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Magnetic diffusion, inductive shielding, and the Laplace transform
American Journal of Physics ( IF 0.9 ) Pub Date : 2021-04-21 , DOI: 10.1119/10.0003508
Alexander E. Krosney 1 , Michael Lang 1 , Jakob J. Weirathmueller 1 , Christopher P. Bidinosti 1
Affiliation  

In the quasistatic limit, a time-varying magnetic field inside a conductor is governed by the diffusion equation. Despite the occurrence of this scenario in many popular physics demonstrations, the concept of magnetic diffusion appears not to have garnered much attention itself as a subject for teaching. We employ the model of a thin conducting tube in a time-varying axial field to introduce magnetic diffusion and connect it to the related phenomenon of inductive shielding. We describe a very simple apparatus utilizing a wide-band Hall-effect sensor to measure these effects with a variety of samples. Quantitative results for diffusion time constants and shielding cutoff frequencies are consistent with a single, sample-specific parameter given by the product of the tube radius, thickness, and electrical conductivity. The Laplace transform arises naturally in regard to the time and frequency domain solutions presented here, and the utility of the technique is highlighted in several places.

中文翻译:

磁扩散,感应屏蔽和拉普拉斯变换

在准静态极限中,导体内部的时变磁场由扩散方程控制。尽管在许多流行的物理演示中都出现了这种情况,但磁扩散的概念本身作为教学的主题似乎并没有引起太多关注。我们采用在时变轴向场中的细导电管模型来引入磁扩散,并将其连接到相关的感应屏蔽现象。我们描述了一种非常简单的设备,该设备利用宽带霍尔效应传感器来测量各种样本的这些效应。扩散时间常数和屏蔽截止频率的定量结果与单个特定于样品的参数一致,该参数由管半径,厚度和电导率的乘积给出。
更新日期:2021-04-22
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