Ответы (1115944), страница 3

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S = 2π1⇒ Q = ω Sτ W ≈ ω 0τ W – \lhjh_hij_2βW (t )2π2π; ijbfZehfaZlmoZgbb e−2γ ≈ 1 − 2γ , lh_klv==−2 β T−2γW (t ) − W (t + T ) 1 − e1− e11Apω 02π ωS== Q – lj_lv_ hij_^_e_gb_.=≈ ω S τ W = Q – q_l\zjlh_ hij_^_e_A (ω → 0 ) 2βω Sγ 2βω1, ihwlhfmQ = ω S τW ≈ S – iylh_ hij_^_e_gb_ Nhjgb_ijbfZehfaZlmoZgbb ∆ω p ≈τW∆ω pS≈fmeZ ^ey ∆ωj Z agZqbl b ihke_^g__ hij_^_e_gb_ \_jgu \ kemqZ_ ω − ω 0 ≤ nβ , ]^_nω0 2π≈= 2Q.βγ3) Hkh[_gghklb\ugm`^_gguodhe_[Zgbckbkl_fk\yaZgguohkpbeeylhjh\:DZ`^ZyghjfZevgZyfh^Zbf__lkh[kl\_ggucj_ahgZgkijbqzf\h[s_fkemqZ_rbjbgZj_ahgZgkguodjb\uobj_ahgZgkgZyZfieblm^ZjZaebqgubaZ\bkylhl^h[jhlghklb^eydZ`^hcbafh^Ijb[hevrboaZlmoZgbyofh^ui_j_klZxl[ulvg_aZ\bkbfufbbbo\\_^_gb_l_jy_lkfukedZdb^eykh[kl\_gguoaZlmoZxsbodhe_[Zgbc±kf‹8. D\ZabklZpbhgZjguci_j_f_gguclhdAZdhgHfZ^eyp_ibkhklhys_cbaihke_^h\Zl_evgh kh_^bgzgguo bg^mdlb\ghklb khijhlb\e_gby b dhg^_gkZlhjZ J_ahgZgkgu_y\e_gby\ihke_^h\Zl_evguobiZjZee_evguop_iyoi_j_f_ggh]hlhdZFhsghklv\u^_eyxsZyky \ p_ib i_j_f_ggh]h lhdZ Wnn_dlb\gu_ ^_ckl\mxsb_ agZq_gby gZijy`_gbyblhdZ1) AZdhgHfZ^eyihke_^h\Zl_evghcp_ibi_j_f_ggh]hlhdZ:QZklh\p_iyoi_j_f_ggh]hlhdZgZijy`_gb_baf_gy_lkyih]Zjfhgbq_kdhfmaZdhgmU =U0cosωt.<wlhfkemqZ__keblhd±d\ZabklZpbhgZj_glh_klv\ex[hcfhf_gl\j_f_gbkbeZlhdZ \h \k_o lhqdZo ihke_^h\Zl_evghc p_ib h^bgZdh\Z \lhjh_ ijZ\beh Dbjo]hnZ ^ey p_ibihke_^h\Zl_evgh kh_^bgzgguo bg^mdlb\ghklb zfdhklb b khijhlb\e_gby aZibr_lky dZdq− L q + U 0 cos ω t = + R q ⇔ q + 2 β q + ω 02 q = u0 cos ω t , qlh b^_glbqgh ^bnn_j_gpbZevghfmCmjZ\g_gbx \lhjh]h aZdhgZ GvxlhgZ ^ey \ugm`^_gguo f_oZgbq_kdbo dhe_[Zgbc kf ‹ Ke_^h\Zl_evgh \ mklZgh\b\r_fky j_`bf_ mjZ\g_gb_ dhe_[Zgbc bf__l \b^q = q0 cos (ω t − α ) , Zq0 bαbsmlkykihfhsvxf_lh^Z\_dlhjguo^bZ]jZff>ey hlukdZgby khhlghr_gby f_`^m Zfieblm^gufb agZq_gbyfb kbeu lhdZ b gZijy`_gby gZ \_dlhjghc ^bZ]jZff_ hldeZ^u\Zxl gZijy`_gby gZ hl^_evguo we_f_glZo p_ibπU R = IR = I 0 R cos  ω t − α +  ; U L = L I = LI 0ω cos (ω t − α + π ) ;22I0q1 22 UC = =cos (ω t − α ) , ihwlhfm U 0 = I 0   ω L −+ R2  ;C ωCωC 12ωL −ω C ; Z =  ω L − 1  + R 2 – ihegh_ khijhlb\e_tg ϕ =ω C Rgb_ihke_^h\Zl_evghcp_ibU0 = I0Z – aZdhgHfZ^eyp_i_ci_j_f_ggh]hlhdZIhZgZeh]bbkp_iyfb ihklhyggh]h lhdZ \\h^yl khijhlb\e_gby bg^mdlb\gh_ χ L = Lω b _fdhklgh_1χC =.

