Ответы (1115944), страница 4

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>Zggh_khhlghr_gb_\_jgh\ex[hcfhf_glV Vx\j_f_gbihwlhfm  t +  fh`_lijbgbfZlvijhba\hevgu_agZq_gbylZdbfh[jZahf ω1 – ω2 V= 0 (ω1 = ω2), ϕ = 0.⇒ (ω1 − ω 2 ) t +3) Wg_j]bywe_dljhfZ]gblghc\hegu:εε 0 E 2B2Iehlghklbwg_j]bbwe_dljbq_kdh]hbfZ]gblgh]hihe_cjZ\gu wE =, wB =.22 µµ 0B2EBIehlghklv wg_j]bb \hegu w = wE + wB = εε 0 E 2 =. LZdbf h[jZahf \ we_dljhfZ]=µµ0 µµ0Vgblghc \heg_ wg_j]by jZkij_^_ey_lky ihjh\gm f_`^m we_dljbq_kdhc b fZ]gblghc khklZ\eyxsbfblZd`_dZd\mijm]hc±f_`^mihl_gpbZevghcbdbg_lbq_kdhckf4) Wg_j]_lbq_kdb_oZjZdl_jbklbdb\heg:Iehlghklv ihlhdZ wg_j]bb ± dhebq_kl\h wg_j]bb i_j_ghkbfhc \heghc \ _^bgbpm \j_f_gb q_j_a _^bgbqgmx iehsZ^dm i_ji_g^bdmeyjgmx d gZijZ\e_gbx jZkijhkljZg_gby \heguQbke_gghjZ\gZwg_j]bbaZdexqzgghc\gmljbpbebg^jZk_^bgbqgufhkgh\Zgb_fbh[EBjZamxs_cV: S (t ) = w (t ) ⋅ V .

>eywe_dljhfZ]gblguo\heg S (t ) =.µµ0Bgl_gkb\ghklv±kj_^g__ih\j_f_gbagZq_gb_iehlghklbihlhdZwg_j]bb I = S (t ) =ρ A2ω 2VEB; ^eywe_dljhfZ]gblguo I = 0 0 .22 µµ0<_dlhj Mfh\Z ± \_dlhj gZijZ\e_gguc \^hev gZijZ\e_gby jZkijhkljZg_gby \hegu bJGJGjZ\guc ih fh^mex iehlghklb ihlhdZ wg_j]bb S (t ) = w (t ) ⋅ V . >ey we_dljhfZ]gblguo \heg= w (t ) ⋅ V . >eymijm]bo\heg I =17JGJGE BJGfh`gh\\_klbZgZeh]bqgmx\_ebqbgmgZa\Zggmx\_dlhjhfIhcglbg]Z: S (t ) =   .µµ0<_dlhjgZybgl_gkb\ghklv\hegu±kj_^g__ih\j_f_gbagZq_gb_\_dlhjZMfh\ZIhcgJGJGJGJGρ A2ω 2 V, ^ey we_dljhfZ]gblguolbg]Z S (t ) = w (t ) ⋅V .

>ey mijm]bo \heg S (t ) =2JJGJJG E0 B0 JG.S (t ) = 2 µµ0JG JJGIhlhd wg_j]bb \hegu ± ihlhd \_dlhjh\ Mfh\Z Ihcglbg]Z Φ (t ) = ∫∫ S (t ) dS . Fh`ghSlZd`_\uqbkeblvkj_^g__ih\j_f_gbagZq_gb_ihlhdZ Φ (t ) = ∫∫JGJJGS (t ) dS .SGZeh`_gb_\hegDh]_j_glgu_\heguBgl_jn_j_gpby\heghl^\molhq_qguobklhqgbdh\ hiul Xg]Z Jhev g_fhghojhfZlbqghklb bklhqgbdh\ b bo dhg_qguo jZaf_jh\<j_fyb^ebgZdh]_j_glghklbqbkehdh]_j_glguodhe_[ZgbcjZ^bmkbm]hedh]_j_glghklbh[tzfdh]_j_glghklb1) GZeh`_gb_\heg:;m^_f kqblZlv qlh \uihegy_lky ijbgpbi kmi_jihabpbb j_amevlbjmxsbc wnn_dl hlgZeh`_gby^\mo\heg_klvkmffZwnn_dlh\hldZ`^hcba\heg\hegug_\ebyxl^jm]gZ^jm]ZJZkkfhljbfgZeh`_gb_^\mo\heg\uau\Zxsbodhe_[ZgbyqZklbp\h^ghfblhf`_gZijZ\e_gbbimklvh[_\heguy\eyxlkyfhghojhfZlbq_kdbfb\dZ`^hcba\hegbf_xlkydhe_[Zgby lhevdh h^ghc qZklhlu Lh]^Z g_h[oh^bfh keh`blv ^\Z dhe_[Zgby gZijZ\e_ggu_\^hev h^ghc ijyfhc, ± wlhl kemqZc jZkkfhlj_g \ A2 = A12 + A22 + 2 A1 A2 cos ∆ϕ ; A2 ==1T 2A dt = A12 + A22 + 2 A1 A2 cos ∆ϕ .

