UNIT-III-Dielectric and Magnetic properties of materials

Transcription

1 UNIT-III-Dilctric and Magntic prprtis f matrials Syllabus: Dilctric cnstant and plarizatin f dilctric matrials - Typs f plarizatin Equatin fr intrnal fild in liquids and slids ( n dimnsinal) Clausius Mstti quatin Frr and Piz lctricity (qualitativ) Frquncy dpndnc f dilctric cnstant- Imprtant applicatins f dilctric matrials. Classificatin f dia, para and frrmagntic matrials. Curi Tmpratur Hystrisis in frrmagntic matrials. Sft and Hard magntic matrials. Applicatins. Intrductin Dilctrics ar insulating r nn-cnducting cramic matrials and ar usd in many applicatins such as capacitrs, mmris, snsrs and actuatrs. Dilctrics ar insulating matrials that xhibit th prprty f lctrical plarizatin, thrby thy mdify th dilctric functin f th vacuum. A dilctric matrial is any matrial that supprts charg withut cnducting it t a significant dgr. In principl all insulatrs ar dilctric, althugh th capacity t supprt charg varis gratly btwn diffrnt insulatrs. Althugh ths matrials d nt cnduct lctrical currnt whn an lctric fild is applid, thy ar nt inrt t th lctric fild. Th fild may caus a slight shift in th balanc f charg within th matrial t frm an lctric dipl. Thus th matrials is calld dilctric matrial. Dilctric matrials ar usd in many applicatins, frm simpl lctrical insulatin t snsrs and circuit cmpnnts. Faraday was carrid ut th first numrical masurmnts n th prprtis f insulating matrials whn placd btwn th tw paralll plats (capacitr), ths matrials, h calld as dilctrics. H has fund that th capacity f a cndnsr was dpndnt n th natur f th matrial sparating th cnducting surfac. This discvry ncuragd furthr mpirical studis f insulating matrials aiming at maximizing th amunt f charg that can b strd by a capacitr. In sarch f suitabl dilctric matrials fr spcific applicatins, ths matrials hav bcm incrasingly cncrnd with th dtaild physical mchanism gvrning th bhavir f ths matrials. Th diffrnc btwn dilctric matrial and insulatr dpnds n its applicatin. Insulating matrials ar usd t rsist flw f currnt thrugh it, n th thr hand dilctric matrials ar usd t str lctrical nrgy. In cntrast t th insulatin aspct, th dilctric phnmna hav bcm mr gnral and fundamntal, as it has th rigin with th dilctric plarizatin.

2 Elctric dipls: Upn applicatin f a dc r static lctric fild, thr is a lng rang migratin f chargs. Hwvr, thr is a limitd mvmnt f chargs lading t th frmatin f charg dipls and th matrial, in this stat, is cnsidrd as plarizd. Ths dipls ar alignd in th dirctin f th applid fild. Th nt ffct is calld Plarizatin f th matrial. A dilctric supprts charg by acquiring a plarisatin in an lctric fild, whrby n surfac dvlps a nt psitiv charg whil th ppsit surfac dvlps a nt ngativ charg. This is mad pssibl by th prsnc f lctric dipls tw ppsit chargs sparatd by a crtain distanc n a micrscpic scal. 1. If tw discrt chargd particls f ppsit chargs ar sparatd by a crtain distanc, a dipl mmnt μ ariss.. If th cntr f psitiv charg within a givn rgin and th cntr f ngativ charg within th sam rgin ar nt in th sam psitin, a dipl mmnt μ ariss. Fr xampl, in th diagram blw th cntr f psitiv charg frm th 8 catins shwn is at X, whil th cntr f ngativ charg is lcatd sm distanc away n th anin. Th scnd viw f dipl mmnt is mr usful, sinc it can b applid vr a larg ara cntaining many chargs in rdr t find th nt dipl mmnt f th matrial. Th dipls can b alignd as wll as b inducd by th applid fild.

3 Nt that in th quatin fr dipl mmnt, r is a vctr (th sign cnvntin is that r pints frm ngativ t psitiv charg) thrfr th dipl mmnt μ is als a vctr Elctric fild intnsity r lctric fild strngth ( E ) Th frc xprincd by a unit tst charg is knwn as lctric fild strngth E Q E..(1) 4r whr is th prmittivity r dilctric cnstant f th mdium in which lctric charg is placd. Fr vacuum = = X1-1 Fm -1 Elctric flux dnsity r lctric displacmnt vctr ( D) Th lctric flux dnsity r lctric displacmnt vctr is th numbr f flux lins crssing nrmal t a unit surfac ara. Th lctric flux dnsity at a distanc frm th pint charg Q is Q D..() 4r thn frm (1) and () D = E.. () Dilctric cnstant ( r ) Th dilctric cnstant f a matrial is dfind as th rati f th prmittivity f th mdium () t th prmittivity f fr spac ( ). It can als dfind as th rati f th capacitanc with dilctric (C d ) and with air ( C A ) btwn th plats. Cd r..(4) C Capacitanc: Th prprty f a cnductr r systm f cnductr that dscribs its ability t str lctric charg. A C = q / V = A ε / d whr C is capacitanc f capacitr q is charg n th capacitr plat V is ptntial diffrnc btwn plats A is ara f capacitr plat ε is prmittivity f mdium d is distanc btwn capacitr plats Units: Farad. Plarizatin Whn an lctric fild is applid t a matrial with dilctrics, th psitiv chargs ar displacd ppsit t th dirctin f th fild and ngativ chargs displacd in th dirctin f th fild. Th displacmnt f ths tw chargs crat a lcal dipl, cratin f dipl by applying lctric fild is calld as plarizatin.

