<\/p>\n
\u53c2\u8003\uff1a<\/p>\n
gnuplot \u3060\u3051\u3067\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3057\u305f\u308a\uff0c\u6570\u5024\u8a08\u7b97\u3057\u305f\u308a\u3059\u308b\u969b\u306e\u53c2\u8003\u3068\u3057\u3066<\/p>\n
\\begin{eqnarray}
\nB_x(x,0,z) &=& \\frac{I}{4\\pi \\varepsilon_0 c^2}
\n\\int_0^{2\\pi} \\frac{a z \\cos \\phi’ }{\\left\\{ x^2 + z^2 + a^2 – 2 a x \\cos\\phi’ \\right\\}^{\\frac{3}{2}}}\\,d\\phi’ \\\\ \\ \\\\
\nB_y(x,0,z) &=& 0 \\\\ \\ \\\\
\nB_z(x,0,z) &=& \\frac{I }{4\\pi \\varepsilon_0 c^2}
\n\\int_0^{2\\pi} \\frac{a^2 – a x \\cos\\phi’}{\\left\\{x^2 + z^2 + a^2 – 2 a x \\cos\\phi’ \\right\\}^{\\frac{3}{2}}}\\, d\\phi’
\n\\end{eqnarray}<\/p>\n
\u9069\u5b9c\uff0c\u5b9a\u6570\u90e8\u5206\u3092\u898f\u683c\u5316\u3057\u3066<\/p>\n
\\begin{eqnarray}
\nB_x(x,z) &\\Rightarrow&
\n\\int_0^{2\\pi} \\frac{a z \\cos \\phi’ }{\\left\\{ x^2 + z^2 + a^2 – 2 a x \\cos\\phi’ \\right\\}^{\\frac{3}{2}}}\\,d\\phi’ \\\\ \\ \\\\
\nB_y(x,z) &=& 0 \\\\ \\ \\\\
\nB_z(x,z) &\\Rightarrow&
\n\\int_0^{2\\pi} \\frac{a^2 – a x \\cos\\phi’}{\\left\\{x^2 + z^2 + a^2 – 2 a x \\cos\\phi’ \\right\\}^{\\frac{3}{2}}}\\, d\\phi’
\n\\end{eqnarray}<\/p>\n
\u78c1\u5834\u30d9\u30af\u30c8\u30eb\u304c\u78c1\u529b\u7dda\u306e\u63a5\u30d9\u30af\u30c8\u30eb\u3067\u3042\u308b\u3053\u3068\u304b\u3089\uff0c\u5b9a\u7a4d\u5206\u3092\u542b\u3080\u5fae\u5206\u65b9\u7a0b\u5f0f<\/p>\n
\\begin{eqnarray}
\nB_x(x,z) &=& \\int_0^{2\\pi} f_1(x,z,\\phi)\\,d\\phi \\\\
\nB_z(x,z) &=&\\int_0^{2\\pi} f_2(x,z,\\phi)\\,d\\phi \\\\
\nf_1(x,z,\\phi) &\\equiv& \\frac{a z \\cos \\phi}{\\left\\{ x^2 + z^2 + a^2 – 2 a x \\cos\\phi\\right\\}^{\\frac{3}{2}}} \\\\
\nf_2(x,z,\\phi) &\\equiv& \\frac{a^2 – a x \\cos\\phi}{\\left\\{x^2 + z^2 + a^2 – 2 a x \\cos\\phi \\right\\}^{\\frac{3}{2}}}\\ \\\\
\nB(x, z) &\\equiv& \\sqrt{B_x(x,z)^2 + B_z(x,z)^2} \\\\
\nF_1(x, z) &\\equiv& \\frac{B_x(x,z)}{B(x,z)} \\\\
\nF_2(x, z) &\\equiv& \\frac{B_z(x,z)}{B(x,z)} \\\\
\n\\frac{dx}{ds} &=& F_1(x, z)\\\\
\n\\frac{dz}{ds} &=& F_2(x, z)
\n\\end{eqnarray}<\/p>\n
\u3092\u6570\u5024\u7684\u306b\u89e3\u3044\u3066\u78c1\u529b\u7dda\u3092\u6c42\u3081\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
