\u96fb\u78c1\u5834\u3092\u8a18\u8ff0\u3059\u308b\u57fa\u672c\u65b9\u7a0b\u5f0f\u3067\u3042\u308b\u30de\u30af\u30b9\u30a6\u30a7\u30eb\u65b9\u7a0b\u5f0f\u306f\u89e3\u8aac\u3057\u305f\u3002\u3067\u306f\uff0c\u305d\u306e\u96fb\u78c1\u5834\u4e2d\u306b\u304a\u3044\u305f\u7c92\u5b50\u306f\uff0c\u3069\u306e\u3088\u3046\u306a\u529b\u3092\u53d7\u3051\u3066\u904b\u52d5\u3059\u308b\u304b\u3002<\/p>\n
\u3059\u3067\u306b\uff0c\u96fb\u5834\u306e\u5f37\u3055\u3092\u8868\u3059\u30d9\u30af\u30c8\u30eb \\(\\boldsymbol{E}\\) \u3092\u5358\u4f4d\u96fb\u8377\u306b\u306f\u305f\u3089\u304f\u529b\u3068\u3057\u3066\u5b9a\u7fa9\u3057\u305f\u3002<\/p>\n
\uff08\u3055\u3089\u306b\uff0c\u78c1\u5834\u306e\u5f37\u3055\u3092\u8868\u3059\u30d9\u30af\u30c8\u30eb \\(\\boldsymbol{H}\\) \u3092\u5358\u4f4d\u78c1\u8377\u306b\u306f\u305f\u3089\u304f\u529b\u3068\u3057\u3066\u5b9a\u7fa9\u3057\u305f\u304c\uff0c\u78c1\u6c17\u5358\u6975\u5b50\u306f\u5b58\u5728\u3057\u306a\u3044\u306e\u3067\uff0c\u529b\u5b66\u7684\u306b\u306f \\(\\boldsymbol{H}\\) \u306e\u51fa\u308b\u5e55\u306f\u306a\u3044\u3002\uff09<\/p>\n
\u96fb\u5834 \\(\\boldsymbol{E}\\)\uff0c\u78c1\u675f\u5bc6\u5ea6 \\(\\boldsymbol{B}\\) \u306e\u96fb\u78c1\u5834\u4e2d\u3092\u901f\u5ea6 \\(\\boldsymbol{v}\\) \u3067\u904b\u52d5\u3059\u308b\u96fb\u8377 \\(q\\) \u306e\u8377\u96fb\u7c92\u5b50\u306f\uff0c\u6b21\u306e\u3088\u3046\u306a\u529b \\(\\boldsymbol{F}\\) \u3092\u53d7\u3051\u308b\u3002<\/p>\n
$$\\boldsymbol{F} = q \\left( \\boldsymbol{E} + \\boldsymbol{v}\\times \\boldsymbol{B} \\right)$$<\/p>\n
\uff08\u5ff5\u306e\u305f\u3081\uff0c\\( \\boldsymbol{v}\\times \\boldsymbol{B}\\) \u306f \\(\\boldsymbol{v}\\) \u3068 \\( \\boldsymbol{B}\\) \u306e\u5916\u7a4d\uff09<\/p>\n
\u3053\u308c\u3092\u30ed\u30fc\u30ec\u30f3\u30c4\u529b\u3068\u3044\u3046\u3002\u3057\u305f\u304c\u3063\u3066\uff0c\u8377\u96fb\u7c92\u5b50\u306e\u904b\u52d5\u3092\u8003\u3048\u308b\u3068\u304d\u306b\u306f\uff0c\u4f7f\u3046\u96fb\u78c1\u5834\u306f \\(\\boldsymbol{E}\\) \u3068 \\(\\boldsymbol{B}\\) \u3060\u304b\u3089\u3068\u3044\u3046\u7406\u7531\u3082\u3042\u308a\uff0c\u96fb\u78c1\u5834\u3092\u8868\u30594\u672c\u306e\u30d9\u30af\u30c8\u30eb\u306e\u3046\u3061\uff0c\u96fb\u5834\u306b\u3064\u3044\u3066\u306f \\(\\boldsymbol{D}\\) \u3067\u306f\u306a\u304f \\(\\boldsymbol{E}\\)\uff0c\u78c1\u5834\u306b\u3064\u3044\u3066\u306f \\(\\boldsymbol{H}\\) \u3067\u306f\u306a\u304f \\(\\boldsymbol{B}\\) \u3092\u63a1\u7528\u3057\uff0c\u3053\u306e2\u672c\u3067\u8a18\u8ff0\u3057\u3088\u3046\u3068\u3044\u3046\u306e\u304c \\(\\boldsymbol{E}\\) – \\(\\boldsymbol{B}\\) \u5bfe\u5fdc\u306e\u7acb\u5834\u3067\u3042\u308b\u3002<\/p>\n