Bgl_gkb\ghklv ijhihjpbhgZevgZ d\Z^jZlm Zfieblm^uT ∫0kf ihwlhfm j_amevlbjmxsZy bgl_gkb\ghklv I = I1 + I 2 + ∆I , ∆I = 2 I1 I 2 cos ∆ϕ .?kebdhe_[Zgbyg_dh]_j_glgulh cos ∆ϕ = 0 ⇒ ∆I = 0; I = I1 + I 2 ^Z`_\wlhf kemqZ_kj_^g__ agZq_gb_ cos∆ϕ aZ fZeuc ijhf_`mlhd \j_f_gb τ hlebqgh hl gmey gh lZdh]h \j_f_gb τg_^hklZlhqgh^eynbdkZpbbbgl_jn_j_gpbhgghcdZjlbguhilbq_kdbfijb[hjhf?kebdhe_[Zgby dh]_j_glgu lh j_amevlbjmxsZy bgl_gkb\ghklv fh`_l hdZaZlv [hevr_ beb f_gvr_kmffubgl_gkb\ghkl_cgZeZ]Zxsboky\heg±ijhbkoh^bli_j_jZkij_^_e_gb_wg_j]bb\ijhkljZgkl\_\wlhfkemqZ_gZeh`_gb_\heggZau\Zxlbgl_jn_j_gpb_cBgl_jn_j_gpby±i_j_jZkij_^_e_gb_wg_j]bbijbgZeh`_gbb^\mo\hegkhojZgyxs__ky\l_q_gb_^hklZlhqgh^ebggh]h\j_f_gbImklv gZdeZ^u\Zxlky ^\_ \hegu jZkijhkljZgyxsb_ky \^hev h^ghc ijyfhcξ1 = A1 cos (ω1t + k1r ) , ξ 2 = A2 cos (ω 2t + k2 r + ϕ ) ; lh]^Z jZaghklv nZa khklZ\ey_l ∆ϕ =(ω1 − ω 2 ) t + k1r1 − k2 r2 − ϕ .

>ey dh]_j_glghklb \heg ihklhygkl\Z bo jZaghklb nZa lj_[m_lkyhq_\b^ghjZ\_gkl\hqZklhldhe_[Zgbc ω1 = ω2bihklhygkl\h\_ebqbgu(k1r1 – k2r2); k ij_^2π ω nω 2π2π VklZ\eyxl\\b^_ k =, bkihevamynhjfmem λ = VT =; λ0± ^ebgZ k\_= ==λ Vcnλ0ω2πlh\hc\heu\\Zdmmf_LZdbfh[jZahf ∆ϕ =∆ + ϕ , ]^_∆ = n1r1 − n2 r2 – hilbq_kdZyjZaghklvλ018oh^Z (∆ = nr – hilbq_kdbc imlv emqZ Ijb ϕ = 0 mkeh\b_ fbgbfmfZ – ∆ϕ = π + 2π m ⇒1∆ =  m +  λ0 ; mkeh\b_fZdkbfmfZ – ∆ϕ = 2π m ⇒ ∆ = mλ0 .22) Bgl_jn_j_gpby\heghl^\molhq_qguobklhqgbdh\hiulXg]Z:Imklv bf_xlky ^\Z lhq_qguo dh]_j_glguo lhq_qguo bklhqgbdZ lh]^Z iheh`_gby bgl_jn_j_gpbhgguofZdkbfmfh\bfbgbfmfh\[m^mlhij_^_eylvkyihklhygkl\hf \_ebqbgu r1 – r2, ]^_ r1 b r2 – jZkklhygby ^h bklhqgbdh\ =_hf_ljbq_kdh_ f_klh ih^h[guolhq_d ± ]bi_j[hehb^u \jZs_gby \ nhdmkZo dhlhjuogZoh^ylkybklhqgbdbJZkkfhljbf bgl_jn_j_gpbhggmx dZjlbgm hl^\mo lhq_qguo bklhqgbdh\ gZ[ex^Z_fmx gZ m^ZezgghfiehkdhfwdjZg_BklhqgbdbgZoh^ylky\lhqdZo:b <;:<=d.

