Week 4: Capacitance 149
that depends only on the free charge and never on the dielectrics present, it will make the more
mathematically involved treatments of this in intermediate and advanced electrodynamics a whole
lot easier later.
Dielectrics, Bound Charge, and Capacitance
At this point you hopefully understand how a dielectric insulator is polarized by a field, how the
polarization appears as a surface charge layer, how the surface charge creates a reaction field that
opposes the applied field and reduces it inside the dielectric so that wecan wrapall of that upin
the simple relation:
Ematerial=E^0
ǫr(257)
whereǫris the relative dielectric permittivity of the material. It seems like a good time to list a few
useful relative permittivities in a table:
Material ǫr Dielectric Strength (MV/m)
Vacuum 1 20 - 40
Air 1.00006 0.4 to 3.0
Paper 3.5
Silicon Dioxide (Quartz) 3.9
Glass 3.7 to 10 9.8 to 13.8
Water 80 30 (Ultra-pure)
Polyethylene 2.25
Ethylene Glycol 37
Strontium titanate 310
Barium strontium titanate 500
Barium titanate 1250Table 2: Table of relative dielectric permittivities at room temperature (20◦C) and some associated
dielectric strenths.
So fine, so what are dielectricsgoodfor? Dielectric insulators are often inserted between the
plates of capacitors! Dielectrics havethree purposesin capacitor design:
a) They mechanically separate the plates.b) They increase the capacitance.c) They prevent dielectric breakdown (most dielectrics have a dielectric strength greater and more
reliable than that of air, which is relatively small and varies with pressure and humidity).You can easily experience all three benefits bybuilding your own capacitor. Take a roll of
aluminum foil, and cut two square pieces 10 cm by 10 cm. Use tape to fasten an unbent paper clip
to each one. Cut a piece of white printer paper 12 cm by 12 cm.
For grins, try setting up the two pieces of foil so they are separated by a perfect 0.1 mm air
gap. Don’t worry, if you wreck the foil you can cut new pieces. Can’tdo it, right? And if you did,
somehow, manage it, the first time you put an equal and opposite charge on the ”plates” they would
attract, and being as how they are made out offoil, they’d bend until they touched, pop, end of
capacitor.