How Much Charge Can a Capacitor Hold Before Failure?

[vysero]

Homework Statement

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?[/B]

Homework Equations

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

with a dielectric completely filling the space between the plates:[/B]

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

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.[/B]

 

[ehild]

Homework Statement

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?[/B]

Homework Equations

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

with a dielectric completely filling the space between the plates:[/B]

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

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