# Different dielectric material with different relative permittivity

I am wondering how to different dielectric material with different relative permittivity behave when put together. Say i have two concentric sphere and the space between them is filled with a dielectric of relative permittivity A from the outer surface of the inner sphere to the mid point between the inner and outer sphere and another dielectric of relative permittivity B fills the remaining space between the spheres. In such case, how do they behave and affect the capacitance of such a capacitor?

The voltage between the plates remains, unchanging, the capcitance is calculated by, $$C_{ca} = {\epsilon}_0 {\epsilon}_r \frac {A}{d}$$. This in fact happens in real life, when capacitors are heated and one of the two plates in a parallel plate capacitor pulls away from the dielectric, another dielectric, air, fills in the gap. The capacitance is of course, reduced, but not only because of the greater gap.

I think it is like 2 separate capacitors (of half the spacing) in series. So the overall permittivity is the product / sum of the individual permittivity. In other words the presence of a conductor at the interface of the two dielectrics would have no effect as long as it was vanishingly thin.

E = E1.E2/E1 + E2