Dielectrics

A dielectric is a non-conducting material – also called an insulator – such as rubber, wood, or glass. When the plates between a capacitor are filled with a dielectric, the capacitance increases by a factor κ, called the dielectric constant of the material. Why does this happen?

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The dielectric consists of polarizable molecules that, when put in the electric field between isolated capacitor plates, are caused to have a charge separation as shown. This charge separation results in a layer of negative charge on the dielectric near the positive capacitor plate and, similarly, a layer of positive charge near the negative capacitor plate. These charges are not free, but bound, and the entire dielectric is still neutral. These layers of bound electric charge reduce the electric field between the isolated capacitor plates, also reducing the potential difference between the plates. The dielectric constant is a measure of the polarizability of the dielectric molecules and therefore a measure of this bound surface charge reducing the potential difference between the plates by the same factor κ. Since C = Q/∆V, and since Q, the charge on the capacitor plates does not change so long as the plates are isolated, then a drop in ∆V by κ implies an increase in C by the factor κ: C = Q/(∆V/κ) = κ(Q/∆V) = κCo, where Co is the capacitance without the dielectric present. Aside from the dielectric constant, dielectrics are also characterized by the maximum electric field that they can sustain, known as the dielectric strength. In air, for example, this is 3 x 106 (V/m). {as an interesting aside, let’s estimate the dielectric strength of the membrane surrounding biological cells. There, the resting potential across the cell membrane is roughly 0.1 V, and the thickness of the membrane is roughly 10 nm. The electric field between the membrane can be estimated as simply 0.1 V/10 nm = 10 x 106 V/m, or larger than could be sustained by air. This is probably quite surprising – the electric field inside a membrane is tremendous. These large electric fields can push ions around quite well and are ultimately responsible for the electrical properties of the membrane (including nerve cells)}

Example: The effect of a dielectric on the stored energy of a capacitor in two cases: when isolated from a battery, or when connected to a battery.