4 Plarizatin is dfind as inducd dipl mmnt pr unit vlum. P (5) Vlum Plarisability Th plarizatin P is dirctly prprtinal t th lctric fild strngth E P E (6) P E Whr prprtinality is cnstant calld as plarisability. Th plarisability is dfind as plarizatin pr unit applid lctric fild. If th matrial cntains N numbr f dipls pr unit vlum thn P NE.(7) Rlatin btwn plarizatin and dilctric cnstant Lt us apply Gauss thrm fr paralll plat cndnsr. q EdA Whr σ is th charg pr unit ara. q E A q E. (1) A Lt a dilctric slab placd btwn tw plats. Du t plarizatin, chargs appar n th tw facs f th slab, and stablish yt anthr fild within th dilctric mdia. Lt this fild b Eʹ. Th dirctin f Eʹ will b ppsit t that f E. Th rsultant fild E in th matrial can b writtn as, E = E - Eʹ.()

5 If σ p is th charg/unit ara n th insrtd dilctric slab surfacs, thn by fllwing quatin (1), w writ, ' ' q p E. () A Frm (1), () and (), p ` E. r E p (4) Sinc th magnitud f plarizatin P = dipl mmnt/ Unit Vlum But dipl mmnt = inducd charg X distanc Thrfr P = inducd charg/ Ara= p W knw that lctric displacmnt fildr lctric flux dnsity D is givn by charg /unit ara D = q/a= Thrfr Equatin 4 bcms E D P P D E..(5) in fr spac whr thr is n dilctric P= D E But in dilctric mdia th D changs. Frm lctrstatics D E Frm () r P E E r P E ( 1).(6) P E r 1 r Whr is lctric suscptibility f th dilctric mdium. It dsn t hav any units. Sinc P and E ar vctrs qn (6) can b writtn as

6 P E ( r 1) (7) This quatin rprsnts plarizatin vctr. Typs f plarizatin Dilctric plarizatin is th displacmnt f charg particls with th applid lctric fild. Th displacmnt f lctric chargs rsults in frmatin f lctric dipl mmnt in atms, ins r mlculs f th matrial. Thr ar fur diffrnt typs f plarizatin, thy ar listd blw. 1. Elctric plarizatin,. Inic plarizatin,. Orintatin plarizatin 4. Spac charg plarizatin Elctric plarizatin Th displacmnt f th psitivly chargd nuclus and th ngativly chargd lctrns f an atm in ppsit dirctins, n applicatin f an lctric fild, rsult in lctrnic plarizatin. On applying a fild, th lctrn clud arund th nuclus shifts twards th psitiv nd f th fild. As th nuclus and lctrn clud ar sparatd by a distanc, dipl mmnt is cratd within ach atm. Th xtnt f this shift is prprtinal t th fild strngth. Inducd dipl mmnt E E Whr is calld lctrnic plarizability. Th dipl mmnt pr unit vlum is calld lctrnic plarizatin. It incrass with incras f vlum f th atm. This kind f plarizatin is mstly xhibitd in mnatmic gass.(.g. H, N, Ar, Kr, X tc..)

7 It is indpndnt f tmpratur. It ccurs nly at ptical frquncis (1 15 Hz) Vast fast prcss: 1-15 ~1-16 s. Calculatin f lctrnic plarizability: Elctrnic plarizatin can b xplaind by classical mdl f an atm in gasss. In gass th atms ar assumd that th intractin amng th atms is ngligibl. Hr th nuclus f charg Z is surrundd by an lctrn clud f charg Z distributd in th sphr f radius R. Z Charg dnsity, (1) ( 4 / ) R Whn an lctric fild E is applid, th nuclus and lctrns xprinc Lrntz frc f magnitud ZE in ppsit dirctin. Thrfr th nuclus and lctrns ar pulld apart. As thy ar pulld apart a Culmb frc dvlps btwn thm. At quilibrium ths tw frcs ar qual and nuclus and lctrn clud ar sparatd by a small distanc x. Lrntz frc = ZE () Charg nclsd int hsphrfradiusx Culmb Frc = Z X 4 x Th charg nclsd = 4 x 4 Z Frm quatin (1) = x 4 R Zx R =

8 Z Hnc Culmb frc is = 4 x Zx Z x () X R 4 R At quilibrium Lrntz frc = Culmb frc (quatin () qual t ()) Z x ZE 4 R 4 R E x (4) Z Th displacmnt f th lctrn clud is prprtinal t applid lctric fild. Th lctric dipl mmnt Zx Z4 R E Z 4 R E E E (5) P Whr 4 R is calld lctrnic plarizability. N N E Whr N is th numbr f atms/m But plarizatin P E ( r 1) N E N ( r 1) r ( r 1) N Inic Plarizatin Inic plarizatin ccurs in inic slids such as NaCl, KBr, and LiBr. Whn an lctric fild is applid t an inic slid th psitiv and ngativ ins displac t thir rspctiv plaritis crating an lctric dipl this is calld as inic plarizatin. In th absnc f an lctric fild thr is n displacmnt f ins. Whn an lctric fild is applid an inducd dipl mmnt i is prducd. Lt x 1 and x b th displacmnt f psitiv and ngativ in rspctivly. Thn th inducd dipl mmnt.

