北野, 正雄

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TitleLC共振回路で光速を測るAuthor(s)北野, 正雄Citation大学の物理教育 (2015), 21(3): 126-129Issue Date2015URL http://hdl.handle.net/2433/202027Right© 一般社団法人 日本物理学会; 許諾条件により本文ファイルは2015-12-15に公開.Type Journal ArticleTextversionauthorKyoto University??????? Vol. 21, No. 3, p. 126 (2015) ?????LC??????????2015 ? 11 ? 25 ?? ? ? ? ????????????1 ???????????????????, ???????????????????, ???????????. ?????????????, ???????????, ???????????. ??????,??????????,????????????????????, 19????????????? [1]. ????????????????Foucault? Fizeau ????????????????, ???????. ???, ??????????????, ??????????????????, ????????????, ???????????.???????????? c0 = 299 792 458m=s????????. ???????????? 1 s???????, ????? 1m ??????????????. ?????, ?????????????????????????, ????????????????????????? [2].??? 19??????, ?????????????????. Weber ? Kohlrausch ?, ???????????????????????????????????????????????????????? [3, 4]. ?????, ???????? 2 ?????, ????, ?????(esu), ????? (emu) ???????????????, ???????????. ?????qesu=qemu  3:1 108m=s ???, ????????????????????. Maxwell?????????????, ????????????????????????, ???????????????, ????????????. ???????????????????????????????????????????????? [5]. ????????????????????????????????.???????????????????????????????, ????????????.???????????????, ???????????, ??????????????????????. ??, ??????? kV ???????????. ??, ??????????????.???, ??????????????????.????, ???????????????, ???Weber-Kohlrausch?????????. ??? qesu=qemu ?, ????? (SI) ????,c0 = 1=p0"0 (1)????. ?????? 0 ??????? "0 ?,????????????????????????????????, 2?????????????? c0 ?????????. ??? 4???, LC??????????? c0 ??????????.?????????? [6]????, ?????????????????????.2 ??????????? c0 ???????? SC ,?? dC ?????????????????????. SC  d2C ???, ???1ω1 ω2C =ε0ΛCL =µ0ΛLVLVCVRVRIIRR(a) (b)? 1: ????????????????????? "0, 0 ???, ?? c0 ????.??, ???????? D ??? E ??????. ??? Q, ?????? VC ?, Q = D  SC ,VC = E  dC ??????, ????????C :=QVC= "0SCdC= "0C ; (2)???. ?? D = "0E ????. ?????????? C := SC=dC ???????????.2?????????? "0 ?, ????????????????????????????. ??VC ??????, ?????????, ???????????: I = dQ=dt = C(dVC=dt).? 1(a) ????, ????? C ????? R???????????, ???? !1 ?????????. ??? I = I^ cos!1t ???. ??,\ ^ "??????????. VC = I^=(!1C) sin!1t,VR = RI^ cos!1t ???, ????k1 :=V^CV^R=XCR=1!1CR(3)????. XC = 1=(!1C) ????????????????. ? (2)????????,"0 = 1=(k1R!1C) (4)????????????????. ????????????, ???????????. ??, ???? R ???????? !1 ??????????????. C ???????, SC , dC ???????????.??, ??????????????????????????. ???, ??, ????????SL, lL, NL ???. SL  l2L ???, ????????????, ????????? H, ???? B ??????. ??? , ?????? I ?, = B  (NLSL), I = H  (lL=NL) ???, ????????L :=I= 0N2LSLlL= 0L; (5)???. ?? B = 0H ????. ???????? L := N2LSL=lL ???????????. I ????????  ???????, ?????????: VL = d=dt = L(dI=dt).? 1(b)????, ??? L ????? R ???????????, ???? !2 ?????????. ????????????, ????k2 :=V^LV^R=XLR=!2LR(6)??????. XL = !2L ??????????????. ??? k2 ??????????,0 = k2R=(!2L) (7)??????????????. ?????????????????????????.?????????? 0, "0 ???? c0 ??????????. ????, ? (4), (7) ??c0 = 1=p0"0 =pk1=k2p!1!2LC : (8)????, ???, ???, ?????????????, ????????????, R ????????. LCR?????, L, C ?????????????????, ????? c0 =pLC=LC?????????? [6].???, ??????????????????????????????? Z0 =p0="0 ???????????????.23 Weber-Kohlrausch ???2?????Weber-Kohlrausch????????????. ???, ???? q ? esu?, emu????????????? qesu=qemu ??????.????, ???????????????????????, SI ????????? [7]. ??,?????????????? 1??????????????: qesu = q=p4"0 (???pNm). ???, ??????????????? 