Curse Instructr r. Raymnd C. Rumpf Office: A-337 Phne: (915) 747-6958 -Mail: rcrumpf@utep.edu Maxwell s quatins: Cnstitutive Relatins -3321 lectrmagnetic Field Thery Outline lectric Respnse f Materials Magnetic Respnse f Materials Classificatin f Materials Maxwell's quatins -- Cnstitutive Relatins Slide 2 1
lectric Respnse f Materials Nte: 0 is the free space permittivity and multiples s that 0 has the same units as P. 0 P Vacuum respnse Material respnse lectric Susceptiility, e The electric susceptiility e is a measure f hw easily und charges are displaced due t an applied electric field. P 0 e Maxwell's quatins -- Cnstitutive Relatins Slide 3 lectric Plarizatin In general, the relatin etween the applied electric field and the electric plarizatin P is nnlinear s it can e expressed as a plynmial. n e 0 e 1 2 2 3 3 P Linear respnse 0 e 0 e Nnlinear respnse electric susceptiility n units These terms are usually ignred. They tend t nly ecme significant when the electric field is very strng. 2 e is prnunced "chi tw" 3 e is prnunced "chi three" Maxwell's quatins -- Cnstitutive Relatins Slide 4 2
Relatin Between Permittivity & Susceptiility The permittivity is related t the electric susceptiility thrugh 1 1 P 1 0 The cnstitutive relatin can als e written in terms f the relative permittivity r. 0 r 0 0 e 1 r 0 e 1 e Vacuum respnse ielectric respnse Maxwell's quatins -- Cnstitutive Relatins Slide 5 Magnetic Respnse f Materials Nte: 0 is the free space permeaility and multiples s that 0 has the same units as M. B 0 M Vacuum respnse Material respnse Magnetic Susceptiility, m The magnetic susceptiility m is a measure f hw easily magnetic diples are aligned due t an applied magnetic field. M 0 m Maxwell's quatins -- Cnstitutive Relatins Slide 6 3
Magnetic Plarizatin In general, the relatin etween the applied magnetic field and the magnetic plarizatin M is nnlinear s it can e expressed as a plynmial. n m 1 2 3 M 2 3 0 m 0 m 0 m Linear respnse Nnlinear respnse magnetic susceptiility n units These terms are usually ignred. They tend t nly ecme significant when the electric field is very strng. 2 m is prnunced "chi tw" 3 m is prnunced "chi three" Maxwell's quatins -- Cnstitutive Relatins Slide 7 Relatin Between Permeaility & Susceptiility The permeaility is related t the magnetic susceptiility thrugh 1 1 B 1 0 r 0 0 m 0 m 1 r 1 m Vacuum respnse Magnetic respnse Maxwell's quatins -- Cnstitutive Relatins Slide 8 4
Types f Magnetic Materials iamagnetic Negative magnetic susceptiility ( m < 0) Tends t ppse an applied magnetic field. All materials are diamagnetic, ut usually very week. Cpper, silver, gld Paramagnetic Small psitive susceptiility ( m > 0 ut small) Material is magnetizale and is attracted t an applied magnetic field. es nt retain magnetizatin when the external field is remved. Ferrmagnetic Large psitive susceptiility Like paramagnetic, ut they retain their magnetism t sme degree when the external field is remved. Irn, nickel, calt, and sme allws. Maxwell's quatins -- Cnstitutive Relatins Slide 9 Anistrpy The dielectric respnse f a material arises due t the electric field displacing charges. ue t structural and nding effects at the atmic scale, charges are ften mre easily displaced in sme directins than thers. This gives rise t anistrpy where the electric field may experience an entirely different permittivity depending n what directin it is riented. tensr x xx xy xz x y yx yy yz y z zx zy zz z ij = hw much f j cntriutes t i Maxwell's quatins -- Cnstitutive Relatins Slide 10 5
Types f Anistrpy (1 f 2) Istrpic Media a 0 0a 0 0 c 0 0 c Uniaxial Media a 0 0a 0 0 c 0 0 e c Biaxial Media a a 0 0a 0 0 c 0 0 c c This is the typical apprximatin made in electrmagnetics. The permittivity tensr reduces t a scalar. Anistrpic materials are said t e irefringent. e rdinary permittivity Psitive irefringence: 0 e extrardinary permittivity Negative irefringence: 0 When rientatin is nt imprtant, it s cnventin t rder the tensr elements accrding t a c Maxwell's quatins -- Cnstitutive Relatins Slide 11 Types f Anistrpy (2 f 2) uly Anistrpic and B Chiral Materials a a j 0 a j a 0 c 0 0 c c Ba a j 0 a B j a 0 B c 0 0 c c Gyrelectric Grymagnetic Maxwell's quatins -- Cnstitutive Relatins Slide 12 6
Ordinary and Bi- Materials Istrpic Materials Anistrpic Materials Ordinary Materials Istrpic Materials B Anistrpic Materials B Bi- Materials Bi-Istrpic Materials B magnetelectric cupling cefficient Bi-Anistrpic Materials B T Maxwell's quatins -- Cnstitutive Relatins Slide 13 7