Khijhlb\e_gb_j_abklhjZRgZau\Z_lkyhfbq_kdbf (Zdlb\gufbg^mdlb\gh_b_fωCdhklgh_±j_Zdlb\guf.<<<<<<<122) J_ahgZgkgu_y\e_gby\p_iyoi_j_f_ggh]hlhdZ:Mkeh\b_j_ahgZgkZlhdZ\ihke_^h\Zl_evghcp_ibkh\iZ^Z_lkmkeh\b_fj_ahgZgkZkdh1. J_ahgZgkmkbeulhdZkhhl\_lkl\m_lfbgbfmfihegh]hkhijhjhklbkf ω = ω 0 =CL1.lb\e_gbyp_iblh_klv χ C = χ L ⇒ ω L =ωC>ey iZjZee_evghc p_ib kh^_j`Zs_c bg^mdlb\ghklv b zfdhklv fbgbfmf ghev kbeu lhdZ lZd`_^hklb]Z_lky ijb jZ\_gkl\_ khhl\_lkl\mxsbo khijhlb\e_gbclh_klv ωj = ω0LZdh_khklhygb_gZau\Z_lky j_ahgZgkhf khijhlb\e_gby beb [ZeZgkhf lhdh\).?keb `_ ihke_^h\Zl_evgh k bg^mdlb\ghklvx ijbkh_^bgzgj_abklhjlh\_dlhjgZy^bZ]jZffZbaf_gblkyUU0ωLωL; tg ϕ =.I= 0=⇒ sin ϕ =2222Z1RR +LωR + L2ω 2U 02U 02CωI =U C ω + 2ωL ⇒−2 2R + L2ω 2R + L2ω 2R 2 + L2ω 2.

Mkeh\b_ j_ahgZgkZ khijhlb\e_gby fb⇒Z =22 2 22ω R C + (1 − ω CL )2020gbfmfZωj =22kbeulhdZ\ih^\h^ysboijh\h^Zo21 R− 2 = ω 02 − 4 β 2 .CL L3) Fhsghklv\u^_eyxsZyky\p_ibi_j_f_ggh]hlhdZ:IU1:gZeh]bqgh P(t ) = U 0 q0ω cos ϕ = 0 0 cos ϕ . Ba \_dlhjghc ^bZ]jZffu U R =222I RI= U 0 cos ϕ = I 0 R, ihwlhfm P(t ) = 0 = I ^2 R, ]^_ I ^ = 0 – ^_ckl\mxs__wnn_dlb\gh_agZ22q_gb_kbeulhdZlh_klvagZq_gb_kbeuihklhyggh]hlhdZ^eydhlhjh]h\p_ib\u^_ey_lkylZU`_fhsghklv:gZeh]bqgh\\h^blky^_ckl\mxs__agZq_gb_gZijy`_gby U ^ = 0 .

