Dielectric Breakdown-max potential difference

[PennStateFan1]

Homework Statement

A typical AAA battery has stored energy of about 3400 J. (Battery capacity is typically listed as 625 mA h, meaning that much charge can be delivered at approximately 1.5 V.) Suppose you want to build a parallel plate capacitor to store this amount of energy, using a plate separation of 2.21 mm and with air filling the space between the plates.

a) Assuming that the potential difference across the capacitor is 1.5 V, what must the area of each plate be? I have the answer to this one 7.547E11 m^2

b) Assuming that the potential difference across the capacitor is the maximum that can be applied without dielectric breakdown occurring, what must the area of each plate be?

Homework Equations

For part A, I got the answer using the formula E=1/2CV^2

Part B I'm using Vmax=Emax*d
and E=1/2CV^2

The Attempt at a Solution

I've tried this two difference ways, as I'm kind of confused as to what its asking.

First attempt I'm using the value for Emax of 3E6 V/m for air and than multiplying that by .00221 m and then plugging it into the equation I used for part A

The other way is using Vmax is 1.5 Volts and solving for Emax and using that E as the E in the equation from part A.

Thanks for any help

 

[gneill]

Your "first attempt" looks like the better way to proceed; It finds Vmax for the given plate separation from the dielectric breakdown field strength.

 

[PennStateFan1]

Using my first attempt

Vmax=6630 V

Then 3400=.5(C)(6630)^2
C=epsilon0*A/d=(8.854E-12)A/(.00221)=.000155
A=38613.1 m^2

Can you guys figure out what I'm doing wrong?

 

[gneill]

I dunno. 3.86 x 10⁴ m² looks good to me.