Circuits, Currents, Kirchhoff, and Maxwell

Author:

Eisenberg RobertORCID

Abstract

Electricity flows in circuits that bring us power and information. The current flow in circuits is defined by the Maxwell equations that are as exact and universal as any in science. The Maxwell-Ampere law defines the source of the magnetic field as a current. In a vacuum, like that between stars, there are no charges to carry that current. In a vacuum, the source of the magnetic field is the displacement current, \(\varepsilon_0\ \partial\mathbf{E}/\partial t\). Inside matter, the source of the magnetic field is the flux of charge added to the displacement current. This total current obeys a version of Kirchhoff’s current law that is implied by the mathematics of the Maxwell equations, and therefore is as universal and exact as they are. Kirchhoff's laws provide a useful coarse graining of the Maxwell equations that avoids calculating the Coulombic interactions of \({10}^{23}\) charges yet provide sufficient information to design the integrated circuits of our computers. Kirchhoff's laws are exact, as well as coarse grained because they are a mathematical consequence of the Maxwell equations, without assumption or further physical content. In a series circuit, the coupling in Kirchhoff’s law makes the total current exactly equal everywhere at any time. The Maxwell equations provide just the forces needed to move atomic charges so the total currents in Kirchhoff’s law are equal for any mechanism of charge movement. Those movements couple processes for any physical mechanism of charge movement. In biology, Kirchhoff coupling is an important part of membrane transport and enzyme function. For example, it helps the membrane enzymes cytochrome c oxidase and ATP-synthase produce ATP, the biological store of chemical energy.

Publisher

Qeios Ltd

Subject

General Medicine

Reference96 articles.

1. Ayers, J.E., Digital Integrated Circuits: Analysis and Design, Second Edition. 2018: CRC Press.

2. Boylestad, R.L. and L. Nashelsky, Electronic Devices and Circuit Theory: Pearson New International Edition PDF eBook. 2013: Pearson Education.

3. Camenzind, H., Designing analog chips. 2005: Virtualbookworm Publishing.

4. Gielen, G. and W.M. Sansen, Symbolic analysis for automated design of analog integrated circuits. Vol. 137. 2012: Springer Science & Business Media.

5. Gray, P.R., et al., Analysis and Design of Analog Integrated Circuits. 2009: Wiley.

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3