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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 –70 mV . This is due to the mainly negatively charged ions in the cell and the predominance of positively charged sodium ( Na + ) ions outside. Things change when a nerve cell is stimulated. Na + 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

E = V d = –70 × 10 –3 V 8 × 10 –9 m = –9 × 10 6 V/m . size 12{E=V/d"=-""70"´"10" rSup { size 8{-3} } V/ left (8´"10" rSup { size 8{-9} } m right )"=-"9´"10" rSup { size 8{+6} } "V/m"} {}

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 size 12{d} {} is made smaller to produce a larger capacitance, then the maximum voltage must be reduced proportionally to avoid breakdown (since E = V / d size 12{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 size 12{d} {} to be as small as possible. Not only does the smaller d size 12{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 = ε 0 A d size 12{C=e rSub { size 8{0} } { {A} over {d} } } {} by a factor κ size 12{k} {} , called the dielectric constant . A parallel plate capacitor with a dielectric between its plates has a capacitance given by

C = κε 0 A d (parallel plate capacitor with dielectric) . size 12{C= ital "ke" rSub { size 8{0} } A/d} {}

Values of the dielectric constant κ size 12{k} {} for various materials are given in [link] . Note that κ size 12{k} {} 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 κ size 12{k} {} , which for Teflon is 2.1.

Take-home experiment: building a capacitor

How large a capacitor can you make using a chewing gum wrapper? The plates will be the aluminum foil, and the separation (dielectric) in between will be the paper.

Dielectric constants and dielectric strengths for various materials at 20ºc
Material Dielectric constant κ size 12{?} {} Dielectric strength (V/m)
Vacuum 1.00000
Air 1.00059 3 × 10 6
Bakelite 4.9 24 × 10 6 size 12{"24" times "10" rSup { size 8{6} } } {}
Fused quartz 3.78 8 × 10 6 size 12{8 times "10" rSup { size 8{6} } } {}
Neoprene rubber 6.7 12 × 10 6 size 12{"12" times "10" rSup { size 8{6} } } {}
Nylon 3.4 14 × 10 6 size 12{"14" times "10" rSup { size 8{6} } } {}
Paper 3.7 16 × 10 6 size 12{"16" times "10" rSup { size 8{6} } } {}
Polystyrene 2.56 24 × 10 6 size 12{"24" times "10" rSup { size 8{6} } } {}
Pyrex glass 5.6 14 × 10 6 size 12{"14" times "10" rSup { size 8{6} } } {}
Silicon oil 2.5 15 × 10 6 size 12{"15" times "10" rSup { size 8{6} } } {}
Strontium titanate 233 8 × 10 6 size 12{8 times "10" rSup { size 8{6} } } {}
Teflon 2.1 60 × 10 6 size 12{"60" times "10" rSup { size 8{6} } } {}
Water 80

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 size 12{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

Practice Key Terms 6

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Source:  OpenStax, General physics ii phy2202ca. OpenStax CNX. Jul 05, 2013 Download for free at http://legacy.cnx.org/content/col11538/1.2
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