<ujZ`_2gby^ey^_ckl\mxsboagZq_gbckbeulhdZbgZijy`_gbyhq_\b^ghg_aZ\bkylhlnhjfup_ibbhij_^_eyxlkyoZjZdl_jhfdhe_[ZgbcgZijy`_gby DeZkkbq_kdh_ ^bnn_j_gpbZevgh_ \hegh\h_ mjZ\g_gb_ MjZ\g_gb_ iehkdhc bkn_jbq_kdhc]Zjfhgbq_kdbo\hegIjh^hevgu_bihi_j_qgu_\hegu<hegh\hc\_dlhjMqzl aZlmoZgby \hegu Mijm]b_ ]Zjfhgbq_kdb_ \hegu Iehlghklv wg_j]bb i_j_ghkbfhcmijm]hc\heghc1) DeZkkbq_kdh_^bnn_j_gpbZevgh_\hegh\h_mjZ\g_gb_:<hegZ±jZkijhkljZgyxs__ky\kj_^_\hafms_gb_Ijhkl_cr_c fh^_evx \hegu y\ey_lky kbkl_fZ [hevrh]h qbkeZ k\yaZgguo hkpbeeylhjh\ Imklv fZkku \k_o hkpbeeylhjh\ h^bgZdh\u b jZ\gu m \k_ hgb k\yaZgu h^bgZdh\ufbijm`bgZfb`zkldhklbkZjZkklhygb_f_`^mkhk_^gbfbhkpbeeylhjZfb\iheh`_gbbjZ\gh\_kby jZ\gh l.

Lh]^Z ^ey ex[h]h hkpbeeylhjZ fh`gh aZibkZlv \lhjhc aZdhg GvxlhgZm ξ n = k (ξ n+1 − ξ n ) − k (ξ n − ξ n−1 ). I_j_oh^ydg_ij_ju\ghckj_^_mklj_fbfqbkehhkpbeeylhjh\<<13d[_kdhg_qghklbZl ±dgmexbihemqbf]eZ^dmxnmgdpbx ξ(x, t). Imklvx – dhhj^bgZlZn-]hhkpbeeylhjZlh]^ZjZaeh`b\ξ\jy^L_cehjZZlZd`_kqblZyqlh\ijhp_kk_dhe_[ZgbcjZkklhygb_ f_`^m khk_^gbfb hkpbeeylhjZfb baf_gy_lky fZeh ihemqbf ξ n +1 ≈ ξ ( x + l , t ) ≈∂ξl 2 ∂ 2ξ∂ξl 2 ∂ 2ξ( x, t ) +,;ξξ,ξ,,xtxltxtlxt≈−≈−⋅+()()()()( x, t ).

