用相对性原理理解电场和磁场

电场和磁场是用来描述电荷之间相互作用的两种效应,不同参照系的观察者可以观测到不同的电场和磁场的比例。就像一个硬币的两个面,只有将电场和磁场看成一个整体,电磁场基本理论才能与相对性原理相互自洽,电场和磁场仅仅只是相互为相对论效应。本文通过3个熟悉的例子进一步说明相对性原理的重要性,只有物理规律才与参照系无关,如何解释物理规律是与参照系相关的。从这个意义上说,电场、磁场是人们"发明"来解释电荷之间相互作用的物理规律。     

利用感应电场与磁场的相似性分析计算多种分布的感应电场

感应电场与磁场在物理实质上是不同的,但它们在矢量场的性质方面却有着共性,那就是感应电场与磁场都是无源有旋的矢量场。特别是稳恒电流产生的磁场与恒定速率变化的似稳磁场产生的感应电场所满足的基本场方程是相似的,因此场方程的解应具有相似的形式,即计算公式应具有相似的形式。利用这种相似性可以将分析计算磁场的方法用来分析计算感应电场。 (一)基本场方程的相似性 稳恒电流在周围空间产生的磁场基本方程为 积分形式　微分形式 恒定速率变化的似稳磁场产生的感应电场基本方程为 积分形式微分形式 如果只讨论真空情况,知道了全空间矢…     

平面磁场的磁感应线

尽管平面电场的电场线和等势线的计算出现在大学的数学物理教学中,平面磁场的磁感应线的计算却很少在教学中涉及。本文通过讨论平面磁场与平面电场的基本性质以及它们之间形式上的对应关系,发现平面磁场的磁感应线与相应特定平面电场的等势线重合;因此可以通过计算相应平面电场的等势线来获得平面磁场的磁感应线,为绘制平面磁场的磁感应线提供了一种简易方法。文中通过一个简单示例来印证平面磁场的磁感应线和平面电场的等势线之间的对应关系。     

聚焦高斯涡旋光束焦区电场和磁场的偏振奇点

以高斯涡旋光束为例,研究了聚焦场中电场和磁场的偏振奇点变化规律.结果表明,高斯涡旋光束经透镜聚焦后,在焦区存在二维和三维电场和磁场的偏振奇点,其位置一般不重合.适当改变与焦面的距离以及光阑截断参数等出现圆偏振奇点的移动、产生和湮没.不同二维和三维电场和磁场圆偏振奇点湮没所对应的各参数临界值不同.在二维电场中,几何焦面上会有V点的产生.     

展示相对性原理和电磁场相对性的一个佳例

以条形磁铁与导体圆环相对运动为例,依据导体圆环产生感应电流这一事实,首先讨论了条形磁铁参考系和导体圆环参考系下电场和磁场的不同.并在条形磁铁参考系下,从产生动生电动势的物理本质洛伦兹力出发,导出了法拉第电磁感应定律.然后,在导体圆环参考系下,由相对性原理直接给出了感生电场性质的数学表述,并深入讨论了电场和磁场的联系.最后,给出了爱因斯坦和费曼对该问题的不同思考并进行了简单分析.     

平面横电磁波模的初值问题

经典理论所描述的电场和磁场处处同相的平面电磁波模并不存在.Maxwell方程组的解依赖于 电磁场的初始值或边界条件,根据不同的初始条件解得的平面电磁波模是不同的.结果表明 ,平面电磁波是横波,在不同的位置,由变化的电场激发的磁场或由变化的磁场激发的电场 振幅不同,电场与磁场的相位差也不同. 关键词： Maxwell方程组 最优微分方程 初始条件 平面电磁波     

感生电场与动生电场的等效性探究

本文认为在感生电场的情况下,磁场的强弱变化可以引起磁场自身的横向运动,使得线圈中电子相对于磁场发生运动,从而等效为一个动生电场,受到洛伦兹力的作用.借助磁感线模拟磁场的运动方式,得到圆形回路中任意一点与磁场相对运动速度的表达式,进而推得该＂等效动生电场＂中的洛伦兹力.以螺线管为例,验证该方法可以解释感生电场所满足的规律.将感生电场与动生电场的产生原因统一为导体中电子与磁场的相对运动,相应电动势的非静电力统一为洛伦兹力.     

运动电荷的电/磁场高斯定理的直接验证

尽管麦氏方程组的张量协变形式已然揭示了高斯定理的相对论协变性,但在大学物理的教学中仍然缺乏对运动电荷的高斯定理的切身体会与直接验证.本文首先运用电磁场张量变换的方法推导出运动电荷的电场与磁场强度,再运用积分及矢量运算的若干技巧,直接而简单地验证了高斯定理对于运动电荷的电场与磁场仍然满足,从而直接验证了电场与磁场的高斯定...     

