4.4 Linear Dielectrics F

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Dulcie Cole
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1 4.4 Lina Dilctics F stal F stal θ magntic dipol imag dipol supconducto Suscptiility, mitivility, Dilctic Constant I is not too stong, th polaization is popotional to th ild. χ (sinc D, D is lctic displacmnt om ρ ) D M χ is calld th lctic suscptiility. χ, χ m H D ( 1 χ ), is calld th pmittivity. 1 χ is calld th lativ pmittivity, o dilctic constant. Matial Dilctic Constant Matial Dilctic Constant Vacuum 1 Bnzn.8 Hlium 1.65 Diamond 5.7 Ai 1.54 Wat 8.1 Nitogn 1.55 KTaNO 4, What is high K matial? Vacuum It may dischag o an lctic ild high than. xampl: A mtal sph o adius a cais a chag. It is suoundd, out to adius, y lina dilctic matial o pmittivity. Find th potntial at th cnt. D ˆ >, ˆ and > > a, ˆ 4π 4π 4π a

2 a 1 1 V d π 4 χ > > a, χ ˆ 4π ρ d 4π a χ a, ( ˆ ) and 4πa χ ˆ 4π, () I th spac is ntily illd with a homognous lina dilctic, thn D ρ and D Whn cossing th ounday: D vacuum xampl: A paalll-plat capacito is illd with insulating matial o dilctic constant. What ct dos this hav on its capacitanc? AD A AD A D,, up, D,, up, out,, up,, down, down, A in V d d, C Cvacuum A V d , doun, out 4.4. Bounday Valu olm with Lina Dilctics I w plac chag insid a lina dilctic, D χ ρ ( χ ) χ ρ 1 χ I w plac th chag on th ounday: D D, aov, low aov, aov low, low V V aov n n aov low low, continuity: V aov Vlow

3 xampl: A sph o homognous lina dilctic matial is placd in an othwis uniom lctic ild. Find th lctic ild insid th sph. Mthod 1: Vout Vin Th chag is on th ounday out in Only ound chag xists, no chag. >> R, V out cosθ R, Vin Vout and Vin Vout A V out cosθ cosθ, V B cosθ in A A R BR, B B, A R R R / V V z in cosθ zˆ zˆ z Mthod : Uniomly polaizd sph with polaization zˆ insid. zˆ may poduc lctic ild Total ild insid: zˆ inducing th polaization: zˆ zˆ χ χ χ zˆ zˆ χ χ xampl: Suppos th nti gion low th plan z is illd with uniom lina dilctic matial o suscptiility χ. Calculat th oc on a point chag q situatd a distanc d aov th oigin. Considing q without dilctic matial: q 1 d z, low 4π ( ) d d Considing dilctic matial without q: zˆ z, aov and

4 z, low Total ct: 1 χ π χ Total ound chag: zˆ χ qd ( d ) / z, low, total χ 4π qd d χ da q χ Us imag chag χ q χ at z -d to solv th polm. V 1 4π x y q ( z d ) x y ( z d ) z > 1 V 4π x q y ( z d ) 1 q attactiv oc on q: F ( d ) z ˆ 4π z < 4.4. ngy in Dilctic Systms To chag up a capacto, it taks ngy o dw Vd 1 W d CV C C Chang o capacitanc in dilctic matials: C C incas th ngy caus o an incas o chag dilctic vacuum W ρ Vdτ, D ( DV ) ( D) V D V Choos V at. W D dτ ( ) ρ W ( D) Vdτ ( D) Vdτ ( D) V ( DV ) D 1 o a lina dilctic D ( D )

5 W 1 D dτ l Focs on Dilctics inging ild V wl wl d d C vacuum C dilctic w w w Cvacuum C x ( l x) ( l χx) d d d Assum that th total chag on th plat is constant ( F dw C dc 1 dc χ w d x CV ), V V attactiv oc W 1 C I you stat om constant voltag, th wok supplid y a atty must includd. d 1 F CV V d I th voltag is constant and th chag is vaying, you must includ th oc du to th atty o maintaining a constant voltag. xcis: 4.18, 4., Dilctic matial incas th capacitanc o a capacito sto much mo chags. /

6 . Folcticity: BaTiO olctic antiolctic Tansition tmpatu? Cui-Wiss law?

DIELECTRICS MICROSCOPIC VIEW

DIELECTRICS MICROSCOPIC VIEW HYS22 M_ DILCTRICS MICROSCOIC VIW DILCTRIC MATRIALS Th tm dilctic coms fom th Gk dia lctic, wh dia mans though, thus dilctic matials a thos in which a stady lctic fild can st up without causing an appcial