# Different dielectric material with different relative permittivity

1. Nov 23, 2008

### FourierX

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?

2. Nov 23, 2008

### ptr

Re: Dilectrics

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.

3. Nov 23, 2008

### Pumblechook

Re: Dilectrics

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