[论文解读] On electromagnetic induction in electric conductors

A. I. Korolev|arXiv (Cornell University)|Feb 22, 2013

Magnetic Field Sensors Techniques参考文献 7被引用 3

一句话总结

本文通过实验研究了导体中的电磁感应，证明感应电动势（emf）不仅取决于磁通量的变化，还取决于穿过导体的磁感线的对称性。本文为弯曲和直线导体建立了广义的电磁感应定律，表明在对称磁场条件下，感应电动势与弧长呈线性关系，并识别出在存在感应电流的情况下感应电动势可能为零的特殊情况。

ABSTRACT

Experimental validation of the Faraday's law of electromagnetic induction (EMI) is performed when an electromotive force is generated in thin copper turns, located inside a large magnetic coil. It has been established that the electromotive force (emf) value should be dependent not only on changes of the magnetic induction flux through a turn and on symmetry of its crossing by magnetic power lines also. The law of EMI is applicable in sufficient approximation in case of the changes of the magnetic field near the turn are symmetrical. Experimental study of the induced emf in arcs and a direct section of the conductor placed into the variable field has been carried out. Linear dependence of the induced emf on the length of the arc has been ascertained in case of the magnetic field distribution symmetry about it. Influence of the magnetic field symmetry on the induced emf in the arc has been observed. The curve of the induced emf in the direct section over period of current pulse is similar to this one for the turns and arcs. The general law of EMI for a curvilinear conductor has been deduced. Calculation of the induced emf in the turns wrapped over it and comparison with the experimental data has been made. The proportionality factor has been ascertained for the law. Special conditions have been described, when the induced emf may not exist in the presence of inductive current. Theoretical estimation of the inductive current has been made at a induced low voltage in the turn. It has been noted the necessity to take into account the concentration of current carriers in calculation of the induced emf in semiconductors and ionized conductors.

研究动机与目标

• 在不同磁场均称性条件下，通过实验验证法拉第电磁感应定律。
• 研究磁场均称性对弯曲和直线导体中感应电动势的影响。
• 推导适用于曲率导体的广义电磁感应定律。
• 识别出尽管存在感应电流但感应电动势可能为零的条件。
• 量化半导体和电离导体中载流子浓度在感应电动势计算中的作用。

提出的方法

• 使用细铜线绕制成的线圈、弧形导体和直线导体，置于大型交变磁场线圈内部的实验装置。
• 在受控的对称与非对称磁场分布下，测量导体中的感应电动势。
• 系统性地改变导体几何形状（线圈、弧形段、直线段）和磁场对称性。
• 将理论预测与弯曲导体上绕制线圈的实验数据进行比较。
• 利用推导出的比例系数计算广义感应定律下的感应电动势。
• 在感应电压较低时，对线圈中的感应电流进行理论估算。

实验结果

研究问题

• RQ1 磁场均称性如何影响弧形导体等弯曲导体中感应电动势的大小？
• RQ2 在对称磁场条件下，直线导体段的感应电动势在多大程度上取决于其长度？
• RQ3 能否为简单回路以外的曲率导体制定广义的电磁感应定律？
• RQ4 在何种条件下，感应电流可以存在但感应电动势不可测量？
• RQ5 载流子浓度在半导体和电离导体的感应电动势计算中起何种作用？

主要发现

• 在对称磁场分布条件下，实验确认了感应电动势与弧长之间存在线性关系。
• 直线导体段的感应电动势与线圈和弧形导体的感应电动势具有相同的时序特性，表明不同几何形状下行为一致。
• 广义感应定律的比例系数通过实验确定，使曲率导体中感应电动势的定量预测成为可能。
• 识别出在存在感应电流的情况下感应电动势为零的特殊情况，挑战了传统认为感应电动势与电流直接对应的假设。
• 理论估算表明，即使在极低感应电压下，感应电流仍可存在，凸显了非金属导体中载流子浓度的重要性。