9 x 1 x ) (6) i ( Lt F b rstring frc F x 1 x x 1 1 x Frm mchanics th spring cnstant f mass attachd t a spring is givn by =m At quilibrium th Lrntz frc = rstring frc E m x E E Thrfr x Thn x 1 m m E x M 1 1 E m M i E (7) 1 1 Whr i is calld as inic plarisability (8) m M Orintatin Plarizatin Orintatin plarizatin ccurs nly in plar mlculs (th mlculs which hav prmannt dipl mmnt g H O, Phnl, tc.). Whn an lctric fild is applid t a plar mlcul, th dipls xprinc a trqu and try t align paralll t th applid fild. Cnsidr a plar mlcul subjctd t an lctric fild E. Th alignmnt f lctric dipl with th lctric fild is similar t th alignmnt f magntic dipl with th applid magntic fild in paramagntic matrial. Th xprssin fr plarizatin can b btaind frm th thry f paramagntism. Th rintatin plarizatin is givn as N E P E KT (9) Whr is calld as rintatin plarisability KT (1) Spac charg plarizatin

10 Spac charg plarizatin ccurs du t th accumulatin f chargs at th lctrds r at intrfacs in a multiphas matrials. In th prsnc f an applid fild, th mbil psitiv ins and ngativ ins migrat tward th ngativ lctrd and psitiv lctrd rspctivly t an apprciabl distanc giving ris t rdistributin f chargs, but thy rmain rmains in th dilctric matrial (lctrd is blcking). Th spac charg plarizatin can b dfind as th rdistributin f chargs du t th applid lctric fild and th chargs accumulat n th surfac f th lctrds. It ccurs whn th rat f charg accumulatin is diffrnt frm rat f charg rmval. Spac charg plarizatin is nt significant in mst f th dilctric matrials. Intrnal fild in liquids and slids (n dimnsinal) In gass stat th atms ar sparatd by larg distancs and th intractin btwn th atms can b nglctd. Whn an xtrnal lctric fild E is applid, th intnsity f th lctric fild xprincd by an atm in gass stat will b qual t th applid lctric fild E. In slids and liquids, th atms ar cls t ach thr lading t strng intractin btwn thm. In slids and liquids th intnsity f th lctric fild at a givn pint f th matrial is nt qual t th applid lctric fild but qual t intrnal fild which is th sum f applid lctric fild and fild du t thr dipls prsnt in th matrial. Intrnal fild E i =E+E` (1) Th intrnal fild can b calculatd by Epstin mdl in th cas f n dimnsinal atmic array. Elctric fild alng th axis f an lctric dipl Cnsidr an lctric dipl f lngth d and charg Q, th fild alng th axis f th dipl at pint A is th sum f th lctric fild du t +Q and Q. Q Th lctric fild du t +Q at pint A is E 4 ( x d) Q Th lctric fild du t +Q at pint A is E 4 ( x d) Elctric fild f dipl at A is E A E E Q ( x d) ( x d) Q dx 4 ( x d) ( x d)

11 sinc x >> d (x-d) (x+d) x thn Q dx 4dQ 4 4 x 4 x i sinc dq = i E A () 4 x Cnsidr an array f n dimnsinal atms alng x- axis. Th all th atms ar similar, qually spacd and hav inducd lctric dipl mmnt i in an applid lctric fild E. Th lctric fild xprincd at th A is th sum f lctric filds f thr dipls and applid lctric fild E. Th fild at th inducd dipl B and L which ar at a distanc x is i E B EL 4 x Th lctric fild at A du t th inducd dipl C and M which ar at a distanc x is i E C EM 4 (x) Thrfr th fild du t thr dipls is lctric A du t E =E B + E L +E C +E M +E D +E N +. () i E 4 x 4i E 4 x i 4 x i 4 (x) i 4 (x) i 4 (x) i 4 (x) 4i 4 (x) 4i 4 (x) i E 1... x whr i E x 1.i Thrfr th intrnal fild Ei E (4) x

12 Th lcal fild in a thr dimnsinal slid is similar th abv quatin th numbr dnsity N f atms rplacs 1/a. Sinc Nμ i =P and 1./π is rplacd by γ. Thn th intrnal fild is E i 1.Ni 1.P E E P E γ dpnds n th intrnal structur Fr a cubic symmtry crystal γ valu is1/ E i P E (5) Th fild givn by th abv quatin is calld Lrntz fild. Clausius - Mstti quatin Lt us cnsidr lmntal slid dilctric which xhibits nly lctrnic plarizatin. If is th lctrnic plarisability pr atm, it is rlatd t th bulk plarizatin P thrugh th rlatin P N E i (6) P (7) NE i Whr N is th numbr f atms pr unit vlum and E i is th lcal fild using th rlatin (5) P (8) P N E By using th rlatin btwn th plarizatin and prmittivity w hav P E ( 1) (9) r P E ( r 1) (1) Substitut th valu f E frm (1) in (8) N ( P P 1) r P N ( 1) r 1 r ( 1) r

