of your capacitor? How much charge can the capacitor hold before it fails?

2. Relevant equations

eq1: C = EoL; L for a parallel-plate capacitor is = A/d

with a dielectric completely filling the space between the plates:

eq 2: C = kEo(A/d)
eq 3: q = CV
eq 4: V = E/d

3. The attempt at a solution

Using those equations I came up with:

q = CV = (kEoL^2/d)(Eb/d) = EbkL^2Eo/d^2

For the second part of the question with k = 3.5 and eq2 I come up with:

C = 3.5(8.85x10^(-12))(.1^2/.0001) = 3.096 x 10^-9 F

and for the final equation where Eb = 16 I said:

q = 16(3.5)(.1)^2(8.85x10^(-12))/(.0001)^2
= 4.96x10^(-4) C

However, I made the assumption that E = Eb in eq3. If someone could check my work and tell me if I did this problem correctly that would be great, any help appreciated.

2. Feb 26, 2015

### ehild

I do not understand what you mean with eq 1, and the last equation (eq 4) is wrong . Check.