1???????? Iemu = Ip0=4 (???pN) ??????. ??????? qemu = qp0=4 ???. ???? q ????, ?????????? qesu, qemu??????, qesu=qemu = 1=p0"0 = c0 ???.??????????, ?????????????????????????????????.??????, ??????????, ?????????????????????????????????. ???????????????????????. ????, ???, ?????? 2????????, ???????????????????????? [8]. ????, ???????, ???????????????????, ????, ??????????????????????????. ?????, ?????????????????????????????. ?????, ?????????????????????????????????????, ????????????, ??????????????????????.??, 2?????,???? R? esu, emu?????, Resu = 1=(k1!1C), Remu = !2L=k2 ?????????????, Weber-Kohlrausch ?? c0 =pRemu=Resu ?????????.4 LC??????? c0 ???2????????????????????????, 2??????????? 2???? "0,ω C = ε0ΛCL = µ0ΛLVRVRr? 2: LC??????? c0 ???.0 ??????? c0 ????????????????. 1???????????????????. ? (8)?, !1 = !2, k1 = k2 ?????????. ????, ? (3), (6) ? LC??????????? !L = 1=(!C) ???. ?????, LC?????????????????????. ? 2?????????. ???????? R, ????????????????? r ???.?????? V^ , ????? ! ????, ????????????I^ = V^"!L  1!C2+ (r +R)2# 1=2(9)???. ! ???????!0 = 1=pLC (10)??????, ???????????. ??????? V^ ??????, ???? ! ?????,??????????? !0 ??????. ????, ???????????????????.? (10)?, L = 0L, C = "0C ??????,c0 = !0pLC = 2=T (11)???, ????????. ???,  :=pLC???????, T := 2=!0 ?????????????? (??) ???. ????????????, ????????????????????c0 ????????????.??????????????????, Z0 ??????????? [6].35 LC????????????? (1) ?????????????????????????. z??????? x????????? Maxwell????@@t("0Ex) =  @Hy@z;@@t(0Hy) =  @Ex@z: (12)??????, d'Alembert ? Ex = f(z  c0t),Hy = Z 10 f(z  c0t) ?????. ???? f????????????, ??????? c0 =1=p0"0 ?????????????.???????????????????, z =d=2?????????, Fabry-Perot???????????????. ???? Ex(d=2; t) = 0??, ???????? Ex(z; t) = E(t) cos(z=d),Hy(z; t) = H(t) sin(z=d)???. ????? (12)??????, ??????????:"0ddtE =  dH; 0ddtH =dE (13)???????? !0 = (=d)=p0"0 ??,c0 = 2d=T (14)?????. ???? 1?? T (= 2=!0) ????? 2d ?????????????????, ????????. ????????, d ??????????????????????????. ???, ????????????, ?? R, ?? l ?????. ???????????????, ???????????????? (14) ????????????. ?????????????????????, ??, ????????? c0 ???????????? [1]. ??, (???)LC?????????,"0ddtV =   1I 0; 0ddtI 0 =1V (15)??????. ???, I 0 :=pC=LI. ? (13)??????, ?? d =  ? Fabry-Perot???????????????. ????, ? (11) ?? (14) ????????.6 ??????????, ?? [6]????????, ????????????? c0 ? 1% ????????????????. ?????????????,?????????????????????, ????????????????. ????????, c0, Z0, "0, 0 ??? 4????????????????, ?????????, ??, ???, ???????????????????. ???,4???E, B, D, H ?????????????? [9]. ????? c0 ???, 150??? Maxwell????????????????, ????????????????????????????.????????, ???????????????,????, ?????, ?????????????.???????[1] ????, ?????????? (??, 1996).[2] ???????????????????????,??????????. ??, ?????????????????????, 1 kg ??????????????????. ????, c0, 0 ???????????, "0 = c20=0 ????????, ????????????????????. ???, ?????????????????, ??????????. ????, ??????????????, 0, "0 ??????????.[3] W. Weber and R. Kohlrausch, Annalen derPhysik 99, 10 (1856).[4] ????, ??????????????? (???, 2003).[5] J.C. Maxwell, Phil. Trans. R. Soc. Lond. 155 459(1865).[6] ????,????,??????? 21, 130 (2015).[7] SI ?????, esu, emu ????????????. ? X ???? mkgsA ????, Xesu =(1=4"0)=2X, Xemu = (0=4)=2X ?, ???? A ?????????????. ??  ?, D,H ???? 4, ??????? 1 ???.[8] Weber? Kohlrausch???????, ??????????????, 2 ????????????????????.[9] ????, ??????? 21, 73 (2015).??? Email:kitano@kuee.kyoto-u.ac.jp4

LC共振回路で光速を測る

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LC共振回路で光速を測る

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