第十二章 电流的磁场

第十二章电流的磁场练习一磁场电流的磁场一、判断题１．所有载流导线周围都有稳定的磁场。（）２．磁力线是起源于Ｎ极，终止于Ｓ极的有头有尾的曲线。（）３．通电螺线管外部的磁力线是北极出来，进入南极，内部的磁力线跟轴线平行，方向由南极指向北极，并和外部的磁力...     

电流在磁场中的受力及运动

安培定律是研究任意形状载流导线在磁场中受力问题的基础,安培力作为通电导线所受的外力参与受力分析,产生了通电导体在磁场中的平衡、加速和做功问题.对物体进行受力分析时,注意安培力大小和方向的确定.     

任意形状磁场区域感生电动势的研究

讨论任意形状磁场区域所产生的感生电动势的计算方法.首先讨论有限长直导线的情况.然后以圆形、矩形和三角形磁场区域为例来计算,结果表明不同形状的磁场区域对相同长度直导线所产生的感生电动势也不相同.其次研究了磁场对无限长直导线所产生的感生电动势.证明了磁场对无限长直导线所产生的感生电动势仅仅依赖磁场区域的面积大小而与磁场区域的具体形状和导线到磁场的距离等因素无关.     

三分量磁场延拓的递推算法

提出一种三分量磁场延拓的递推算法,主要目的是解决三分量磁场的向下延拓问题.应用微分学基本原理,将具有相同水平坐标,不同垂向坐标的点上的三分量磁场,通过磁场的垂向偏导数的积分联系起来.根据磁场向量散度和旋度的性质,将磁场的垂向偏导数与水平方向的偏导数联系起来.这样,在已知一个平面上的磁场时,可以通过递推的办法逐层求取该平面以下任意平面上的三分量磁场.应用实例证明方法的快速性和准确性.     

求任意形状截面无限长直载流螺线管磁场的一种方法

在电磁学中,无限长直载流螺线管的磁场是一个基本与核心的问题,为了得到这一系统的磁场,通常的做法是：先就圆截面情况计算,然后把截面为任意形状无限长直螺线管看成是由无数大大小小的圆截面螺线管叠加而成,由此得到螺线管内的磁场均匀而管外磁场为零的一般结论.这里给出了一种推导截面为任意形状无限长直螺线管内外磁场的直接方法.先计算螺线管表面一窄条的磁场,再算总磁场.这种方法物理图像清楚,数学过程简单,可以在教学中加以应用.     

探究直流导线周围磁场的变化

利用螺绕环、线圈、电流计和可变电阻器等设备,设计了探究直流导线周围磁场变化的实验装置.由电源、转向开关和电阻来改变导线中电流大小和方向,进而改变直流导线周围的磁场,通过灵敏电流计来探究缠有线圈的螺绕环中感应电流的变化,由此得出直流导线周围的磁场大小和方向与直流导线中电流的大小和方向的关系.     

螺旋对称磁场的计算

本文对于分布在无限长圆柱周界上的螺线电流产生的磁场用标势方法得出了普遍解,并且给出了导线在圆柱周界上平均分布时的磁场公式。同时,用矢势方法计算了导线为非无限长时的磁场公式。以上结果,在螺距趋于零的极限下得到了波纹磁场。     

磁场对电流的作用定量分析仪

磁场对电流的作用是教学中的重点,研制“磁场对电流的作用定量分析仪”,目的在于较精确地演示磁场对电流的作用与电流强度成正比、与导线长度成正比、与磁感应强度成正比、与导线与磁场的夹角的正弦成正比。一、仪器的结构与原理仪器的结构如图1,当电磁铁1和导线2通电后,通电导线因受磁场力的作用,使指针5偏转(注意电流的方向,使指针向右偏转)。移动测力游码12,使指针回到平衡线6,由游码在测力刻度     

镜像对称的载流导线磁场方向的分析

电磁场的对称性分析在大学物理教学中有着极其重要的地位,但是现有的大学物理教材很少给出如何利用稳恒磁场的对称性来分析磁感强度的方向.文章针对此问题应用毕奥-萨伐尔定律并结合矢量的分解更加便捷地分析了一对镜像对称的载流导线在中间面上任意点处的磁场方向:其方向必定垂直于该面.应用这一结论可以很容易判断出像密绕螺线管、直螺线管和圆柱形导线等这一类电流分布具有镜像对称的载流导线在其中间面上的磁感强度的方向.     

任意形状三角形电流空间磁场的再计算

本文从大家熟悉的一段载流直导线的磁场表达式出发,首先导出了载流直导线空间磁场的x、y、z分量表达式.然后将这一表达式运用到任意三角形电流,从而得到了它的空间磁场分布.最后对正三角形电流及其平面和中心轴线的特殊情况进行了讨论.与文献[1]相比,本文采用的是代数、几何的方法,所得到的磁场分布是空间坐标的函数,更贴近大学物理教学实际.利用这一方法,原则上还可以计算任意多边形电流的磁场,便于在大学物理教学中推广运用.     

Magnetic guide of cold atoms using a U-shaped current-carrying conductor

We propose a new scheme to magnetically guide cold neutral atoms using a U-shaped current carrying conductor. The spatial magnetic field distribution from the U-shaped current-carrying conductor and the relationship between the magnetic field and parameters of the U-shaped conductor are analysed. Our study shows that U-shaped current-carrying conductor can be used to realize single- or double-channel magnetic guiding of cold atoms in weak-field-seeking states and to construct various atom-optical elements. By using Monte Carlo simulations, the dynamic process of the guided atomic-beam splitting in an atomic-beam splitter composed by the U-shaped current-carrying conductor is studied, and some results are presented.     

