Maxwell Equations. Dr. Ray Kwok sjsu

Transcription

1 Maxwell quains. Ray Kwk sjsu eeence: lecmagneic Fields and Waves, Lain & Csn (Feeman) Inducin lecdynamics,.. Giihs (Penice Hall) Fundamenals ngineeing lecmagneics,.k. Cheng (Addisn Wesley)

2 Maxwell quains. Ray Kwk lecdynamics ρ ε µ Gauss s Law Faaday s Law N magneic chage Ampee s Law

3 Maxwell quains. Ray Kwk Incnsisence? ( ) div. cul div. k µ µ ( )??? why?

4 Maxwell quains. Ray Kwk Cninuiy quain d ρ((), ) d dρ ρ ρ d ρ dρ ρ d ρ d d ρ v ( ρv) ρ nain (?) cnsevain mae : dρ/d Hee, cnsevain chages. ee, bund, al.

5 Maxwell quains. Ray Kwk Maxwell s wk Gauss s Law Cninuiy qn ρ ( ε ) ε ρ ε Faaday Maxwell µ µ µ ε such ha ε ames Clek Maxwell ( ) ~displacemen cuen densiy

6 Maxwell quains. Ray Kwk Maxwell quains ρ ε µ ε Tgehe wih Lenz Fce Gauss s Law Faaday s Law N magneic chage Mdiied Ampee s Law (Maxwell) F q( v ) descibe all classical elecdynamics in ee space u, wha ae ρ and?

7 Maxwell quains. Ray Kwk In dielecics εεε ε ε P ρ ρ ρ ρ ρ ρ b b P ρ ε ( ) b ρ cninuiy linea, hmgeneus, ispic P bund chage ρ plaizain cuen densiy b P ρ ρ b b ( P)

8 Maxwell quains. Ray Kwk Plaizain cuen P np p I I d I d I N dc cuen because dp/d N ee chage lw m ne side he he.. S. Ne: is he unim beween he plaes. is dieen. is n necessay // inside dielecic!!! (ε is a ens!!) F ac, scillaing diple lks like he chage is cssing he dielecic!!

9 Maxwell quains. Ray Kwk Plaizain cuen AC ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± I

10 Maxwell quains. Ray Kwk In magneic maeials µ Hµ µ Hµ (H M) µ ( H M) m µ m M MχmH µ (Hχ H) µ (1χ )H µ linea, hmgeneus, ispic 1χ m m is he equivalen cuen densiy magneized mae χ m is he magneic suscepibiliy m µ can be < 1 negaive!!! > paamagneic quanum, spin, bial < diamagneic ee e (sceening) >>1 emagneic magne << 1 aniemagneic ec ne: m exiss even in saic ield, bu equie spaial vaiain M

11 Maxwell quains. Ray Kwk Magneizain Cuen e.g. in a peecly magneized 2 maeial, m unim inside and uside. M nm m i ne cuen n he bunday In ealiy, m dn line up peecly and has a spaial vaiain, which pduce a vlume magneizain cuen bund cuen. Again, n ee elecn ansp m ne place anhe in macscpic sense.

12 Maxwell quains. Ray Kwk Tal cuen densiy M P µ ε ε µ ε µ M P M P ( ) µ M Check wih Maxwell s mah M ρ ρ mah cninuiy OK

13 Maxwell quains. Ray Kwk In ems ee chage and cuen ρ da I d H da da d Q da H l l ( ) M H M µ µ n m

14 Maxwell quains. Ray Kwk & H vs. & H is elaed ee cuen depends n maeial & hisy (hyseesis) H is measued when ne builds elecmagnes is elaed ee chages u we measued vlage which is dl n chages Since & H ae wha we measue diecly, hey ae me cmmnly used han &.

15 Maxwell quains. Ray Kwk unday Cndiins 1 2 1n da 1n 1n A 2n Q 2n A σ σ s s A suace chage densiy 2n dl l l da (aea ) same bunday cndiins as in saic case

16 Maxwell quains. Ray Kwk unday Cndiins H 1 2 1n da 1n 1n A 2n 2n A 2n 1 2 nˆ2 H 1 H 2 H nˆ nˆ H dl l H 2 I l sl ( H ) 1 H2 ( H ) 1 H2 s da s same bunday cndiins as in saic case Ne: s nly exiss n cnducs

17 Maxwell quains. Ray Kwk Summay

18 Maxwell quains. Ray Kwk Phas quains One can wie, H,, in ems ime hamnic ields in m : (Fuie) (, ) Re { ()e j } ω The ampliude () is a Vec Phas. The Maxwell quains ( & H) and he cespnding phas m ae: ε ρ H µ H H ε ρ ε jωµ H H H jωε

19 Maxwell quains. Ray Kwk xecise H(, ) xˆ.1cs(9 Wha is, λ,? βz) A/m in vacuum wih n cuen suce. ω 2π 9, 143 Hz λ c/ (3 x 1 8 )/(143) 294 km ppagae he z diecin H jωε () a y j3.77 sin(9 3(1 6 )z) V/m (z) a y 3.77 cs(9 3(1 6 )z) V/m

20 Maxwell quains. Ray Kwk Hmewk (, ) ŷ.1sin(1πx) cs(6π 1 1. Given ha V/m in ai, ind H(,) and β using he phas equains. xˆ 2. An ininie cuen shee 5 A/m cinciding wih he xyplane sepaaes ai (egin 1, z > ) m he medium wih µ 2 2 (egin 2, z < ). Given ha H A/m, ind 1 3xˆ 4ŷ 2ẑ (a) H 2, (b) 2, (c) angle α 1 ha 1 makes wih he zaxis, and (d) angle α 2 ha 2 makes wih he zaxis. 9 βz) 3. A 6 MHz elecmagneic wave exiss in an aidielecic caxial cable having an inne cnduc wih adius a and an ue cnduc wih inne adius b. Assuming peec cnducs, and he phas m he elecic ield inensiy be (a < < b) V/m, (a) ind k, (b) ind H m he, e (c) ind he suace cuen densiies n he inne and ue cnducs. ˆ jωµ H jkz