Ih^klZn −12 ∂x 22 ∂x 2∂x∂x\bf ^Zggu_ \ujZ`_gby \ ^bnn_j_gpbZevgh_ mjZ\g_gb_ \lhjh]h aZdhgZ GvxlhgZ2∂ 2ξ kl 2 ∂ 2ξ∂ 2ξ2 ∂ ξ,lh_klvv– deZkkbq_kdh_ ^bnn_j_gpbZevgh_ \hegh\h_ mjZ\g_gb_==m ∂x 2∂t 2∂t 2∂x 2^ey h^ghf_jgh]h kemqZy ]^_ v ± dhwnnbpb_gl bf_xsbc jZaf_jghklv kdhjhklb Imklv V –kdhjhklv jZkijhkljZg_gby \hegu lh _klv kdhjhklv jZkijhkljZg_gby \hafms_gbc lh]^ZkqblZydhe_[Zgby\gZqZe_dhhj^bgZl]Zjfhgbq_kdbfb[_agZqZevghcnZau ξ ( 0, t ) = A cos ω t ,≈ ξ ( x, t ) + l ⋅ihemqbfqlh ξ ( x, t ) = A cos (ω (t − τ )) = A cos (ω t − kx ) , ]^_ τ±\j_fyjZkijhkljZg_gby\heguxω 2π 2π, k= =; λ – ^ebgZ\hegujZk=VV TVλklhygb_gZdhlhjh_jZkijhkljZgy_lky\hegZaZh^bgi_jbh^dhe_[ZgbcIh^klZ\b\nmgdpbxξ\\hegh\h_mjZ\g_gb_fh`ghm[_^blvkyqlhhgZm^h\e_l\hjy_lwlhfmmjZ\g_gbxijbqzfdhgklZglZ v = V LZdbf h[jZahf dhgklZglZ \ \hegh\hf mjZ\g_gbb bf__l kfuke kdhjhklbjZkijhkljZg_gby\hegugZau\Z_fhcnZah\hckdhjhklvx.Mkeh\byijbf_gbfhklbdeZkkbq_kdh]h\hegh\h]hmjZ\g_gbyfZeu_\hafms_gbykj_^ukj_^Z y\ey_lky g_^bki_j]bjmxs_c lh _klv kdhjhklb jZkijhkljZg_gby \heg jZaguo qZklhlh^bgZdh\u<lhjh_lj_[h\Zgb_k\yaZghkl_fqlhmjZ\g_gbxhq_\b^gh^he`gum^h\e_l\hjylv]Zjfhgbq_kdb_nmgdpbbjZaguoqZklhlZwlh\k\hxhq_j_^viha\hey_ljZkijhkljZgblvmjZ\g_gb_ gZ ex[u_ i_jbh^bq_kdb_ nmgdpbb m^h\e_l\hjyxsb_ mkeh\bx >bgb b ij_^klZ\bfu_\\b^_kmffuk\h_]hjy^ZNmjv_∂ 2ξ>ey ljzof_jgh]h kemqZy \hegh\h_ mjZ\g_gb_ aZibr_lky dZd= V 2 ⋅ ∆ξ , ]^_∂t 2∂ 2ξ ∂ 2ξ ∂ 2ξ∆ = 2 + 2 + 2 ±hi_jZlhjEZieZkZ∂x ∂y∂z\lhqdmkdhhj^bgZlhcx; k – \hegh\h_qbkeh: τ =2) MjZ\g_gbyiehkdhcbkn_jbq_kdhc\heg:<hegh\Zyih\_joghklv±]_hf_ljbq_kdh_f_klhlhq_ddhe_[exsboky\h^ghcnZa_Njhgl\hegu±i_j_^gyy\hegh\Zyih\_joghklv<hegu fh`gh deZkkbnbpbjh\Zlvih \b^m bo \hegh\uo ih\_joghkl_c iehkdb_ kn_jbq_kdb_pbebg^jbq_kdb_b^j<hegm fh`gh jZkkfZljb\Zlv dZd iehkdmx _keb jZaf_jubklhqgbdZfgh]h[hevr_jZkklhygby^hg_]hξ ( x, t ) = A cos (ω t − kx ) – mjZ\g_gb_iehkdhc\heguwg_j]bydhe_[exsbokyqZklbpg_aZ\bkblhljZkklhygby^hbklhqgbdZihkdhevdm \ dZ`^hc iehkdhklb \k_ qZklbpu dhe_[exlky kbgnZagh<hafh`ghjZkkfhlj_gb_iehkdhc\hegu\iheyjghckbkl_Gf_dhhj^bgZl k – \hegh\hc\_dlhj\_dlhji_ji_g^bdmeyjgucd njhglm \hegu b gZijZ\e_gguc \ klhjhgm _z jZkijhkljZg_GGgby kx = kr cos ϕ = kr , ihwlhfmmjZ\g_gb_fh`ghaZibkZlvdZdGGξ ( x, t ) = A cos ω t − kr .()< kn_jbq_kdhc \heg_ \kydmx \hegm fh`gh kqblZlv kn_jbq_kdhc _keb jZkklhygb_ ^hbklhqgbdZfgh]h[hevr__]hjZaf_jh\wg_j]bydhe_[exs_ckyqZklbpuh[jZlghijhihjpbh-14gZevgZyiehsZ^bkhhl\_lkl\mxs_c_c\hegh\hcih\_joghklblh_klv ~1; wg_j]byijhihjr2A1pbhgZevgZd\Z^jZlmZfieblm^ukfihwlhfm A ~ .