Ih l_hj_f_ IbnZ]hjZ22ddr = l +  + y  , r22 = l 2 +  − y  ⇒ r12 − r22 =22212= ( r1 + r2 ) ∆r = 2dy. ?keb d l , lh r1 , r2 ≈ l ; l ⋅ ∆r ≈ dy ⇒ y ≈l ∆r. LZdbf h[jZahf mkeh\b_dmλl;d1mkeh\b_ fbgbfmfZ ∆r =  m +  λ ⇒21 m +  λl2⇒ ymin = .d<hiul_Xg]Zemqbhlh^gh]hblh]h `_ bklhqgbdZ ijhoh^yl q_j_ajZagu_ hl\_jklby \ wdjZg_ ihwlhfmj_Zebam_lkyko_fZbgl_jn_j_gpbbhl^\molhq_qguobklhqgbdh\ Bgl_jn_jbjmxsb_emqbbf_xlh^gmblm`_Zfieblm^mihwlhfm\dZ`^hclhqdb©kdeZ^u\Zxlkyª^\ZemqZE1 = E0 cos (ω t − kr1 ) ,fZdkbfmfZ∆r = mλ ⇒ ymax =kk E2 = E0 cos (ω t − kr2 ).

E = E1 + E2 = 2 E0 cos  ∆r  ⋅ cos  ω t − ( r1 + r2 )  , lh _klv Zfieblm^Z j_22 amevlbjmxsbodhe_[ZgbcaZ\bkblhl∆r. Ihwlhfmbgl_gkb\ghklvemq_cihiZ^ZxsbogZwdπ ydkkydjZg I ( y ) = 4 I 0 cos ∆r = 4 I 0 cos 2= 4 I 0 cos 2.λl22l3) Jhevg_fhghojhfZlbqghklbbklhqgbdh\:<j_fydh]_j_glghklb±\j_fy\l_q_gb_dhlhjh]hfh`gh gZ[ex^Zlvbgl_jn_j_gpbhggmxdZjlbgmImklv^\ZbklhqgbdZbkimkdZxl\heguqZklhl ω1b ω2Lh]^Z\j_fy\l_q_gb_dhlhjh]hfh`ghgZ[ex^Zlvbgl_jn_j_gpbhggmxdZjlbgmjZ\gh\j_f_gbaZdhlhjh_jZaghklvnZadhπe_[Zgbc baf_gy_lky gZ π ihwlhfm ω1 − ω 2 tk = π ⇒ tk =. ?keb bklhqgbd bkimkdZ_lω1 − ω 2g_ij_ju\guc ki_dlj \heg qZklhlu dhlhjuo baf_gyxlky hl ω ^h ∆ω lh ihegh_ baf_g_gb_bgl_jn_j_gpbhgghc dZjlbgu ijhbahc^zl ijb jZaghklb nZa f_`^m khk_^gbfb \hegZfb \ π19^eydZ`^hc\hegukqZklhlhchlω^hω + ∆ω/2)gZc^zlky\hegZkqZklhlhchlω + ∆ω/^h(ω + ∆ωbf_xsZykg_ck^\b]nZaπ\dhg_qghfkqzl_\k_\hegu©g_cljZebamxlª^jm]^jm2π.]ZLZdbfh[jZahf^eywlh]hkemqZy tk =∆ωt2πωλ.

