磁场中有限长铁钉稳定位形和相变

THE STABLE CONFIGURATIONS OF A FINITE SIZE NAIL IN A MAGNETIC FIELD AND THE PHASE TRANSITION

磁铁附近磁场中铁钉站立和倒下是一个常见的现象,本文通过计算无限长导线、平行无限长导线及圆环电流磁场中有限长度铁钉势函数,分析势函数稳定点的位置来判断铁钉的指向。当考虑铁钉固有磁矩后,铁钉移动过程中所处位置由一个亚稳定点变成了一个非稳定点,铁钉随后就倒向了稳定点。我们利用描述对称性破缺的朗道连续相变理论来分析相变之后稳定位形的具体规律。结果表明相变之后稳定位形与朗道连续相变理论预言的临界指数非常符合,铁钉的站立和倒下这样常见现象可以作为讲解相变理论经典力学例子。理论物理的抽象概念在经典物理世界找到对应,深刻体现了物理理论的美妙。

The standing and tumbling of a nail in a magnetic field is a daily phenomena,We calculated potentials of the finite size nail in the fields of a infinite long wire,the parallel infinite long wires and the circular current loop,respectively.The stable points of the potential determine the stable configurations of the nail.Involved in the intrinsic magnetic moment of the nail,the standing point of nail will change from a meta-stable point to a unstable point while moving in the magnetic field,then tumbling down.Landau theory of phase transition can be used to analyze the stable configuration of the nail.The numerical results shows that the critical index are exactly consistent with the prediction of Landau theory.making the standing and tumbling of a nail to be a perfect model of Landau theory.It is very charming that the abstract concept in theoretical physics are demonstrated in a simple classical phenomena.