Find energy of a lightning strike

[sfgoat]

Consider the Earth and the cloud layer 800 meters above the Earth to be the place of a parallel-plate capacitor. The cloud layer has an area of one kilometer squared. Assume this capacitor discharge that is lightning occurs, when the electric field strength between the plates reaches 3.0X10^6 V/m. What is the energy released if the capacitor discharge completely during a lightning strike?

Attempt:
C=(€*A)/d=((8.85*10^-12)(1*10^6m))/800=1.11*10^-8 F
Energy density=(0.5)(€)(E^2)=(.5)(8.85*10^-12)(3*10^6)^2=39.83=energy/volume therefore energy=39.83*(A*800)=3.19*10^10 J

Is this correctly done? Any help is appreciated.

 

[jackarms]

Yes, that looks right. It's a bit indirect to go through energy density though -- you could solve it a bit more directly with $U = \frac{1}{2}CV^{2}$. Either is fine though, of course.

 

[sfgoat]

Thanks.