Ly thuyet truong_dien_tu_va_sieu_cao_tan

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1. HC VIN CNG NGH BU CHNH VIN THNG L THUYT TRNG IN T V SIU CAO TN (Dng cho sinh vin h o to i hc t xa) Lu hnh ni b H NI - 2007 2. HC VIN CNG NGH BU CHNH VIN THNG L THUYT TRNG IN T V SIU CAO TN Bin son : THS. TN THT BO T THS. DNG HIN THUN 3. 3 CHNG 1: CC NH LUT V NGUYN L C BN CA TRNG IN T mn hc trng in t, chng ta s tm hiu phn b ca cc i lng in v t, nguyn nhn to ra chng v xc nh cc i lng khi bit mt s i lung khc.Trong chng ny, chng ta s tm hiu v cc vn c bn nht ca trng in t bao gm cc i lung ca in v t, cc nh lut c bn nht nu ln mi lin h gia cc i lung vi nhau. Trong chng ny s c nhiu khi nim mi m chng ta cn nm vng trc khi chuyn sang cc chng k tip. Cc hc vin cn ch n cch dn ra cc phng trnh ton hc t cc pht biu. c th c hiu c, cc hc vin cn trang b kin thc ton: hm nhiu bin, gii tch vect vi cc ton t gradient, divergence, rotate hc trong chng trnh ton cao cp. Nu khng nm vng cc phn ton hc trn s rt kh hiu uc v theo kp cc phn chng minh trong chng ny. Cui chng s l phn tm tt cc h thc trong chng v cc bi tp. 1.1. Cc i lng c trng c bn cho trng in t 1.1.1. Vec t cng in trng Mt in tch th q t trong trng in, chu tc dng ca lc in eF . Ti mi im ca trng in, t s eF /q l mt i lng khng i, i lng y c gi l cng trng in ti im . K hiu E q F E e = (V/m) (1.1.1) Vi q nh khng nh hng n trng in ban u. 1.1.2. Vec t in cm Khi t in mi vo trng in, in mi b phn cc. Mc phn cc in mi c c trng bi vec t phn cc in P . Vec t phn cc in P xc nh trng thi phn cc in mi ti mi im. Vec t cm ng in D c nh ngha bi h thc: PED += 0 (C/m2 ) (1.1.2) Vi 0 = 1/4.9.109 (F/m) c gi l hng s in. i vi mi trng tuyn tnh, ng hng: EP .00 = (1.1.3) Thay (1.1.3) vo (1.1.2): ED ED r e 0 0 )1( = += ED = (1.1.4) Vi r = 1 + e c gi l thm t i ca mi trng vi chn khng. = 0. r (F/m) c gi l thm in ca mi trng 4. 4 1.1.3. Vect cm ng t Mt in tch th q chuyn ng vi vn tc v trong trng t, chu tc dng lc mF BxvqFm = (1.1.5) Vec t B c gi l vec t cm ng t. 1.1.4. Vec t cng t trng Khi t t mi vo trng t, t mi b phn cc. Mc phn cc t mi c c trng bi vec t phn cc t M . Vec t phn cc t mi xc nh trng thi phn cc t ti mi im ca t mi. Vec t cng trng t H c nh ngha bi h thc: M B H = 0 (A/m) (1.1.6) Vi 0 = 4.10-7 H/m, c gi l hng s t. i vi mi trng tuyn tnh, ng hng: HM m .= (1.1.7) Thay (1.7) vo (1.6): HB HB r m 0 0 )1( = += HB = (1.1.8) Vi r = 1 + m, c gi l thm t t i ca mi trng vi chn khng. = 0r (H/m) l thm t ca mi trng. 1.2. nh lun Ohm v nh lut bo ton in tch 1.2.1. nh lut Ohm Dng in l dng chuyn di c hng ca cc ht mang in di tc dng ca in trng. Cng dng in I chy qua mt din tch S t vung gc vi dng chy bng lng in tch Q dch chuyn qua mt S trong mt n v thi gian. dt dQ I = (1.2.1) m t y hn s chuyn ng c1o hng ca cc ht mang in, ngi ta a ra khi nim mt dng in J : EVVNeJ === (A/m2 ) (1.2.2) Vi: N l s lng ht mang in, mi ht c in tch e. l mt in tch khi (n v C/m3 ) v l dn in ca mi trng (n v S/m). Biu thc (1.2.2) c gi l dng vi phn ca nh lut Ohm. Xt mt vng dn c dng khi lp phng, cnh L, 2 mt i din c ni vi in p khng i U. Cng dng in i qua khi lp phng : == S S SdESdJI R U LUEdSI S === (1.2.3) Vi S = LxL l din tch mt bn. R = L/S : in tr ca khi vt dn. 1.2.2. nh lut bo ton in tch 5. 