Spherical capacitor with two dielectrics

What is a spherical capacitor filled with dielectrics?

Figure 5.10.4 Spherical capacitor filled with dielectrics. The system can be treated as two capacitors connected in series, since the total potential difference across the capacitors is the sum of potential differences across individual capacitors. The equivalent capacitance for a spherical capacitor of inner radius 1r and outer radius r

How many dielectrics are in a capacitor?

Let us first suppose that two media are in series (Figure V. V. 16). Our capacitor has two dielectrics in series, the first one of thickness d1 d 1 and permittivity ϵ1 ϵ 1 and the second one of thickness d2 d 2 and permittivity ϵ2 ϵ 2. As always, the thicknesses of the dielectrics are supposed to be small so that the fields within them are uniform.

What is an example of a spherical capacitor?

As a third example, let’s consider a spherical capacitor which consists of two concentric spherical shells of radii a and b, as shown in Figure 5.2.5. The inner shell has a charge +Q uniformly distributed over its surface, and the outer shell an equal but opposite charge –Q. What is the capacitance of this configuration?

What factors affect the capacitance of a spherical capacitor?

Once again, we see that the capacitance C depends only on the geometrical factors, L, a and b. As a third example, let’s consider a spherical capacitor which consists of two concentric spherical shells of radii a and b, as shown in Figure 5.2.5.

How do you find the total capacitance of a dielectric?

As always, the thicknesses of the dielectrics are supposed to be small so that the fields within them are uniform. This is effectively two capacitors in series, of capacitances ϵ1A/d1 and ϵ2A/d2 ϵ 1 A / d 1 and ϵ 2 A / d 2. The total capacitance is therefore C = ϵ1ϵ2A ϵ2d1 +ϵ1d2. (5.14.1) (5.14.1) C = ϵ 1 ϵ 2 A ϵ 2 d 1 + ϵ 1 d 2.

What happens when a capacitor has a capacitance 0?

To see how this happens, suppose a capacitor has a capacitance C 0 when there is no material between the plates. When a dielectric material is inserted to completely fill the space between the plates, the capacitance increases to is called the dielectric constant.