Question

The dielectric in a capacitor serves two purposes. It increases the capacitance, compared to an otherwise identical capacitor with an air gap, and it increases the maximum potential difference the capacitor can support. If the electric field in a material is sufficiently strong, the material will suddenly become able to conduct, creating a spark. The critical field strength, at which breakdown occurs, is 3.0 MV/m for air, but 60 MV/m for Teflon.

A parallel-plate capacitor consists of two square plates 18 cm on a side, spaced 0.50 mmapart with only air between them. What is the maximum energy that can be stored by the capacitor?

What is the maximum energy that can be stored if the plates are separated by a 0.50-mm-thick Teflon sheet?

Answer 1

As energy stored by a capacitor E = 1/2 A epsilon_0 R E^2_0 d As A = 0.18 times 0.18 = 0.0324 m^2 epsilon_0 = 8.85 times 10^-12 c^2 m^-2 N^-1 k = 1 for air k = 60 MV/m/3.0 MV/m = 20 for Teflon E_0 = 3.0 MV/m for air, 60 MV/m for Teflon (it is max volume) d = 0.50 times 10^-3 m So E = 1/2 (0.0324) (8.85 times 10^-12) (1) (3.0 times 10^6)^2 (0.50 times 10^-3) for air = 0.6452 times 10^-3 J for air cap and for Teflon sheet E = 20(0.6452 times 10^-3) (20/3)^2 = 573.51 times 10^-3 J for Teflon sheet in gap.