5 nh lut bo ton in tch c Faraday tm ra bng thc nghim, n c xem l mt tin ca l thuyt trng in t: Tng in tch trong mt h c lp v in khng thay i. Nh vy, lng in tch trong mt th tch V b gim i trong mt n v thi gian bng lng in tch i ra khi th tch V trong mt n v thi gian v bng cng dng in I i xuyn qua mt kn S bao quanh th tch V . Gi Q l in tch ca th tch V. l mt in tch khi ca V. Vy: dt dQ I = (1.2.4) Vi = V dVQ (1.2.5) Thay (1.2.5) vo (1.2.4): = V dV dt d I p dng: = S SdJI Ta c: = VS dV t SdJ p dng biu thc nh l divergence cho v tri, ta c: = VV dV t dVJdiv Biu thc trn ng vi mi th tch V, v vy: t Jdiv = 0= + t Jdiv (1.2.6) Biu thc (1.2.6) c gi l dng vi phn ca nh lut bo ton in tch hay cn gi l phng trnh lin tc. 1.3. Cc c trng c bn ca mi trng c tnh ca mi trng vt cht c th hin qua cc tham s in v t ca n: thm in (F/m) thm in t i r (khng th nguyn) thm t (H/m) thm t t i r (khng th nguyn) dn in (S/m) Cc biu thc (1.1.4), (1.1.8), v (1.2.2) c gi l cc phng trnh lin h hay cn gi l cc phng trnh cht. Da trn cc tham s in v t, ngi ta chia vt cht (mi trng in t) ra thnh cc lai sau: - Mi trng tuyn tnh: cc tham s , , v khng ph thuc cng trng. Khi , cc phng trnh lien h l tuyn tnh. 6. 6 - Mi trng ng nht v ng hng: cc tham s in v t l hng s. Trong mi trng ny, cc vect ca cng mt phng trnh lin h song song vi nhau. - Nu cc tham s in t theo cc hng khc nhau c cc gi tr khng i khc nhau th c gi l khng ng hng. - Mi trng c cc i lng in t l cc hm ca ta c gi l mi trng khng ng nht. Trong t nhin, hu ht cc cht c thm in t i ln hn 1 v l mi trng tuyn tnh. - Mi trng c thm t t i ln hn gi l cht thun t, nh hn 1 gi l cht nghch t. - Cht dn in l cht c > 104 (S/m). - Cht bn dn l cht c 104 > > 10-10 (S/m) - Cht cch in l cht c < 10-10 (S/m) - Mi trng l dn in l tng nu = , l cch in l tng nu = 0. 1.4. Cc phng trnh Maxwell 1.4.1. Khi nim v dng in dch i vi dng in khng i, ta c 0= t . T phng trnh lin tc, ta suy ra: 0=Jdiv (1.4.1) Da theo nh ngha ca ton t divergence, h thc (1.4.1) chng t cc ng dng dn khng i khp kn hoc i ra xa v cng, khng c im bt u v im kt thc. i vi dng in bin i: 0 = t Jdiv (1.4.2) H thc (1.4.2) chng t cc ng ca dng dn bin i khng khp kn, chng bt u v kt thc ti nhng im c mt in tch bin i theo thi gian, chng hn ti cc ct t ca t in. Dng in bin i i qua c mch c t, d khng tn ti dng chuyn dch c hng ca cc ht mang in i qua lp in mi ca t. Maxwell a ra gi thit c mt qu trnh xy ra tng ng vi s c mt ca dng in gia hai ct t v a ra khi nim dng in dch. Dng in dch khp kn dng in dn trong mch. trng in bin i to nn dng in dch ny. Dng chuyn di c hng ca cc ht mang in c Maxwell gi l dng in dn. Dng in bao gm dng in dn v dng in dch c gi l dng in ton phn. 1.4.2. Phng trnh Maxwell th ba v th t Phng trnh Maxwell th t c dn ra da theo nh lut Gauss i vi trng in. nh lut Gauss c pht biu nh sau: Thng lng ca vec t cm ng in gi qua mt mt kn S bt k bng tng cc int ch t do phn b trong th tch V c bao bi mt kn S y. Gi: q l tng in tch ca th tch V D l vec t cm ng in trn mt kn S. l mt in tch khi bn trong th tch V. Theo nh lut Gauss: = = VS S dVSdD qSdD p dng nh l Divergence i vi v tri: 7. 7 = VV dVdVDdiv H thc ny lun ng vi mi th tch V. V vy: =Ddiv (1.4.3) Nu trong V khng c in tch th 0=Ddiv , ng sc ca vec t cm ng in khng c im bt u v kt thc trong th tch V, hay ni cch khc V khng phi l ngun ca vect cm ng in. Nu > 0, thng lng ca vect cm ng in qua S dng, chng t ng sc ca vect cm ng in i ra khi V. Ngc li, ng sc ca vec t cm ng in i vo V. T biu thc (1.4.3), ta c th rt ra kt lun: ngun ca trng vec t cm ng in l n tch, ng sc ca vec t cm ng in bt u in tch dng v kt thc in tch m. Biu thc (1.4.3) chnh l phng trnh th t ca h phng trnh Maxwell. Phng trnh Maxwell th ba c dn ra t nh lut Gauss i vi trng t: Thng lng ca vec t cm ng t B qua mt kn th bng khng. Tng t nh cch dn phng trnh Maxwell th t, ta c: 0=Bdiv (1.4.4) H thc (1.4.4) chnh l phng trnh th ba ca h phng trnh Maxwell. 