ξ ( x, t ) = 0 cos (ω t − kr ) – mjZ\g_gb_rrkn_jbq_kdhc\hegu.3) MqzlaZlmoZgby\heg:AZlmoZgb_ \heg mqblu\Z_lky k ihfhsvx ^hihegbl_evgh]h wdkihg_gpbZevgh]h fgh`bGGl_ey dZd b \ kemqZ_ aZlmoZxsbo dhe_[Zgbc ± kf ξ ( x, t ) = A0 e −η x cos ω t − k r ^ey ieh-(kdhc\hegub ξ ( x, t ) =)A0 −η re cos (ω t − kr ) ^eykn_jbq_kdhcr4) Mijm]b_\hegu:Mijm]Zy \hegZ ± ^_nhjfZpbhggu_ \hafms_gby jZkijhkljZgyxsb_ky \ mijm]hc kj_^_lh_klvkj_^_^_nhjfZpbbdhlhjhcy\eyxlky mijm]bfb ± l_eh \ha\jZsZ_lky \ ij_`g__ khklhygb_ijbkgylbb\g_rg_]h\ha^_ckl\byDeZkkbq_kdh_\hegh\h_mjZ\g_gb_\u\_^_gh^eymijm]bo\hegh^gZdhhgh\_jghb^ey^jm]bokemqZ_\gZijbf_jwe_dljhfZ]gblguo\heg±kfMijm]b_\hegufh]ml[ulvijh^hevgufbkf_s_gb_qZklbpiZjZee_evghgZijZ\e_gbxjZkijhkljZg_gby\hegubihi_j_qgufbkf_s_gb_qZklbpi_ji_g^bdmeyjghdgZijZ\e_gbxjZkijhkljZg_gby\heguJZkkfhljbfmijm]bckl_j`_gvkk_q_gb_fSbiehlghklvx ρIjb_]hjZkly`_gbbgZ∆lFFS σ S\hagbdZ_l kbeZ mijm]hklb F = k ∆l ⇒ k =, ]^_ σ – f_oZgbq_kdh_ gZijy`_gb_.==∆l S ∆l ∆lσlkl 2Ihhij_^_e_gbx E =– fh^mevmijm]hklbfh^mevXg]ZfZl_jbZeZkl_j`gyLh]^Z=m∆lσ Sl 2∆V E==E= = V 2 , ihwlhfm kdhjhklv ijh^hevghc ijb \u\h^_ jZkkfZljb\Zebkv ^_ρm∆lmE.

:gZeh]bqgZy nhjfmeZ \_jgZ ^eyρihi_j_qguo\heg\l\zj^hfl_e_\wlhfkemqZ_fh^mevmijm]hklbaZf_gyxlgZfh^mevk^\bF]ZG _kebγ±m]hek^\b]ZZ τ = ±gZijy`_gb_k^\b]Z (S ±iehsZ^vk^\b]Z_fhc]jZgblhSτG = ).γWg_j]byi_j_ghkbfZymijm]hc\heghckdeZ^u\Z_lkybaihl_gpbZevghcbdbg_lbq_kdhc2m  ∂ξ k2wg_j]bc h^ghc ba dhe_[exsboky qZklbp T =   ; U = (ξ n +1 − ξ n ) , gh ba jZaeh`_gbc2  ∂t 2nhjfZpbb jZkly`_gby ± k`Zlby mijm]hc \hegu V =kl 2  ∂ξ  mV 2  ∂ξ ∂ξξ(x, t \ jy^ L_cehjZ kf ξ n +1 − ξ n ≈ l.