\u9759\u96fb\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u30fb\u4fdd\u5b58\u529b\u30fb\u529b\u5b66\u7684\u30a8\u30cd\u30eb\u30ae\u30fc\u4fdd\u5b58<\/h3>\n
\u5225\u9014\u8aac\u660e\u3059\u308b\u3088\u3046\u306b\uff0c\u6642\u9593\u7684\u306b\u5909\u52d5\u3057\u306a\u3044\u96fb\u78c1\u5834\u306e\u5834\u5408\u306b\u306f\uff0c\u96fb\u5834\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u30b9\u30ab\u30e9\u30fc\u5834 $\\phi$\uff08\u3053\u308c\u3092\u9759\u96fb\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u3068\u3044\u3046\uff09\u306e\u52fe\u914d\u306b\u8ca0\u53f7\u3092\u3064\u3051\u3066\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n
$$ \\boldsymbol{E} = – \\nabla \\phi$$<\/p>\n
\u7c21\u5358\u306e\u305f\u3081\u306b\uff0c$\\boldsymbol{B} = \\boldsymbol{0}$ \u3068\u3059\u308b\u3068\uff0c\u9759\u96fb\u5834\u4e2d\u306e\u96fb\u8377 $q$ \u304c\u53d7\u3051\u308b\u529b\u306f<\/p>\n
$$\\boldsymbol{F} = q \\boldsymbol{E} = – \\nabla (q \\phi) \\equiv – \\nabla U$$<\/p>\n
\u3053\u306e\u3088\u3046\u306b\uff0c\u529b $\\boldsymbol{F}$ \u304c\u30b9\u30ab\u30e9\u30fc\u95a2\u6570 $U$ \u306e\u52fe\u914d\u306b\u8ca0\u53f7\u3092\u3064\u3051\u305f\u91cf\u3067\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u3068\u304d\uff0c\u3053\u306e\u529b\u3092\u300c\u4fdd\u5b58\u529b<\/strong><\/span>\u300d\u3068\u3044\u3046\u3002<\/p>\n \u4f55\u304c\u4fdd\u5b58\u3055\u308c\u308b\u306e\u304b\u3068\u3044\u3046\u3068\uff0c\u904b\u52d5\u30a8\u30cd\u30eb\u30ae\u30fc\u3068\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u30a8\u30cd\u30eb\u30ae\u30fc $U$ \u306e\u548c\u3067\u3042\u308b\u529b\u5b66\u7684\u5168\u30a8\u30cd\u30eb\u30ae\u30fc $E$ \u304c\u4fdd\u5b58\u3055\u308c\u308b\uff0c\u3064\u307e\u308a\u904b\u52d5\u306e\u9593\uff0c\u4e00\u5b9a\u3067\u3042\u308a\u7d9a\u3051\u308b\u3002\u3053\u306e\u3053\u3068\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u904b\u52d5\u65b9\u7a0b\u5f0f\u304b\u3089\u793a\u3055\u308c\u308b\u3002<\/p>\n \u307e\u305a\uff0c<\/p>\n $$m \\frac{d^2 \\boldsymbol{r}}{dt^2} = \\boldsymbol{F} = – \\nabla U$$<\/p>\n \u4e21\u8fba\u306b $\\displaystyle \\frac{d\\boldsymbol{r}}{dt} \\cdot$ \uff08\u5185\u7a4d\uff09\u3092\u304b\u3051\u3066\u3084\u3063\u3066…<\/p>\n \\begin{eqnarray} \u4eca\u5ea6\u306f\u7c21\u5358\u306e\u305f\u3081\u306b $\\boldsymbol{E} = \\boldsymbol{0}$ \u3068\u3057\u3088\u3046\u30021\u500b\u306e\u8377\u96fb\u7c92\u5b50\u306b\u306f\u305f\u3089\u304f\u529b\u306f<\/p>\n $$\\boldsymbol{F} = q \\boldsymbol{v} \\times \\boldsymbol{B}$$<\/p>\n \u4eca\uff0c\u5358\u4f4d\u4f53\u7a4d\u3042\u305f\u308a $n$ \u500b\u306e\u8377\u96fb\u7c92\u5b50\u304c\u540c\u3058\u901f\u5ea6 $\\boldsymbol{v}$ \u3067\u904b\u52d5\u3057\u3066\u3044\u308b\u3068\u3059\u308b\u3002<\/p>\n \\begin{eqnarray} \u3053\u3053\u3067\uff0c\u96fb\u6d41\u5bc6\u5ea6\u30d9\u30af\u30c8\u30eb\u306f $\\boldsymbol{J} \\equiv n q \\boldsymbol{v}$ \u3067\u3042\u308a\uff0c\u96fb\u6d41\u30d9\u30af\u30c8\u30eb\u306f $ \\boldsymbol{I}\u00a0 \\equiv \\boldsymbol{J} \\varDelta S\u00a0 $ \u3067\u3042\u308b\u3002<\/p>\n \u3057\u305f\u304c\u3063\u3066\uff0c\u3053\u306e\u96fb\u6d41\u7d20\u7247\u306b\u306f\u305f\u3089\u304f\u5358\u4f4d\u9577\u3055\u3042\u305f\u308a\u306e\u529b $\\boldsymbol{f}$ \u306f<\/p>\n $$\\boldsymbol{f}\\equiv\\frac{\\varDelta \\boldsymbol{F} }{\\varDelta L} = \\boldsymbol{I} \\times \\boldsymbol{B}$$<\/p>\n \u3053\u306e\u5f0f\u306f\uff0c\u5f8c\u306b\u300c\u5e73\u884c\u76f4\u7dda\u96fb\u6d41\u306b\u306f\u305f\u3089\u304f\u529b<\/a>\u300d\u306e\u3068\u3053\u308d\u3067\u4f7f\u3046\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n
\nm \\frac{d\\boldsymbol{r}}{dt} \\cdot \\frac{d^2 \\boldsymbol{r}}{dt^2} &=& – \\nabla U \\cdot \\frac{d\\boldsymbol{r}}{dt} \\\\
\n\\frac{d}{dt} \\left\\{\\frac{1}{2} m \\frac{d\\boldsymbol{r}}{dt} \\cdot \\frac{d\\boldsymbol{r}}{dt} + U \\right\\} &=& 0 \\\\
\n\\therefore\\ \\ \\frac{1}{2} m \\frac{d\\boldsymbol{r}}{dt} \\cdot \\frac{d\\boldsymbol{r}}{dt} + U &=& \\mbox{const.} \\equiv E
\n\\end{eqnarray}<\/p>\n\u96fb\u6d41\u7d20\u7247\u306b\u306f\u305f\u3089\u304f\u529b<\/h3>\n
![\"\"](\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Denryusohen2-640x429.png\")
$\\boldsymbol{v}$ \u306b\u5782\u76f4\u306a\u5fae\u5c0f\u9762\u7a4d $\\varDelta S$ \u3068 $\\boldsymbol{v}$ \u306b\u5e73\u884c\u306a\u5fae\u5c0f\u9577\u3055 $\\varDelta L$ \u304b\u3089\u306a\u308b\u9818\u57df\u3092\u8003\u3048\u308b\u3068\uff0c\u3053\u306e\u9818\u57df\u306e\u4f53\u7a4d\u306f $\\varDelta V =\\varDelta L\\times\u00a0 \\varDelta S$\uff0c\u3053\u306e\u4f53\u7a4d\u5185\u306b\u3042\u308b\u8377\u96fb\u7c92\u5b50\u306e\u500b\u6570\u306f $\\varDelta N = n \\varDelta V = n \\,\\varDelta L \\,\\varDelta S$ \u3067\u3042\u308a\uff0c\u3053\u306e\u7d20\u7247\u306b\u50cd\u304f\u529b $\\varDelta \\boldsymbol{F}$ \u306f<\/p>\n
\n\\varDelta \\boldsymbol{F} &=& \\varDelta N \\,q \\boldsymbol{v} \\times \\boldsymbol{B} \\\\
\n&=& n \\,\\varDelta L \\,\\varDelta S \\,q \\boldsymbol{v} \\times \\boldsymbol{B} \\\\
\n&=& \\varDelta L \\,\\varDelta S\u00a0 \\,\\boldsymbol{J} \\times \\boldsymbol{B} \\\\
\n&=& \\varDelta L \\,\\boldsymbol{I} \\times \\boldsymbol{B}
\n\\end{eqnarray}<\/p>\n