# Questions tagged [maxwell-equations]

A set of four equations that define electrodynamics. They comprise the Gauss laws for the electric and magnetic fields, the Faraday law, and the Ampère law. Together, these equations uniquely determine the electric and magnetic fields of a physical system. Do not use this tag for the thermodynamical equations known as Maxwell's relations.

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### Validity of Maxwell's laws

I know Lorentz's force changes, according to Wikipedia, when the charges are moving nearly light speed but what about Maxwell's laws? Are they still valid when particles move at light speed? I ask ...
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### Were the original Maxwell quaternion equations different than Heaviside's vector equations in any of their predictions?

Gibbs vector calculus removed scalar quaternion parts of equations thus predicting no scalar waves that transfer energy. Did Maxwell have a different take on similar predictions.
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### Maxwell equations and continuity equation

I want to show the following equation with the maxwell equations: $$\frac{\partial}{\partial t}W+\vec{\nabla} \cdot \vec{S} = 0$$ The problem is that I'm not understanding why I can do the following ...
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### Electric field for point charge in a smoothly-varying dielectric?

A classic textbook E&M problem is to calculate the electric field produced by a point charge $Q$ located at $(\mathbf{r}_0,z_0)$ inside a medium with two semi-infinite dielectric constants defined ...
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### For a constant total charge arbitrarily distributed on a fixed closed surface boundary: is every internal and external field unique? [duplicate]

As an example: in free space, a constant total charge Q distributed uniformly on a fixed spherical surface gives rise to a zero internal and Coulombic external electric field. As far as I can see, ...
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### Reduction of Maxwell's equations to classical circuit theory

Can classical circuit theory based on lumped element models be obtained from Maxwell's equations as a limiting case in an appropriate sense? If this is the case, what exactly are all the assumptions ...
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### Boundary conditions of electrostatics

As we have seen that while deriving the boundary conditions in Griffith's electrodynamics he stated some conclusions, that were The Perpendicular components of Electric field and Gradient of ...
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### Why does gauge invariance have physical consequences?

My understanding is that gauge invariance occurs when the description of a physical field as a mathematical field (i.e., function whose domain is space-time) contains a redundancy: there are ...
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### Deriving the wave equation for electromagnetic waves

I'm currently referring to the wave equation derivation given in "Introduction to Electrodynamics" by David J. Griffiths. It follows something like this: The electromagnetic wave equations are given ...
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### Is dispalcement current produced in inductor?

As we know in case of capacitor, changing electric field inside it produces a current which is called a displacement current (Amperes law modified by Maxwell). In case of inductor, is there any ...
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### Eddy currents and diamagnetism

In this video showing magnetic melting of aluminum the metal piece levitates above the solenoid due to eddy currents: https://www.youtube.com/watch?v=8i2OVqWo9s0 So aluminum behaves as a diamagnet ...
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### Writing an expression for the scalar value of the electric field $E$

I am currently studying Optics, fifth edition, by Hecht. In chapter 2.7 Plane Waves, the following example is given: An electromagnetic plane wave is described by its electric field $E$. The wave ...
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### Does Maxwell's Equations on Magnetic Field holds good in year 2020? [duplicate]

Does "Maxwell's equations" on "Magnetic Field" still hold good in year 2020? Till now no parameters are changed or corrected? Why does speed of Magnetism always relate to Speed of Electromagnetic ...
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### What are the physics implications of a world with magnetic monopoles? [closed]

When I studied Electromagnetism, even though I was already used to the idea of always finding magnets with two poles, one thing that was really shocking for the first time was seeing one of Maxwell's ...
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### Induced electric field from homogeneous magnetic field in free space points in all directions

If there is a homogeneous magnetic field varying with time, say $\vec{B} = B_0 \sin(t) \hat z$, then this should, from faradays law of induction, induce an electric field. Since the problem looks ...
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### What it means for the wave equation of light in vacuum to be a solution of the maxwell equations? [closed]

I know how to get the wave equation of light from Maxwell's equation, but I never understood why it is called the solution of the Maxwell equations. If say we have a positive charge standing still ...
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### Maxwell's Equations: Taking the real part of the product $\mathbf{E}\exp(j \omega t)$ in order to get the “complete field”

My textbook, Laser Electronics, Third Edition, by Verdeyen, says the following in a section on Maxwell's equations: To describe an electromagnetic wave, we need two field-intensity vectors, \$\...
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