LZdbf h[jZahf⇒U ==2  ∂x 2  ∂x ∂t22m   ∂ξ 2  ∂ξ wg_j]by i_j_ghkbfZy mijm]hc \heghc W = U + T =    + V    ; wlm aZ\bkbfhklv2   ∂t  ∂x  fh`ghjZkijhkljZgblvgZijhba\hevgmxkj_^maZf_gb\wg_j]bx\heguiehlghklvxwg_j]bb22ρ   ∂ξ  ∂ξ  w =    + V 2    . >ey iehkdhc \hegu jZkijhkljZgyxs_cky \^hev hkb x, T = U =2   ∂t  ∂x  2152ρ A2ω 2m 2 2 2222.= A ω sin (ω t − kx ) ⇒ w = ρ A ω sin (ω t − kx ) ; w (t ) =22We_dljhfZ]gblgu_\hegu\h^ghjh^ghcg_ijh\h^ys_ckj_^_K\yavf_`^mZfieblm^Zfb b nZaZfb dhe_[Zgbc \_dlhjh\ gZijy`_gghklb we_dljbq_kdh]h b bg^mdpbbfZ]gblgh]h ihe_c \ we_dljhfZ]gblghc \heg_ Wg_j]_lbq_kdb_ oZjZdl_jbklbdb we_dljhfZ]gblguo b mijm]bo \heg iehlghklv ihlhdZ wg_j]bb bgl_gkb\ghklv \_dlhjuMfh\ZbIhcglbg]Z1) MjZ\g_gb_we_dljhfZ]gblghc\hegu:ImklvE b<±nmgdpbblhevdhdhhj^bgZlux(jZkklhygb_^hbklhqgbdZagZqbl_evghij_\urZ_l_]h jZaf_ju <u[_j_f \ iehkdhklb XY ijyfhm]hevguc dhglmj k h[oh^hf \ gZijZ\e_gbb ±±G2 JGJJ±Lh]^ZEdl∫1 = E y ( x + dx ) dy;GGG4 JGJJ3 JGJJ4 JGJJEdl=−Exdy;Edl=−Edl()y∫∫∫ ih wlbf mqZ321kldZ h[oh^ kh\_jrZ_lky \ jZaguo gZijZ\e_gbyoJGJJGIhwlhfmv∫ Edl = ( E y ( x + dx ) − E y ( x )) ⋅ dy =1234JGJJG∂E= y dxdy; ∫∫ BdS = Bz dxdy kqblZ_f dx fZeuf∂x1234ihwlhfmagZq_gb_B \ij_^_eZo iehsZ^db fh`ghkqblZlv ihklhygguf :gZeh]bqgh \u[bjZ_f \ iehkdhklb XZ dhglmj ±±±JGJJG ∂BJGJJG∂ JGJJG∫5678 Bdl = ∂xz dxdz; 5678∫∫ EdS = − E y dxdz.

<hkihevam_fky mjZ\g_gbyfbFZdk\_eeZ − ∂t ∫∫S BdS =vJGJJGJGJJG∂ JGJJGεεµµ=vEdl;⋅EdS=00∫lv∫l Bdl. Ih^klZ\eyy ihemq_ggu_ agZq_gby ihlhdh\ b pbjdmeypbc∂t ∫∫S∂E∂E∂B ∂Bzihemqbf y = − z ;= −εε 0 µµ 0 ⋅ y . Ijh^bnn_j_gpbjm_f wlb jZ\_gkl\Z ih x b baf_∂x∂t∂x∂t2∂ Ey∂  ∂Bz  ∂ 2 Bz∂  ∂E gbf ihjy^hd ^bnn_j_gpbjh\Zgby=−= −εε 0 µµ0 ⋅  y  ; ih^klZ\bf;22∂x∂t  ∂x  ∂x∂t  ∂x ∂ 2 Ey∂ 2 Ey2∂ 2 Bz2 ∂ BzjZ\_gkl\Zihemq_ggu_bamjZ\g_gbcFZdk\_eeZ 2 = V;.