Wlh qbkeh jZ\gh fZdkbQbkeh dh]_j_glguo dhe_[Zgbc: N k = k ==≈T T ⋅ ∆ω ∆ω ∆λfZevghfmihjy^dmbgl_jn_j_gpbbdhlhjucfh`ghgZ[ex^Zlvijb^Zgghcg_fhghojhfZlbqghklbbklhqgbdZ\hegZ<hegh\hc pm] ± k_jby dhe_[Zgbc bkimkdZ_fuo Zlhfhf aZ \j_fy \uk\_qb\Zgby τ lh_klvaZ\j_fyi_j_oh^Zba\ha[m`^zggh]hkhklhygby\g_\ha[m`^zggh_τ ~ 10–8 c).>ebgZ dh]_j_glghklb ± ^ebgZ pm]Z \heg gZ dhlhjhc khojZgy_lky dh]_j_glghklvlλtλ2λ2. tk = k ≈.lk = Vtk = k = λ N k ≈TV V ⋅ ∆λ∆λ4) JhevjZaf_jh\bklhqgbdZ:M]hedh]_j_glghklb±l_e_kgucm]he\dhlhjhfemqbbkimkdZ_fu_bklhqgbdhffh`ghkqblZlvdh]_j_glgufbJZ^bmk dh]_j_glghklb ± ebg_cguc jZaf_j mqZkldZ kn_jbq_kdhc ih\_joghklb hdjm`Zxs_cbklhqgbdgZdhlhjhfemqbfh`ghkqblZlvdh]_j_glgufb<uqbkebf mdZaZggu_ iZjZf_lju ^eykemqZy gZ[ex^_gby bgl_jn_j_gpbhgghc dZjlbgu \ hiul_ Xg]Z bklhqgbd ij_^klZ\ey_lkh[hc kl_j`_gv ^ebgu D.

Lh]^Z hq_\b^ghbgl_jn_j_gpbhggu_ dZjlbgu hl lhq_d A b <[m^ml k^\bgmlu gZ m]he β IjbD. Lh]^Z bgl_jn_j_gpbhgL D β ≈ tg β =2LgZydZjlbgZ[m^_lgZ[ex^Zlvkyijbβ < α]^_α ± m]eh\Zy ihemrbjbgZ i_j\h]h fbgbfmfZy1λD λα = min = kf β < α ⇒ < ⇒l2dL drk λλLλ. ϕk = = =, ]^_ β –⇒ d < rk =DL D βLm]eh\hcjZaf_jbklhqgbdZH[tzfdh]_j_glghklb±h[tzfh[eZklbijhkljZgkl\Z\dhlhjhcemqbbkimkdZ_fu_ijhly`zggufg_fhghojhfZlbq_kdbfbklhqgbdhffh`ghkqblZlvdh]_j_glgufb Vk = π rk2lk .Bgl_jn_j_gpby\heghljZ`zgguohlh^ghcih\_joghklbklhyqb_\heguNZaZ hljZ`zgghc \hegu ± mijm]hc b we_dljhfZ]gblghc Bgl_jn_j_gpby \heg hljZ`zgguo hl ^\mo ih\_joghkl_c Ihehku jZ\ghc rbjbgu b jZ\gh]h gZdehgZ IjhkljZgkl\_ggZyehdZebaZpbybgl_jn_j_gpbhgghcdZjlbguNhjfmeZ<mevnZ;jw]]Z1) Bgl_jn_j_gpby\heghljZ`zgguohlh^ghcih\_joghklb:Imklv mjZ\g_gby iZ^Zxs_c b hljZ`zgghc \heg jZkijhkljZgyxsboky \^hev h^ghc blhc `_ ijyfhc bf_xl \b^ ξ1 = A0 cos (ω t + kx ) , ξ 2 = A0 cos (ω t − kx − ϕ 0 ).

