[MarioNintendo]

Hey y'all. I'm trying to help a student who's stumped on a question... which I can't even answer myself. Am I missing something?

Basically you have a dielectric with varying dielectric constants inside it.

b=1cm
a=5cm (the armatures have a square shape, meaning A=a^2)
1/5 of the dielectric has k1=4
4/5 of the dielectric has k2=6.5

We're looking for the analytic and numerical dielectric constant of this dielectric as a whole.



If you could help, I'd really appreciate it. Is it as simple as taking the average of the k's? We know that C=(k*epsilon)*A/d, where epsilon is the vacuum permittivity. How must we use this? Do we need integrals? Etc.