LZdbfh[=V∂t∂x 2∂t 2∂x 2jZahf \hafms_gby we_dljbq_kdh]h b fZ]gblgh]hihe_c jZkijhkljZgyxlky \ ijhkljZgkl\_ k1h^ghcblhc`_kdhjhklvx V =, ijbqzf\hafms_gb_we_dljbq_kdh]hihey\uau\Z_lεε 0 µµ 0\hafms_gb_fZ]gblgh]hbgZh[hjhlIjb \u\h^_ mjZ\g_gby we_dljhfZ]gblghc \hegu [ueb bkihevah\Zgu mjZ\g_gby FZdk\_eeZaZibkZggu_\ mkeh\byohlkmlkl\bylhdZijh\h^bfhklbihwlhfmbihemq_ggu_ mjZ\g_gby\_jgulhevdh^eyg_ijh\h^ysbokj_^1Qbkeh c =≈ 3 ⋅108 fk y\ey_lky kdhjhklvx we_dljhfZ]gblghc \hegu \ \Zdmmf_ε 0 µo2cn = εµ –ihdZaZl_evij_ehfe_gbykj_^ukdhjhklv\hegu\kj_^_ V = .n162) K\yav f_`^m gZijy`zgghklvx we_dljbq_kdh]h ihey b bg^mdpb_c fZ]gblgh]h \we_dljhfZ]gblghc\heg_:JZkkfhljbf kemqZc ]Zjfhgbq_kdhc we_dljhfZ]gblghc \hegu E = E0 cos (ω t − kx ) ,∂E∂Bz ∂Bz,= −εε 0 µµ 0 ⋅ y :∂x∂t∂x∂tkE0 sin (ω t − kx ) = ω B0 sin (ω t − kx + ϕ ) ; kB0 sin (ω t − kx + ϕ ) = ω E0εε 0 µµ0 sin (ω t − kx ).

Wlb mjZ\B = B0 cos (ω t − kx + ϕ ) ; ih^klZ\bf \ mjZ\g_gby kf i ∂E y=−g_gby \uihegyxlky \ kemqZ_ jZ\_gkl\Z khhl\_lkl\mxsbo Zfieblm^ b nZa ihwlhfm ϕ = 0;B2εε 0 E02 = 0 , ZihkdhevdmnZaudhe_[ZgbcE b<kh\iZ^ZxllhjZ\_gkl\h\uihegy_lky\exµµ0B2 EB = .µµ 0 VDZd ke_^m_l ba ijb jZkijhkljZg_gbb \hegu \^hev hkb x f_gyxlky lhevdh khklZ\JG JG JGeyxsb_ ?y b Bz lZdbf h[jZahf \_dlhjZ E , B bV \aZbfgh hjlh]hgZevgu ijbqzfJGJGJGV ↑↑  E B  nZau?b<kh\iZ^Zxllh_klvbbofZdkbfmfukh\iZ^ZxlAZf_qZgb_\]Zjfhgbq_kdhcwe_dljhfZ]gblghc\heg_qZklhludhe_[Zgbc\_dlhjh\?bω<kh\iZ^ZxlImklvqZklhlujZaebqguω1b ω2lh]^Zb\hegh\u_qbkeZjZaebqgu  k =  ;VdZd m`_ [ueh ihdZaZgh nZau dhe_[Zgbc kh\iZ^Zxl lh _klv (ω1 − ω 2 ) t + ( k1 − k2 ) x = ϕ ⇒[hcfhf_gl\j_f_gb εε 0 E 2 =xx(ω1 − ω 2 ) = (ω1 − ω 2 )  t +  = ϕ .

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