Maxwell's equations are interpreted by treating the right side as the origin and the left side as the consequence
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While introductory textbooks and common interpretations often treat the right side of Maxwell's equations as the source or origin and the left side as the consequence, physics literature and critiques caution that such causal interpretations can be overly simplistic or misleading.
# Is it true that Maxwell equations are interpreted by taking right side of formula as the "origin" and the left part as "consequence"?
Tags: maxwell-equations
- Score: 19
- Views: 3290
- Answers: 5
- Answered: yes
- Asked by: Mathieu Krisztian (975 rep)
- Asked: 2021-08-19
- Edited: 2021-08-19
- Site: physics
## Question
When books or various references interpret the meaning of Maxwell equations, they typically state that the source (origin of the phenomena) is the right part of the formula, and the resulting effect is on the left part of the formula.
For example, for Maxwell-Faraday law, $\vec{\nabla} \times \vec{E}=-\frac{\partial \vec{B}}{\partial t}$
one states
"a time varying magnetic field creates ("induces") an electric field."
(see for example : https://en.wikipedia.org/wiki/Maxwell%27s_equations#Faraday's_law )
It seems to me that this is not true. One could interpret in both direction.
For the example above, we could also state that a change of direction of the electric field will create a temporal change of the magnetic field.
Is it true that Maxwell equations should be interpreted by taking right side of formula as the "origin" and the left part as "consequence"?
Cause-effect relationships in Maxwell’s equations and their implications in the teaching of electromagnetism in introductory physics courses
# Cause-effect relationships in Maxwell’s equations and their implications in the teaching of electromagnetism in introductory physics courses
Álvaro Suárez alsua@outlook.com Departamento de Física, Consejo de Formación en Educación, Montevideo, Uruguay Arturo C. Martí marti@fisica.edu.uy Instituto de Física, Facultad de Ciencias, Universidad de la República, Iguá 4225, Montevideo, 11200, Uruguay Kristina Zuza kristina.zuza@ehu.eus Department of Applied Physics, University of Basque Country, Spain Jenaro Guisasola jenaro.guisasola@ehu.eus Department of Applied Physics, University of Basque Country, Spain
(January 3, 2025)
###### Abstract
A thoughtless treatment of Maxwell’s equations can lead to the interpretation of the existence of a causal relationship between their different terms and, therefore, that an electric field that varies in time generates a magnetic one and vice versa. In this article we address the problems associated with these interpretations and their consequences for the teaching of physics in introductory university ph
# Interpretation of the displacement current
Tags: electromagnetism, maxwell-equations
- Score: 6
- Views: 456
- Answers: 4
- Answered: yes
- Asked by: Dargscisyhp (5390 rep)
- Asked: 2015-02-27
- Edited: 2020-01-02
- Site: physics
## Question
From Maxwell's equations, why is the displacement current viewed as a source for a magnetic field? If the displacement current were moved to the other side of the equation, it would be like a current density gives rise to both a magnetic field and a time-varying electric field. So why is the former interpretation preferred over the latter?
## Answers
### Answer by Buzz (score: 2)
In fact, it is commonplace (especially in relativistic electrodynamics problems) to move the time-dependent terms in the Ampere-Maxwell Law (and similarly in Faraday's Law) to the left-hand side of the equation, yielding (in Gaussian units)
$$\vec{\nabla}\times\vec{E}+\frac{1}{c}\frac{\partial\vec{B}}{\partial t}=0 \\
\vec{\nabla}\times\vec{B}-\frac{1}{c}\frac{\partial\vec{E}}{\partial t}=\vec{J}. $$
Writing the equations this way puts the fields entirely on the left and the sources entirely on the right. In this way, it is possible to see the electric and mag
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