7.1 Capacitors and dielectrics  (Page 3/12)

Another interesting biological example dealing with electric potential is found in the cell’s plasma membrane. The membrane sets a cell off from its surroundings and also allows ions to selectively pass in and out of the cell. There is a potential difference across the membrane of about $\text{–70 mV}$ . This is due to the mainly negatively charged ions in the cell and the predominance of positively charged sodium ( ${\text{Na}}^{\text{+}}$ ) ions outside. Things change when a nerve cell is stimulated. ${\text{Na}}^{\text{+}}$ ions are allowed to pass through the membrane into the cell, producing a positive membrane potential—the nerve signal. The cell membrane is about 7 to 10 nm thick. An approximate value of the electric field across it is given by

This electric field is enough to cause a breakdown in air.

Dielectric

The previous example highlights the difficulty of storing a large amount of charge in capacitors. If $d$ is made smaller to produce a larger capacitance, then the maximum voltage must be reduced proportionally to avoid breakdown (since $E=V/d$ ). An important solution to this difficulty is to put an insulating material, called a dielectric    , between the plates of a capacitor and allow $d$ to be as small as possible. Not only does the smaller $d$ make the capacitance greater, but many insulators can withstand greater electric fields than air before breaking down.

There is another benefit to using a dielectric in a capacitor. Depending on the material used, the capacitance is greater than that given by the equation $C={\epsilon }_0\frac{A}{d}$ by a factor $\kappa$ , called the dielectric constant . A parallel plate capacitor with a dielectric between its plates has a capacitance given by

Values of the dielectric constant $\kappa$ for various materials are given in [link] . Note that $\kappa$ for vacuum is exactly 1, and so the above equation is valid in that case, too. If a dielectric is used, perhaps by placing Teflon between the plates of the capacitor in [link] , then the capacitance is greater by the factor $\kappa$ , which for Teflon is 2.1.

Note also that the dielectric constant for air is very close to 1, so that air-filled capacitors act much like those with vacuum between their plates except that the air can become conductive if the electric field strength becomes too great. (Recall that $E=V/d$ for a parallel plate capacitor.) Also shown in [link] are maximum electric field strengths in V/m, called dielectric strengths , for several materials. These are the fields above which the material begins to break down and conduct. The dielectric strength imposes a limit on the voltage that can be applied for a given plate separation. For instance, in [link] , the separation is 1.00 mm, and so the voltage limit for air is