Radial electric potential in a metallic wire carrying a steady current

A radial electric potential is established in a metallic wire carrying a steady current. The steady current induces a magnetic field inside the conductor. A resultant Lorentz force drives a moving electron to distribute on the surface of the wire. An electric potential deference between two points along a radial direction in the conductor is proportional to a quadratic of the current.     

从运动电荷受力看磁场与电场的相对性与整体性--《费曼物理学讲义》中的一个问题的再讨论

本文通过对载流导体附近运动电荷受力的再讨论，直观地展现了电场与磁场的相对性与整体性．     

Magnetoelectric effect in one-dimensional metallic conductors

The effect of a transverse magnetic field on a one-dimensional metallic current carrying conductor is considered. The field produces a transverse electric polarization which is wavevector dependent, and which causes a transverse magnetoelectric field. The magnitude of the effect is estimated for typical one dimensional conductors.     

The large-scale vortex structures in plasma-like media and the electric explosion of conductors

Formation of large-scale hydrodynamic convective patterns in plasma-like current-carrying media is considered. This process is shown to be described by the same equations, as Benard rolls, except that a temperature field must be replaced by a magnetic field. A simple low-mode model of spatial pattern formation for a case of cylindrical liquid-metal conductor with current is proposed and investigated. Nonlinear interaction of perturbations of the magnetic field and the velocity field results in an increase of effective conductor resistance even when transport coefficients are constant. In our opinion, it is this instability, that is of first importance at the initial stages of the electric explosion of conductors. In particular, it leads to conductor stratification and electric current interruption. (c) 1996 American Institute of Physics.     

Zero-magnetic-field hall effect in broken-mirror-symmetry conductors under illumination

A novel effect is predicted for conductors with a broken mirror symmetry [e.g., polar metals and asymmetrical quantum well (QW) structures]: if such a conductor is under the direct current J approximately E(d), the circular polarized infrared radiation should induce an additional transverse current JH approximately E(d)xc, where E(d) is the driving electric field and c is a vector directed either along the polar axis or perpendicular to a QW. The sign of the current JH can be reversed by switching the helicity of the light from right to left-handed. Thus the phenomenon is, in fact, something like the Hall effect in which light acts as an external magnetic field.     

D.c. drift and hot carrier effects on E.M. wave propagation in a current carrying bismuth2

This paper presents an investigation of d.c. drift and hot carrier effects on electromagnetic wave propagation in current carrying bismuth when the directions of the d.c. electric field, static magnetic field and of the propagation of waves are all along the trigonal axis. The anisotropic band structure and mass tensor of carriers have been taken into account. A generalised dispersion relation has been derived for a bismuth sample with arbitrary compensation. The enhanced heating of the carriers with a d.c. electric field causes a progressive decrease in the refractive index and the absorption coefficient; this effect is more pronounced in the case of upper band microwaves. The heating of the electrons is reduced by the presence of a static magnetic field while that of the holes is unchanged. The hot carrier effects in Faraday rotation and ellipticity for high frequency waves in bismuth have also been investigated.     

电流连续的细导体段模型的磁场及电感

传统的载流细导体段模型是分析导体闭合回路磁场的基本模型,尽管不满足电流连续性定律,但适用于导体闭合回路的磁场分析.然而,对于工程中只关注导体闭合回路中某一局部的多分支导体段并联的电流分配问题,传统模型将不能完整地反映各分支导体段之间磁场的相互作用.为此,现有文献提出的位移电流模型,满足了电流连续性定律,较好地解决了上述问题,但是,仍然存在理论不完整、不自洽以及计算公式复杂等问题.本文提出载流细导体段的传导电流模型,确保了载流细导体段在段内、段端及段外的电流连续性.推导出物理内涵更加深刻的总磁场微分方程和矢量磁位计算公式.提出载流细导体段传导电流模型磁场能量和电感的计算公式,极大地降低了计算复杂度,弥补了现有文献的不足.本文算例从模型、公式、计算等方面验证了本文理论和计算公式的正确性.     

String behaviour of magnetic field lines and their rotation in neutron star’s interior

It is found from Maxwell’s equations that the magnetic field lines are good analogues of relativistic strings. The Lorentz force per unit length of magnetic tube is interpretable as Magnus force acting on each individual magnetic tube. It is shown that the superconducting current in pulsar’s interior causes local rotation of magnetic flux tubes carrying quantized flux. Such local rotation remains operative as long as the induced magnetic field of normal electron fluid is above the lower critical field but below the upper. The conservation of magnetic flux leads to a geometrical condition in the form of the Weingarten identity which ensures the existence of family of “magnetic world sheetrdquo;. Each “magnetic world sheet” is a magnetic flux conserving surface. In the process of collapse, a compact spacelike cross-section of a magnetic tube terminates into a trapped surface if the magnetic energy grows faster along the fluid flow lines than that along the magnetic field lines.     

Solving elastic plane problems involving the effect of Lorentz forces on conductors carrying a uniform current

It is shown that the solution of the first fundamental problem of the linear theory of elasticity in regard to the effect of the Lorentz force on a long conductor carrying a uniform longitudinal current in a magnetic field having an a priori unknown distribution can be reduced to the solution of homogeneous equations. Zh. Tekh. Fiz. 68, 128–129 (May 1998)