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|
Capacitance is the ratio of charge to voltage.
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.
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
with the SI unit of coulomb per square meter.
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.
rest my brain
The quantity κ [kappa] is unitless.
|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|
|cellulose||3.7 - 7.5||silicon carbide (αSiC)||10.2|
|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|
|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, 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|
|polyester||3.2 - 4.3||cartilage, ear||47|
|polyethylene||2.26||eye, aqueous humor||67|
|polypropylene||2.2 - 2.3||eye, cornea||61|
|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|
Every insulator can be forced to conduct electricity. This phenomena is known as dielectric breakdown.
Say all the vowels. Piezoelectricity is an effect by which energy is converted between mechanical and electrical forms.
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