%gnu<\/span>plot<\/span> inline<\/span> svg<\/span> size<\/span> 480<\/span>,<\/span>480<\/span> fixed<\/span> enhanced<\/span> font<\/span> 'Noto Sans CJK JP,14'<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\nIn\u00a0[2]:<\/div>\n\n\n\n# \u88ab\u7a4d\u5206\u95a2\u6570<\/span>\r\nf1<\/span>(x,z,ph) =<\/span> a<\/span>*<\/span>z<\/span>*<\/span>cos<\/span>(<\/span>ph<\/span>)<\/span>\/<\/span>sqrt<\/span>(<\/span>x<\/span>**<\/span>2<\/span>+<\/span>z<\/span>**<\/span>2<\/span>+<\/span>a<\/span>**<\/span>2-2<\/span>*<\/span>a<\/span>*<\/span>x<\/span>*<\/span>cos<\/span>(<\/span>ph<\/span>))<\/span>**<\/span>3<\/span>\r\nf2<\/span>(x,z,ph) =<\/span> (<\/span>a<\/span>**<\/span>2<\/span>-<\/span>a<\/span>*<\/span>x<\/span>*<\/span>cos<\/span>(<\/span>ph<\/span>))<\/span>\/<\/span>sqrt<\/span>(<\/span>x<\/span>**<\/span>2<\/span>+<\/span>z<\/span>**<\/span>2<\/span>+<\/span>a<\/span>**<\/span>2-2<\/span>*<\/span>a<\/span>*<\/span>x<\/span>*<\/span>cos<\/span>(<\/span>ph<\/span>))<\/span>**<\/span>3<\/span>\r\n\r\n# 2*pi \u7a4d\u5206\u533a\u9593\u3002<\/span>\r\n# N \u5206\u5272\u6570 N \u306f\u5076\u6570\u3068\u3059\u308b\u3053\u3068\uff08\u30b7\u30f3\u30d7\u30bd\u30f3\u6cd5\u306e\u6c7a\u3081\u4e8b\uff09<\/span>\r\n# \u4e09\u9805\u6f14\u7b97\u5b50\u306b\u3088\u308b\u518d\u5e30\u7684\u5b9a\u7fa9\u95a2\u6570\u3067\u548c\u3092\u3068\u308b\u3002<\/span>\r\n\r\nsimp_f1<\/span>(x, z, N, i) =<\/span> (<\/span>i<\/span> ==<\/span> 2<\/span> ?<\/span> \\\r\n (<\/span>2<\/span>*<\/span>pi<\/span>)<\/span>\/<\/span>(<\/span>N<\/span>*<\/span>3.0<\/span>)<\/span>*<\/span> \\\r\n (<\/span>f1<\/span>(<\/span>x<\/span>,<\/span>z<\/span>,<\/span>(<\/span>i<\/span>-2<\/span>)<\/span>*<\/span>2<\/span>*<\/span>pi<\/span>\/<\/span>N<\/span>)<\/span> +<\/span> 4.0<\/span>*<\/span>f1<\/span>(<\/span>x<\/span>,<\/span>z<\/span>,<\/span>(<\/span>i<\/span>-1<\/span>)<\/span>*<\/span>2<\/span>*<\/span>pi<\/span>\/<\/span>N<\/span>)<\/span> +<\/span> f1<\/span>(<\/span>x<\/span>,<\/span>z<\/span>,<\/span>i<\/span>*<\/span>2<\/span>*<\/span>pi<\/span>\/<\/span>N<\/span>))<\/span> :<\/span> \\\r\n simp_f1<\/span>(<\/span>x<\/span>,<\/span> z<\/span>,<\/span> N<\/span>,<\/span> i<\/span>-2<\/span>)<\/span> +<\/span> \\\r\n (<\/span>2<\/span>*<\/span>pi<\/span>)<\/span>\/<\/span>(<\/span>N<\/span>*<\/span>3.0<\/span>)<\/span>*<\/span> \\\r\n (<\/span>f1<\/span>(<\/span>x<\/span>,<\/span>z<\/span>,<\/span>(<\/span>i<\/span>-2<\/span>)<\/span>*<\/span>2<\/span>*<\/span>pi<\/span>\/<\/span>N<\/span>)<\/span> +<\/span> 4.0<\/span>*<\/span>f1<\/span>(<\/span>x<\/span>,<\/span>z<\/span>,<\/span>(<\/span>i<\/span>-1<\/span>)<\/span>*<\/span>2<\/span>*<\/span>