13 r 1 r N (11) Th abv quatin is knwn as Clausius Mstti quatin which is valid fr nnplar slids Dilctric lss: Dilctric lss is th dissipatin f nrgy thrugh th mvmnt f chargs in an altrnating lctrmagntic fild as plarisatin switchs dirctin. An fficint dilctric supprts a varying charg with minimal dissipatin f nrgy in th frm f hat is calld dilctric lss. Thr ar tw main frms f lss that may dissipat nrgy within a dilctric. In cnductin lss, a flw f charg thrugh th matrial causs nrgy dissipatin. Dilctric lss is spcially high arund th rlaxatin r rsnanc frquncis f th plarisatin mchanisms as th plarisatin lags bhind th applid fild, causing an intractin btwn th fild and th dilctric s plarisatin that rsults in hating. This is illustratd by th diagram blw (rcall that th dilctric cnstant drps as ach plarisatin mchanism bcms unabl t kp up with th switching lctric fild.) Dilctric lss quantifis a dilctric matrial's inhrnt dissipatin f lctrmagntic nrgy int,.g., hat. It can b rprsntd in trms lss tangnt tan δ and is dfind: Dilctric Brakdwn : Th dilctric brakdwn is th suddn chang in stat f a dilctric matrial subjctd t a vry high lctric fild, undr th influnc f which, th lctrns ar liftd int th cnductin band causing a surg f currnt, and th ability f th matrial t rsist th currnt flw suffrs a brakdwn. Or Whn a dilctric matrial lss its rsistivity and prmits vry larg currnt t flw thrugh it, thn th phnmnn is calld dilctric brakdwn Or At high lctric filds, a matrial that is nrmally an lctrical insulatr may bgin t cnduct lctricity i.. it cass t act as a dilctric. This phnmnn is knwn as dilctric brakdwn.

14 Frquncy dpndnc f plarizability: On applicatin f an lctric fild, plarizatin prcss ccurs as a functin f tim. Th plarizatin P(t) as a functin f tim. Th plarizatin P(t) as a functin f tim t is givn by P(t) = P[ 1- xp ( - t / t r )] Whr P max. Plarizatin attaind n prlngd applicatin f static fild. t r - rlaxatin tim fr particular plarizatin prcss Th rlaxatin tim t r is a masur f th tim scal f plarizatin prcss. It is th tim takn fr a plarizatin prcss t rach.6 f th max. valu. Elctrnic plarizatin is xtrmly rapid. Evn whn th frquncy f th applid vltag is vry high in th ptical rang ( 1 15 Hz), lctrnic plarizatin ccurs during vry cycl f th applid vltag. Inic plarizatin is du t displacmnt f ins vr a small distanc du t th applid fild. Sinc ins ar havir than lctrn clud, th tim takn fr displacmnt is largr. Th frquncy with which ins ar displacd is f th sam rdr as th lattic vibratin frquncy ( 11Hz). Hnc, at ptical frquncis, thr is n inic plarizatin. If th frquncy f th applid vltag is lss than 11 Hz, th ins rspnd. Orintatin plarizatin is vn slwr than inic plarizatin. Th rlaxatin tim fr rintatin plarizatin in a liquid is lss than that in a slid. Orintatin plarizatin ccurs, whn th frquncy f applid vltag is in audi rang (11 Hz). Spac charg plarizatin is th slwst prcss, as it invlvs th diffusin f ins vr svral intratmic distancs. Th rlaxatin tim fr this prcss is rlatd t frquncy f ins undr th influnc f applid fild. Spac charg plarizatin ccurs at pwr frquncis (5-6 Hz).

15 Frquncy Dpndnc f dilctric cnstant Whn a dilctric matrial is subjctd t an altrnating fild, th plarizatin cmpnnt rquird t fllw th fild in rdr t cntribut t th ttal plarizatin f th dilctrics. Th rlativ prmittivity which is a masur f th plarizatin als dpnds n th frquncy. Th dpndnc f r n frquncy f th lctric fild is shwn in th figur. At vry lw frquncy, th dipls will gt sufficint tim t rint thmslvs cmpltly with th fild and all typs f plarizatin xist. Sinc th dilctric is charactrizd by plarisability ( = + i + ) at lw frquncy i. at radifrquncy rgin th dilctric cnstant will b du t all plarisability. Th rintatin plarizatin, which is ffctiv at lw frquncis, is dampd ut fr highr frquncis. In th micrwav rgin th dipls fail t fllw th fild and th plarisability rducs t ( = + i ), as a rsult r dcrass t sm amunt. In th IR rgin th inic plarizatin fails t fllw th fild s th cntributin f inic plarizatin dis away. In this rgin nly lctrnic plarizatin cntributs t th ttal plarizatin. Thrfr ( = ) th r still dcrass and nly lctrnic plarizatin xist. W knw that P N E ( 1 E r ) Thn th rlativ prmittivity is r N 1 (1) In th ultravilt rgin vn th lctrn clud culd nt fllw th fild and lctrnic plarizability bcms almst zr and th prmittivity bcms n. 1 r X ray Fr xampl at lw frquncy th dilcric cnstant f watr at rm tmpratur is abut 8, but it fall t abut 1.8 in th ptical rgin.