ξ = ξ1 + ξ 2 =ϕ ϕ = 2 A0 cos  kx + 0  cos  ω t − 0  . LZdbfh[jZahf Zfieblm^Z dhe_[Zgbc g_ aZ\bkbl hl \j_f_2 2 gb \hagbdZ_l lZd gZau\Z_fZy ©klhyqZyª \hegZ FZdkbfmfZf imqghklyf Zfieblm^u khhl20ϕ0ϕ 1= mπ ; fbgbfmfZfmaeZfZfieblm^ukhhl\_lkl\mxl kx + 0 =  m +  π .22 2Hij_^_ebfjZaghklvnZaiZ^Zxs_cbhljZ`zgghc\hegu_kebgZ]jZgbp_gZ[ex^Z_lkyimqghklvhljZ`_gb_hlf_g__iehlghckj_^u±kdhjhklv\lZdhckj_^_\ur_lhijbx = 0(]jZgbpZjZa^_eZnZa ϕ0 = 2πmqlhwd\b\Ze_glghhlkmlkl\bxjZaghklbnZa?kebgZ]jZgbp_gZ[ex^Z_lkyma_ehljZ`_gb_hl[he__iehlghckj_^ulhijbx = 0 ϕ0 = π + 2πm ±jZaghklvnZaπ©ihl_jyihe\heguª:gZeh]bqgZy dZjlbgZ gZ[ex^Z_lky \ kemqZ_ we_dljhfZ]gblguo \heg ± a^_kv gZb[he__\Z`gudhe_[Zgby\_dlhjZ?bf_gghhgbh[mkeh\eb\Zxl\hkijbylb_we_dljhfZ]gblguo\heghilbq_kdbfb ijb[hjZfb Imqghklv \hagbdZ_l ijb hljZ`_gbb hl hilbq_kdb f_g__ iehlghckj_^ukj_^ukf_gvrbfεlh_klvkf_gvrbfn±k^\b]nZahlkmlkl\m_lma_e±ijbhljZ`_gbbhlih\_joghklbhilbq_kdb[he__iehlghckj_^ukj_^uk[hevrbfn±k^\b]nZaπ.<we_dljhfZ]gblghc\heg_ijbbaf_g_gbbgZijZ\e_gbykdhjhklbhljZ`_gbbhl]jZgbpujZa^_eZnZafh`_lbaf_gblvkygZijZ\e_gbblhevdhh^gh]h\_dlhjZ±eb[h?eb[h<ihJGJGJGkdhevdm V ↑↑  E B  .

Ihwlhfm\©klhyq_cª\heg_ijhbkoh^blk^\b]nZaf_`^mdhe_[Zgbyfb?\_lkl\mxl kx +b < ± imqghklyf ? khhl\_lkl\mxl maeu < fZdkbfmfu we_dljbq_kdhc b fZ]gblghc khklZ\eyxs_c wg_j]bb jZa^_e_gu ijhkljZgkl\_ggh :gZeh]bqgh_ y\e_gb_ gZ[ex^Z_lky ^ey mijm]bo\heg±fZdkbfmfudbg_lbq_kdhcwg_j]bbgZoh^ylky\f_klZoimqghkl_cfZdkbfmfuihl_gpbZevghc±\maeZo2) Bgl_jn_j_gpby\heghljZ`zgguohl^\moih\_joghkl_c:Imklv ljb jZaebqgu_ kj_^u jZa^_e_guiehkdbfb ]jZgbpZfb Emq k\_lZ iZ^Z_l gZ]jZgbpm kj_^ b ih^ m]ehf α qZklv wg_j]bbiZ^Zxs_]hemqZi_j_oh^bl\hljZ`zggucemqZ^jm]ZyqZklv±\ij_ehfezgguc\kj_^m ih^ m]ehf β :gZeh]bqgh_ y\e_gb_ ijhbkoh^bl gZ ]jZgbp_ jZa^_eZ kj_^ b ± hljZ`zgguc a^_kv emq II \gh\v ij_ehfey_lky gZi_j\hc ]jZgbp_ b \uoh^bl \ kj_^m ih^ m]ehfα<j_amevlZl_iZjZee_evgu_emqbI bIIbgl_jn_jbjmxlHimklbfbalhq_dKbFi_ji_g^bdmeyju gZ emqb I b III: AH1 = MH 2 == AM sin β ; AD1 = D1D2 == AM sin α ;sin α n2= ⇒ n2 AH1 = n1 AD1 , lh _klv hilbq_sin β n1kdb_ imlb gZ mqZkldZo AH1 + CH2 b AD2 kh\iZ^Zxl LZdbf h[jZahf∆ = n2 ( BH1 + BH 2 ) = 2dn2 cos β .

