The effect of a dielectric on energy storage of a capacitor

[Zift]

Homework Statement

You are an intern at an engineering company that makes capacitors used for energy storage in pulsed lasers. Your manager asks your team to construct a parallel-plate, air-gap capacitor that will store 120 kJ of energy.

(a) What minimum volume is required between the plates of the capacitor?

(b) Suppose you have developed a dielectric that has a dielectric strength of 3.40 x 10⁸V/m and has a dielectric constant of 5.50. What volume of this dielectric, between the plates of the capacitor, is required for it to be able to store 120 kJ of energy?

Homework Equations

U=(1/2)*\epsilon₀*E²*VOL

The Attempt at a Solution

I got part (a) by plugging in 120 kJ into U and the dielectric break down of air into E_max and solved for volume. turned out to be 3012 m³.

I tried to do the same thing for par (b) but it didn't work. Then I realized that it probably wouldn't be necessary to charge the capacitor such that the electric field is at the dielectric breakdown point to be able to store 120kJ. So I tried to insert the new electric field due to the dielectric (using the relationship E=E₀/k where E₀ is the electric field before the dielectric is in place and k is the dielectric constant) being put into place and then solving for the volume, however, this still did not yield the correct answer. I have a feeling that there is some conceptual gap in my thought process, but I cannot see it right now, and this is due at midnight and I'm kinda stressed so that's not helping either. Can anyone help point me in the right direction? Any help is appreciated

 

[ehild]

show your calculation.

ehild