16 Frquncy Dpndnc f dilctric lss: Dilctric lss tnds t b highr in matrials with highr dilctric cnstants. This is th dwnsid f using ths matrials in practical applicatins. Dilctric lss is utilisd t hat fd in a micrwav vn: th frquncy f th micrwavs usd is cls t th rlaxatin frquncy f th rintatinal plarisatin mchanism in watr, maning that any watr prsnt absrbs a lt f nrgy that is thn dissipatd as hat. Th xact frquncy usd is slightly away frm th frquncy at which maximum dilctric lss ccurs in watr t nsur that th micrwavs ar nt all absrbd by th first layr f watr thy ncuntr, thrfr allwing mr vn hating f th fd. Frrlctrics Blw crtain tmpratur it is fund that sm matrials spntanusly acquir an lctric diplmmnt. Ths matrials ar calld as frrlctric matrials r frrlctrics.th tmpratur at which frrlctric prprty f th matrial disappars is calld as frrlctric Curi tmpratur. Frrlctric matrials ar anistrpic crystals which xhibit a hystrsis curv P vrsus E which can b xplaind by dmain hypthsis. Frr lctricity: Frr lctric matrials ar an imprtant grup nt nly bcaus f intrinsic Frr lctric prprty, but bcaus many pssss usful piz lctric, birfringnt and lctr ptical prprtis. Th intrinsic Frr lctric prprty is th pssibility f

17 rvrsal r chang f rintatin f th plarizatin dirctin by an lctric fild. This lads t hystrsis in th plarizatin P, lctric fild E rlatin, similar t magntic hystrsis. Abv a critical tmpratur, th Curi pint T c, th spntanus plarizatin is dstryd by thrmal disrdr. Th prmittivity shws a charactristic pak at T c. Piz Elctric Matrials and Thir Applicatins: Singl crystal f quartz is usd fr filtr, rsnatr and dlay lin applicatins. Natural quartz is nw bing rplacd by synthtic matrial. Rchll salt is usd as transducr in gramphn pickups, ar phns, haring aids, micrphns tc. th cmmrcial cramic matrials ar basd n barium titanat, lad zircnat and lad titanat. Thy ar usd fr high vltag gnratin (gas lightrs), acclrmtrs, transducrs tc. Piz lctric smicnductrs such as GaS, ZnO & CdS ar usd as amplifirs f ultrasnic wavs. Applicatins f Dilctric Matrials: Almst any typ f lctrical quipmnt mplys dilctric matrials in sm frm r anthr. Wirs and cabls that carry lctrical currnt, fr xampl, ar always catd r wrappd with sm typ f insulating (dilctric) matrial. Sphisticatd lctrnic quipmnt such as rctifirs, smicnductrs, transducrs, and amplifirs cntain r ar fabricatd frm dilctric matrials. Th insulating matrial sandwichd btwn tw cnducting plats in a capacitr is als mad f sm dilctric substanc. Liquid dilctrics ar als mplyd as lctrical insulatrs. Fr xampl, transfrmr il is a natural r synthtic substanc (minral il, silicn il, r rganic strs, fr xampl) that has th ability t insulat th cils f a transfrmr bth lctrically and thrmally.

18 1. Capacitrs Charg sparatin in a paralll-plat capacitr causs an intrnal lctric fild. A dilctric (rang) rducs th fild and incrass th capacitanc. Cmmrcially manufacturd capacitrs typically us a slid dilctric matrial with high prmittivity as th intrvning mdium btwn th strd psitiv and ngativ chargs. This matrial is ftn rfrrd t in tchnical cntxts as th capacitr dilctric. Th mst bvius advantag t using such a dilctric matrial is that it prvnts th cnducting plats, n which th chargs ar strd, frm cming int dirct lctrical cntact. Mr significantly, hwvr, a high prmittivity allws a gratr strd charg at a givn vltag. This can b sn by trating th cas f a linar dilctric with prmittivity ε and thicknss btwn tw cnducting plats with unifrm charg dnsity σ ε. In this cas th charg dnsity is givn by and th capacitanc pr unit ara by Frm this, it can asily b sn that a largr ε lads t gratr charg strd and thus gratr capacitanc. Dilctric matrials usd fr capacitrs ar als chsn such that thy ar rsistant t inizatin. This allws th capacitr t prat at highr vltags bfr th insulating dilctric inizs and bgins t allw undsirabl currnt.. Dilctric rsnatr A dilctric rsnatr scillatr (DRO) is an lctrnic cmpnnt that xhibits rsnanc f th plarizatin rspns fr a narrw rang f frquncis, gnrally in th micrwav band. It cnsists f a "puck" f cramic that has a larg dilctric cnstant and a lw dissipatin factr. Such rsnatrs ar ftn usd t prvid a frquncy rfrnc in an scillatr circuit. An unshildd dilctric rsnatr can b usd as a Dilctric Rsnatr Antnna (DRA).