?kebgZdZ`^hcba]jZgbphljZ`_gb_ijhbkoh^blhlhilbq_kdb[he__iehlghckj_^ulhdZ`^ucbaemq_c©l_jy_lª λ/ihwlhfmk^\b]nZaf_`^mbgl_j∆n_jbjmxsbfb emqZfb ϕ = 2π . Mkeh\b_ fZdkbfmfh\: 2dn2 cos β = mλ0 ; mkeh\b_ fbgbfmλ1fh\: 2dn2 cos β =  m +  λ0 . ?keb kj_^Z b^_glbqgZ kj_^_ lh emq I l_jy_l λ/2, Z emq II –21g_lMkeh\b_fZdkbfmfh\: 2dn2 cos β =  m +  λ0 ; mkeh\b_fbgbfmfh\: 2dn2 cos β = mλ0 .2< jZkkfhlj_gghf kemqZ_ bgl_jn_j_gpbhggZy dZjlbgZ ehdZebah\ZgZ gZ [_kdhg_qghklbihwlhfm^ey_zgZ[ex^_gbygm`gh mklZgh\blvgZimlbemq_ckh[bjZxsmxebgamihf_klb\21wdjZg\nhdZevghciehkdhklb<Z`gh_ ijbf_g_gb_ bgl_jn_j_gpbb \heg hljZ`zgguo hl ^\mo iZjZee_evguo iehkdhkl_ck\yaZghklZdgZau\Z_fuf©ijhk\_le_gb_fªhilbdbGZih\_joghklvebgahilbq_kdboijb[hjh\ gZghkyl lhgdb_ iezgdb lZdhc lhesbgu qlh bgl_jn_j_gpby ©]Zkblª hljZ`zggu_emqb\j_amevlZl_g_ijhbkoh^blihl_jvwg_j]bbbaaZhljZ`_gby3) Bgl_jn_j_gpbhggu_wnn_dlu:P\_lZlhgdboiezghdijbgZ[ex^_gbblhgdboiezghd\[_ehfk\_l_hgbhdjZrb\Zxlky\p\_lZ^eydhlhjuo^ebgu \heg m^h\e_l\hjyxl mkeh\bx fZdkbfmfh\ kf Bgl_jn_j_gpbhggZydZjlbgZehdZebah\ZgZgZ[_kdhg_qghklb Ihehku jZ\ghc rbjbgu ijb hk\_s_gbb [_euf k\_lhf iezgdb i_j_f_gghc lhesbgu mqZkldb jZaghc lhesbgu[m^mlhdjZr_gu\jZagu_p\_lZkhhl\_lkl\mxsb_ p\_lZf lhgdbo iezghd wlhclhesbgu Ih^h[gmx bgl_jn_j_gpbhggmx dZjlbgm fh`gh gZ[ex^Zlv gZijbf_j ijb bgl_jn_j_gpbb k\_lZ hljZ`zggh]h hl lhgdh]h debgZ Hij_^_ebf ijhkljZgkl\_ggmx ehdZebaZpbx bgl_jn_j_gpbhgghcdZjlbguimklvemqb iZ^ZxlgZdebgih^m]ehf αlh]^Z m]heij_ehfe_gby βh^bgZdh\^ey\k_oemq_cZ\k_hklZevgu_m]eu±nmgdpbb β, θm]heijbj_[j_debgZbnLZdbfh[jZahfemqb\uoh^ysb_badebgZlZd`_iZjZee_evguImklvM bN – lhqdbi_j_k_q_gbykhhl\_lkl\mxsbohljZ`zggh]hbij_ehfezggh]hemq_cdhlhju_\hafh`ghg_e_`ZlgZh^ghcijyfhcklhqdhcHBaih^h[bylj_m]hevgbdh\OC2D bOA2<, OC1D bOA1<OC2 OD OC1CCOC1, ihwlhfmb 1 2 =.

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