外场下GaAs/AlGaAs超晶格中载流子的动力学行为

基于分立漂移模型研究了磁场对载流子在弱耦合GaAs/AlAs超晶格中的动力学行为的影响。研究表明磁场较小时超晶格中载流子的集聚形成电场畴,该电场畴的周期移动引起电流振荡的产生,随着磁场的增加系统中形成的电场畴变得稳定,电流振荡也逐渐消失。因此,磁场控制下系统的状态可以从动态转变到稳定态。受交流电场驱动时,由于内部电流振荡信号和外部交流信号的耦合,载流子运动展现出很多的非线性行为。     

高斯涡旋光束在自由空间传输中电场和磁场的偏振奇点

利用矢量菲涅尔衍射积分公式, 以高斯涡旋光束为例, 推导出傍轴高斯涡旋光束在自由空间传输过程中电场分量和磁场分量的解析表达式, 详细研究了自由空间中电场和磁场的偏振奇点变化规律. 结果表明, 高斯涡旋光束在自由空间传输中, 存在二维和三维电场和磁场的偏振奇点, 其位置一般不重合. 改变光束束腰宽度比、 振幅比以及传输距离, 偏振奇点出现移动. 在二维电场和磁场中, 当满足一定条件时, 会有V点产生.     

Effective field theory in background field gauge

It is shown how to construct effective lagrangians to the two-loop level for non-abelian gauge theories, quantized in background field gauge. This construction is no more difficult than the analogous computation in abelian gauge theories when minimal subtraction is employed. It is argued that for three or more loops, one can no longer separate heavy or mixed light-heavy graphs in an intermediate renormalization, and the more general algorithm presented by us in an earlier work must be employed even in background field gauge.     

恒定流速场与静电场、静磁场的类比

本文将“物理类比法”引入大学物理电磁学部分的教学,将恒定流速场与静电场和静磁场在特征量、场的分布及其描述等方面进行了类比,使学生对电磁场有一个较清晰和全面的认识,对电磁学的理论有一个较深刻的理解和掌握,收到了较理想的教学效果.     

Partial field decomposition of multi-source cyclostationary sound field

The cyclostationary sound field is a kind of special non-stationary field which has obvious modulation phenomena. Conventional planar near-field acoustic holography (PNAH) technique cannot exactly reflect its modulation characteristics. If the cyclic spectral density (CSD) instead of the complex sound pressure is adopted as the reconstruction variable, the modulating wave and carrier wave components of the cyclostationary sound field can be extracted effectively. A new technique called cyclostationary PNAH utilizing the CSD is proposed in this paper. Based on this technique, the problem of partial field decomposition by singular value decomposition (SVD) of multiple incoherent cyclostationary sound sources is researched. The results of numerical simulation and experiments show that the CPNAH technique and SVD decomposition method are effective.     

On weyl's gauge field in a non-local field

In this paper, a non-local field (i.e. the (x, ψ)-field) is constructed by regarding the spinor (ψ) as the internal freedom attached to each point (x). Since this field is likened to a unified field between the (x)- and (ψ)-fields, the metric is given bydσψ=gλ dx ^λψ. Concerning this, some conformally equivalent relations are considered. Next, Weyl's gauge field is introduced into the concept of connection in order to consider the gauge invariance. Finally, some essential features underlying our non-local field are grasped by formulating some fundamental equations of the spin curvature tensors.     

Two-dimensional quantum field theories containing a massless scalar field

The following new findings are briefly reported:

1. A consistent quantum theory can be formulated for a free massless scalar field in two-dimensional spacetime.
2. Satisfactory operator solutions in terms of asymptotic fields can be constructed in the Thirring and Schwinger models.
3. Gauge invariance is spontaneously broken in the Thirring model as well as in the Schwinger model.

     

Calculations of field ionization in the field ion microscope

The ionization of a gas atom as it occurs in the field ion microscope is discussed. A wide range of values for the electric field intensity at the metal surface are considered in calculating the ionization occurring both far away from and close to the tip. Ionization distribution curves are calculated and electric fields strengths are determined at points where the distributions peak. Calculations of ionization zone widths and best image conditions are made and a new interpretation of best image conditions is considered. A new field calibration method is suggested.     

Scalar field solutions to Yang-Mills and Vierbein field theories

Covariant solutions to the Vierbein (gravitational) field equations are related to solutions of scalar field equations. New solutions to the latter are also given.     

Towards UV finite quantum field theoriesfrom non-local field operators

A non-local toy model whose interaction consists of smeared, non-local field operators is presented. We work out the Feynman rules and propose a power counting formula for arbitrary graphs. Explicit calculations for one loop graphs show that their contribution is finite for sufficient smearing and agree with the power counting formula. UV/IR mixing does not occur.Received: 26 February 2004, Published online: 5 May 2004     

Antiferromagnets in a field and ferromagnets in a random field

A new mean field approach for antiferromagnets in a field is shown to be equivalent to a mean field treatment of ferromagnets in a random field. Phase diagrams of the two systems are analogous.