19 . Insulatrs- Rquird Qualitis f Gd Insulating Matrials: Th rquird qualitis can b classifid as undr lctrical, mchanical, thrmal and chmical applicatins. i) Elctrical: 1. lctrically th insulating matrial shuld hav high lctrical rsistivity and high dilctric strngth t withstand high vltag..th dilctric lsss must b minimum.. Liquid and gasus insulatrs ar usd as clants. Fr xampl transfrmr il, hydrgn ii) Mchanical: 1. insulating matrials shuld hav crtain mchanical prprtis dpnding n th us t which thy ar put.. Whn usd fr lctric machin insulatin, th insulatr shuld hav sufficint mchanical strngth t withstand vibratin. iii) Thrmal: Gd hat cnducting prprty is als dsirabl in such cass. Th insulatrs shuld hav small thrmal xpansin and it shuld b nn-ignitabl. iv) Chmical: 1. chmically, th insulatrs shuld b rsistant t ils, liquids, gas fums, acids and alkali s.. Th insulatrs shuld b watr prf sinc watr lwrs th insulatin rsistanc and th dilctric strngth. and hlium ar Othr Applicatins: Slid dilctrics ar prhaps th mst cmmnly usd dilctrics in lctrical nginring, as vry gd insulatrs. Sm xampls includ prclain, glass, and mst plastics. Air, nitrgn and sulfur hxaflurid ar th thr mst cmmnly usd gasus dilctrics. Industrial catings such as paryln prvid a dilctric barrir btwn th substrat and its nvirnmnt. Minral il is usd xtnsivly insid lctrical transfrmrs as a fluid dilctric and t assist in cling. Dilctric fluids with highr dilctric cnstants, such as lctrical grad castr il, ar ftn usd in high vltag capacitrs t hlp prvnt crna discharg and incras capacitanc. Bcaus dilctrics rsist th flw f lctricity, th surfac f a dilctric may rtain strandd xcss lctrical chargs. This may ccur accidntally whn th dilctric is rubbd (th triblctric ffct). This can b usful, as in a Van d Graaff gnratr r lctrphrus, r it can b ptntially dstructiv as in th cas f lctrstatic discharg. Pizlctric matrials ar anthr class f vry usful dilctrics which ar usd fr transducrs and snsrs. Frrlctric matrials ftn hav vry high dilctric cnstants, making thm quit usful fr capacitrs.

20 Magntic Matrials Classificatin f dia, para and frrmagntic matrials. Curi Tmpratur Hystrisis in frrmagntic matrials. Sft and Hard magntic matrials. Applicatins. Intrductin Th matrials that can b magntisd ar calld as magntic matrials Magntic dipls and magntic dipl mmnt Any tw ppsit pls sparatd by distanc cnstitut an magntic dipl. A magnt is a dipl which has nrth pl and suth pl and th lngth f th magnt is th distanc f sparatin. Magntic dipl mmnt is th prduct f magntic pl strngth (m) and lngth f th magnt(l) m ml. Magntic fild intnsity (H) Th frc xprincd by a unit nrth pl ( f strngth 1 Wb) placd at a pint in a magntic fild is a masur f th` fild intnsity r `fild strngth Magntisatin r Intnsity f magntisatin (M) Magntizatin may b dfind as th prcss f cnvrting a nn magntic bar int a magntic bar Magntic Inductin Or Flux Dnsity(B) Magntic inductin r magntic flux dnsity in an any matrial is th numbr f lins f magntic frc passing thrugh unit ara prpndicular. Wb/m B ( M H) A Magntic Suscptibility (χ) Th rati f th magntizatin t th fild strngth M H Prmability () Th ratin f th amunt f magntic dnsity B t th applid magntic fild. It is usd t masur magntic lins f frcs passing thrugh th matrial B H Origin f Magntic mmnt Bhr Magntn Whn vr a chargd particl has an angular mmntum, it cntributs t prmannt dipl mmnt. Cnsidr an hydrgn atm, lctrn rvlving arund th nuclus is qual t a currnt lp. Orbital angular mmntum ariss du this currnt lp. Th lctrn spin angular mmntum and nuclar spin angular mmntum ariss du t spin f th lctrn and nuclus rspctivly.

21 Thr ar thr angular mmntum f an atm 1. Orbital angular mmntum f th lctrn. Elctrn spin angular mmntum. Nuclar spin angular mmntum Ttal angular magntic mmntum Bhr Magntn Th rbital angular mmntum f an lctrn in an atm can b xprssd in trms f atmic unit f magntic mmnt calld Bhr Magntn. h B 4m Classificatin f th magntic matrials Th magntic matrials ar bradly classifid in t tw typs. Thy ar 1. Ths atms r mlculs d nt hav prmannt dipl mmnts and. Ths atms r mlculs hav prmannt dipl mmnts vn in th absnc f xtrnal magntic fild. Basd n th magntic mmnts th matrials ar classifid as Diamagntic matrials Paramagntic matrials Frrmagntic matrials Anti frrmagntic matrials Frri magntic matrials Diamagntic matrials Dia magntic matrials has cmpltly filld sub shll lctrnic structur rsultant magntic mmnt is zr. Thr ar n prmannt dipls and hnc th magntic ffct ar small. Whn a diamagntic matrial is placd in a magntic fild, thr will b a small inducd magntic mmnt which always pps th applid fild(accrdanc with Lnz`s Law). Du t this ffct th magntic lins f frcs xplld frm th matrials. Mstly th cvalnt and inic crystals xhibits th diamagntic prprtis. Th magntic suscptibility is small and ngativ and is indpndnt f tmpratur. Th xampls f diamagntic matrials ar 1. Cvalnt matrials such as Si,G, diamnd, ii) sm mtals such as cppr, silvr, gld.