1.4.3. Phng trnh Maxwell th nht Phng trnh Maxwell th nht c dn ra t nh lut lu s Ampere-Maxwell, hay cn gi l nh lut dng in ton phn. nh lut ny thit lp lin h gia cng trng t v dng in ton phn to nn trng t: Lu s ca vect cng trng t H theo ng kn C ty bng t i s cng cc dng in chy qua din tch bao bi ng kn C. = i i C IldH (1.4.5) Ii > 0 nu chiu ca dng in hp vi chiu ca ng ly tch phn theo quy tc inh c thun. Trong trng hp dng I chy qua in tch S phn b lin tc vi mt dng J , nh lut lu s Ampere Maxwell c dng: = SC SdJldH (1.4.6) p dng nh l Stokes i vi v tri, chuyn v, ta c: = S SdJHrot 0)( (1.4.7) V v tri lun bng khng vi mi S, biu thc di du tch phn phi bng khng, rt ra: JHrot = (1.4.8) Tip theo, ta ly divergence c hai v ca (1.4.8): JdivHdivrot = V tri lun bng khng vi mi vec t H (xem chng trnh ton). Lin h vi phng trnh lin tc: t Jdiv = t = 0 (1.4.9) 8. 8 H thc (1.4.9) ch t c khi dng in l dng khng i. Vy h thc (1.4.5) v (1.4.8) ch ng khi dng in l dng khng i. By gi ta xt trng hp dng in bin thin. Khi : 0 = t Jdiv Thay (1.4.3) vo, ta c: Ddiv t Jdiv = 0)( = + t D Jdiv (1.4.10) H thc (1.4.10) chng t ng dng ca vec t )( t D JJtp += khp kn. Vec t tpJ chnh l vec t mt dng in ton phn cp mc 1.4.1. Dng in ton phn l tng ca dng in dn c vec t mt dng in dn: EJ = (1.4.11) V dng in dch c vec t mt dng in dch: t D Jd = (1.4.12) Biu thc ton hc ca nh lut lu s ca Ampere (1.4.6) c Maxwell m rng nh sau, khi c k n dng in dch: += SC Sd t D JldH )( (1.4.13) t D JHrot += (1.4.14) H thc (1.4.14) chnh l phng trnh th nht ca h phng trnh Maxwell. H thc ny chng t khng ch dng in dn m ngay c in trng bin thin cng c th sinh ra trng t. 1.4.4. Phng trnh Maxwell th hai Phng trnh th hai ca h phng trnh Maxwell c dn ra t nh lut cm ng in t Faraday. nh lut ny thit lp mi quan h gia trng t bin i trong khng gian vi trng in phn b trong khng gian do trng t gy ra: Sc in ng sinh ra trn mt vng dy c gi tr bng v ngc du vi tc bin thin ca t thng gi qua din tch gii hn bi vng dy . = SC SdB dt d ldE (1.4.15) Vi S l mt gii hn bi ng cong kn C. Yu t din tch Sd ca mt S c chiu hp vi chiu ca ly tch phn C theo quy tc inh c thun. p dng nh l Stokes vi v tri: = SC SdErotldE (1.4.16) Nu mt ly tch phn S khng ph thuc thi gian: Sd t B SdB dt d SS = (1.4.17) Thay (1.4.16) v (1.4.17) vo (1.4.15)m ta c: = SS Sd t B SdErot (1.4.18) 9. 9 H thc (1.4.18) lun ng vi mi S, v vy: t B Erot = (1.4.19) H thc (1.4.19) biu din ton hc ca nh lut Faraday, chnh l phng trnh th hai trong h phng trnh Maxwell. H thc ny chng t trng t bin thin theo thi gian lm sinh ra trng in xay phn b trong khng gian. n y, ta c h phng trnh Maxwell gm 4 phng trnh: t D JHrot += t B Erot = (1.4.20) 0=Bdiv =Ddiv Cn lu rng h phng trnh Maxwell (1.4.20) cng cc phng trnh lin h ch ng vi mi trng cht khng chuyn ng, cc thng s ca mi trng khng phi l cc hm ca thi gian, trong mi trng khng c cht st t, khng c nam chm vnh cu. 1.4.5. H phng trnh Maxwell vi ngun ngoi: Trong trng hp xt trng c to ra bi ngun kch thch l ngu