capacitors with dielectrics

Place a dielectric layer between two parallel charged metal plates with an electric field pointing from right to left. (Why not left to right? Well, I read from right to left, so it makes the diagrams easier for me to "read".) The positive nuclei of the dielectric will move with the field to the right and the negative electrons will move against the field to the left. Field lines start on positive charges and end on negative charges, so the electric field within each stressed atom or molecule of the dielectric points from left to right in our diagram — opposite the external field from of the two metal plates. The electric field is a vector quantity and when two vectors point in opposite directions you subtract their magnitudes to get the resultant. The two fields don't quite cancel in a dielectric as they would in a metal, so the overall result is a weaker electric field between the two plates.


Let me repeat that — the overall result is a weaker electric field between the two plates. Let's do some math.

Electric field is the gradient of electric potential (better known as voltage).

Ex = −  ΔV & Ey = −  ΔV & Ez = −  ΔV  ⇒  E = − ∇V
Δx Δy Δz

Capacitance is the ratio of charge to voltage.

C =  Q

Introducing a dielectric into a capacitor decreases the electric field, which decreases the voltage, which increases the capacitance.

V ∝ E (d constant) & C ∝  1  (Q constant) C ∝  1  (d, Q constant)

A capacitor with a dielectric stores the same charge as one without a dielectric, but at a lower voltage. Therefore a capacitor with a dielectric in it is more effective.

About the first discoveries of the Leyden jar. Removing the rod lowers the capacitance. (Air has a lower dielectric constant than water.) Voltage and capacitance are inversely proportional when charge is constant. Reducing the capacitance raises the voltage.

susceptibility, permittivity, dielectric constant

The electric dipole moment of anything — be it an atom stretched in an external electric field, a polar molecule, or two oppositely charged metal spheres — is defined as the product of charge and separation.

p = q r

with the SI unit of coulomb meter, which has no special name.

[Cm = Cm]

The polarization of a region is defined as the dipole moment per unit volume

P =  Σp

with the SI unit of coulomb per square meter.

Cm  =  C
m3 m2

Calculating polarization from first principles is a difficult procedure that is best left to the experts. Don't concern yourself with the details of why the polarization has the value that it has, just accept that it exists and is a function of some variables. And what are those variables? Why they're material and field strength, of course. Different materials polarize to different degrees — we'll use the greek letter χe [chi sub e] to represent this quantity known as the electric susceptibility — but for most every material, the stronger the field (E), the greater the polarization (P). Add a constant of proportionality ε0 and we're all set.

P = ε0χe E

The electric susceptibility is a dimensionless parameter that varies with material. Its value ranges from 0 for empty space to whatever. I bet there are even some bizarre materials for which this coefficient is negative (although I don't know for sure). The constant of proportionality ε0 [epsilon nought] is known as the permittivity of free space and will be discussed a bit more later. For now, it's just a device for getting the units to work out.

C  =  C2   N

m2 Nm2 C

rest my brain

The quantity κ [kappa] is unitless.

material κ   material κ
air 1.005364   quartz, crystalline (∥) 4.60
acetic acid 6.2   quartz, crystalline (⊥) 4.51
alcohol, ethyl (grain) 24.55   quartz, fused 3.8
alcohol, methyl (wood) 32.70   rubber, butyl 2.4
amber 2.8   rubber, neoprene 6.6
asbestos 4.0   rubber, silicone 3.2
asphalt 2.6   rubber, vulcanized 2.9
bakelite 4.8   salt 5.9
calcite 8.0   selenium 6.0
calcium carbonate 8.7   silicon 11.8
cellulose 3.7 - 7.5   silicon carbide (αSiC) 10.2
cement ~2   silicon dioxide 4.5
cocaine 3.1   silicone oil 2.7 - 2.8
cotton 1.3   soil 10 - 20
diamond, type I 5.87   strontium titanate, +25 ℃ 332
diamond, type IIa 5.66   strontium titanate, –195 ℃ 2080
ebonite 2.7   sulfur 3.7
epoxy 3.6   tantalum pentoxide 27
flour 3 - 5   teflon 2.1
freon 12, -150 ℃ (liquid) 3.5   tin antimonide 147
freon 12, +20 ℃ (vapor) 2.4   tin telluride 1770
germanium 16   titanium dioxide (rutile) 114
glass 4 - 7   tobacco 1.6 - 1.7
glass, pyrex 7740 5.0   uranium dioxide 24
gutta percha 2.6   vacuum 1 (exactly)
jet fuel (jet a) 1.7   water, ice, –30 ℃ 99
lead oxide 25.9   water, liquid, 0 ℃ 87.9
lead magnesium niobate 10,000   water, liquid, 20 ℃ 80.2
lead sulfide (galena) 200   water, liquid, 40 ℃ 73.2
lead titanate 200   water, liquid, 60 ℃ 66.7
lithium deuteride 14.0   water, liquid, 80 ℃ 60.9
lucite 2.8   water, liquid, 100 ℃ 55.5
mica, muscovite 5.4   wax, beeswax 2.7 - 3.0
mica, canadian 6.9   wax, carnuba 2.9
nylon 3.5   wax, paraffin 2.1 - 2.5
oil, linseed 3.4   waxed paper 3.7
oil, mineral 2.1      
oil, olive 3.1   human tissues κ
oil, petroleum 2.0 - 2.2   bone, cancellous 26
oil, silicone 2.5   bone, cortical 14.5
oil, sperm 3.2   brain, gray matter 56
oil, transformer 2.2   brain, white matter 43
paper 3.3, 3.5   brain, meninges 58
plexiglas 3.1   cartilage, general 22
polyester 3.2 - 4.3   cartilage, ear 47
polyethylene 2.26   eye, aqueous humor 67
polypropylene 2.2 - 2.3   eye, cornea 61
polystyrene 2.55   eye, sclera 67
polyvinyl chloride (pvc) 4.5   fat 16
porcelain 6 - 8   muscle, smooth 56
potassium niobate 700   muscle, striated 58
potassium tantalate niobate, 0 ℃ 34,000   skin 33 - 44
potassium tantalate niobate, 20 ℃ 6,000   tongue 38
Dielectric constant for selected materials (~300 K except where indicated)

dielectric breakdown

Every insulator can be forced to conduct electricity. This phenomena is known as dielectric breakdown.

piezoelectric effect

Say all the vowels. Piezoelectricity is an effect by which energy is converted between mechanical and electrical forms.

type sounds produce
changes in …
which cause
changes in …
which result in
changes in …
carbon granule density resistance voltage
condenser plate separation capacitance voltage
dynamic coil location flux voltage
piezoelectric compression polarization voltage
Microphones and how they work