22 Para magntic matrials. Atms r mlculs f paramagntic matrials hav prmannt magntic mmnt rintd in randm dirctin. Th magntic intractin btwn th dipls try t align thmslvs but th thrmal agitatin disturb th alignmnt. In paramagntic matrials vctr sum f magntic mmnts is zr in th absnc f fild. Whn an xtrnal magntic fild is applid th partial alignmnt f prmannt atmic magntic mmnts ccur Whn a magntic fild is applid, th individual magntic mmnt taks th alignmnt alng th applid fild as shwn in figur. Th magntizatin f a paramagntic matrial incrass with th incras in th applid fild. Incras in tmpratur it rducs th magntizatin and dstrys th alignmnt f dipls with applid fild. Cnsidr a paramagntic matrial placd in nn-unifrm magntic fild. Th paramagntic matrials xprinc a nt magntic frc twards th gratr fild. Th magntic suscptibility is small and psitiv and is dpndnt n tmpratur. Th suscptibility f th magntic fild is givn by C T Whr C is th curi tmpratur and T is th tmpratur in Klvin scal. Th magntizatin in frrmagntic matrial is linar and gts saturatd whn a larg magntic fild is applid at lw tmpratur. Th xampls f paramagntic matrials ar Mg, gasus and liquid xygn, frrmagntic matrial ( F), and anti-frrmagntic matrials at high tmpratur and frrmagntic matrial (F O 4 ) at high tmpratur.

23 Frrmagntic matrials Atms r mlculs f frrmagntic matrials hav prmannt magntic mmnt. In frrmagntic matrials all th dipls ar alignd paralll as shwn in th figur if a small valu f magntic fild is applid, a larg valu f magntizatin is prducd. As th frrmagntic matrial hav prmannt magntic dipl mmnt and th suscptibility is psitiv. Th magntizatin in frrmagntic matrial is nn linar and gts saturatd whn a larg magntic fild is applid. A frrmagntic matrials xhibits tw diffrnt prprtis. It bhavs as a frrmagntic matrial blw a crtain tmpratur knwn as frrmagntic curi tmpratur. Abv th tmpratur it bhavs as a paramagntic matrial. In th frrmagntic rgin, it xhibits wll knwn curv knwn as hystrsis curv as shwn in th figur. Th suscptibility f a frrmagntic matrial abv th frrmagntic curi tmpratur C is givn by T f Whr C is th Curi cnstant and θ f is th frrmagntic Curi tmpratur.th transitin and rar arth mtals such as F,C, Ni,Gd ar th xampls f frrmagntic matrials. Hystrsis in frrmagntic matrials (B-H curv) Blw th frrmagntic Curi tmpratur (T < θ f ) Frrmagntic matrial xhibits a wll knwn curv calld hystrsis curv. Th variatin f B( magntic inductin) with H(applid fild) can b rprsntd by a clsd curv calld hystrsis lp r curv. This rfrs lagging f magntizatin bhind th magntising fild.

24 If a magntic fild is incrasd gradually, th flux dnsity incrass and it bcms maximum. Th maximum valu f flux dnsity is calld saturatd magntizatin.if th fild is rvrsd, th frrmagntic matrials is fund t hav magntizatin in th absnc pf xtrnal fild. This is calld as rtntivity r rmannt magntizatin (B R ) and this prprty is calld as spntanus magntizatin. If th fild is furthr rducd th flux dnsity rducs t zr. Th fild rquird in th ppsit dirctin t bring magntizatin t zr is calld as crciv fild r crcivity (-H c ). If th fild is incrasd in psit dirctin it attains saturatin magntizatin. If an altrnating fild is applid a clsd lp as shwn in th figur is btaind. Accrding t Wiss, a virgin spcimn f frrmagntic matrial cnsist f numbr f rgins r dmains( 1-6 m r abv) which ar spntanusly magntizd. Whn magntic fild is nt applid th dirctin f spntanus magntizatin varis frm dmain t dmain. Th rsultant magntizatin may hnc b zr r narly zr. Ths dmains ar sparatd frm thr by a wall knwn as dmain wall r Blch wall Th dmain cncpt is usd t xplain th hystrsis prprty. Whn an xtrnal fild is applid tw pssibl ways f alignmnt dmain grwth ar pssibl n by dmain wall mtin and thr by rtatin f dmain wall and dmain grwth is als rvrsibl. Hystrsis curv is xplaind by dmain cncpt. Antifrrmagntic matérils : Ths ar th frrmagntic matrials in which qual n f ppsit spins with sam magnitud such that th rintatin f nighburing spins is in antiparalll mannr ar prsnt. Suscptibility is small and psitiv and it is invrsly prprtinal t th tmpratur. χ=c /(T+θ) th tmpratur at which anti frrmagntic matrial cnvrts int paramagntic matrial is knwn as Nl s tmpratur. Exampls: FO, Cr O.

25 Frrimagntic matrials: Ths ar th frrmagntic matrials in which qual n f ppsit spins with diffrnt magnituds such that th rintatin f nighburing spins is in antiparalll mannr ar prsnt. Suscptibility psitiv and larg, it is invrsly prprtinal t tmpratur χ=c /(T ± θ) T> T N ( Nl s tmpratur) Exampls : ZnF O 4, CuF O 4 Sft and Hard magntic matrials Sft magntic matrials Th magntic matrials that ar asy t magntiz and dmagntiz ar calld as sft magntic matrials. Prprtis: 1. Lw rmannt magntizatin. Lw crcivity. Lw hystrsis nrgy lss 4. Lw ddy currnt lss 5. High prmability 6. High suscptibility Exampls f sft magntic matrials ar i) Prmallys ( allys f F and Ni) ii) Si F ally iii) Amrphus frrus allys ( allys f F, Si, and B) iv) Pur Irn (BCC structur) Applicatins f sft magntic matrials: Mainly usd in lctr- magntic machinry and transfrmr crs. Thy ar als usd in switching circuits, micrwav islatrs and matrix strag f cmputrs.

26 Hard magntic matrials Th magntic matrials that ar difficult t magntiz and dmagntiz ar calld as hard magntic matrials. Prprtis: 1. High rmannt magntizatin. High crcivity. High saturatin flux dnsity 4. Lw initial prmability 5. High hystrsis nrgy lss 6. High prmability 7. Th ddy currnt lss is lw fr cramic typ and larg fr mtallic typ. Exampls f hard magntic matrials ar, i) Irn- nickl- aluminum allys with crtain amunt f cbalt calld Alnic ally. ii) Cppr nickl irn allys. iii) Platinum cbalt ally. Applicatins f hard magntic matrials: Fr prductin f prmannt magnts, usd in magntic dtctrs, micrphns, flux mtrs, vltag rgulatrs, damping dvics and magntic sparatrs. Hard magntic matrials Difficult t magntiz and dmagntiz larg hystrsis lp ara Hav larg hystrsis lss Th dmain wall mvmnt is difficult and it is irrvrsibl in natur Th crcivity and rtntivity ar larg Magntstatic nrgy is larg Sft magntic matrials Easy t magntiz and dmagntiz small hystrsis lp ara Hav vry lw hystrsis lss Dmain wall mvmnt is rlativly asir. Evn fr small chang in th magntizing fild,magntizatin changs by larg amunt Th crcivity and rtntivity ar small Magntstatic nrgy is small. Small valus f prmability and suscptibility Larg valus f prmability and suscptibility Usd t mak prmannt magnts Exampls- Irn-nickl-aluminium allys (alnicl) Cppr nickl irn (cunif) Usd t mak lctrmagnt Exampls- F-Si, Frrus nickl allys,frrits,garnts

27 Sampl Qustins: Dilctric Matrials: 1. Explain th phnmnn f lctric plarizatin in dilctric matrials?.. Dscrib in brif (a)lctrnic plarizatin (b) inic plarizatin (c) Orintatin plarizatin (d) Spac charg plarisatin with diagrams. Als find th ttal plarizability.. Diffrntiat btwn plar and nnplar dilctrics. 4. Driv an xprssin fr intrnal fild in slids and liquids. Or Driv an xprssin fr fr intrnal fild by Lrntz mthd? 5. Driv Clausius-Mssti quatin. 6. What ar frrlctric matrials? Dscrib in dtail th Frrlctric hystrsis. 7. Applicatins f Dilctric matrials. 8. Driv th rlatin btwn dilctric plarizatin and dilctric cnstant? 9. What is its dilctric cnstant? Explain its imprtanc in dilctric matrials? 1. Which f th fllwing prprtis ar typical fr dilctrics? 11. Writ a nt n (a) Frrlctricity (b) Dilctric cnstant (c) intrnal fild in slids 1. Discuss th frquncy dpndnc f varius plarizatin prcsss in dilctric matrials. 1. What is dilctric lss? And als xplain Dilctric Brakdwn. 14. Dscrib th frquncy dpndnc f dilctric cnstant. 15. Explain th applicatins f dilctric matrials as insulatrs. Magntic Matrials: 1. Dfin magntizatin and shw that B= ( H ) M. Explain th classificatin f magntic matrials in dtail?. Giv imprtant faturs f frrmagntic matrials. Explain th hystrsis curv n th basis f dmains. 4. What is hystrsis lss? Explain. 5. Distinguish btwn sft and hard magnts. 6. What is frrmagntic Curi tmpratur? Discuss th bhaviur f a frrmagntic matrial blw th Curi tmpratur. 7. What ar frrits? Explain th magntic prprtis f frrits and mntin thir industrial applicatins. 8. Writ th imprtanc f hard magntic matrials in nginring applicatins? 9. What ar th applicatins f sft and hard magntic matrials?

28 Imprtant frmula:

29 Prblms

30 .

31 . Th dilctric cnstant f Sulphur is.4. Assuming a cubic lattic fr its structur, calculat th lctrnic plarizability fr Sulphur. Givn: Sulphur dnsity=.7 gm/cc, and atmic wight =.7 Givn data:

32 4. Find th plarizatin prducd in a dilctric mdium f rlativ prmittivity 15 in prsnc f an lctric fild f 5 V/m. Givn data: 1. In a magntic matrial, th fild strngth is 1 6 Am -1. Th magntic suscptibility f th matrial is.5x1-5. Calculat th intnsity f magntizatin and th flux dnsity f th matrial. M H M H B ( M H ) A (5 1 ) 1.57Wbm. If a magntic fild f 18Am -1 prducs a magntic fild x 1-5 Wb in an irn bar f crss sctinal ara.cm, Calculat prmability. B H B r 1.5Wbm A B 1.5 r H Calculat th saturatin magntizatin fr Ni frrit. Th lattic paramtr f a cubic unit cll f Ni frrit is.85nm and th magntic mmnt pr unit cll is 18.4 B. 4 ( B= ) M Magnticmmnt vlum (.851 ).991 5

33