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# 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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### Demystifying the connection between magnetic and electric fields

Part (1): In the classical theory of electromagnesitm, as given by Maxwell, we know that by just looking at the four famous equations: An electric field has a source: there are charged particles (...
4answers
402 views

### Why all theories are Lorentz invariant?

Ok, in studying of Maxwell equations we have violation of Galilean relativity. This implies necessity of other transformations which make Maxwell equations covariant (invariant in form) under this ...
5answers
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### Is Gauss' law valid for time-dependent electric fields?

The Maxwell's equation $\boldsymbol{\nabla}\cdot \textbf{E}(\textbf{r})=\frac{\rho(\textbf{r})}{\epsilon_0}$ is derived from the Gauss law in electrostatics (which is in turn derived from Coulomb's ...
5answers
870 views

### Why are the $\mathbf E$ and $\mathbf B$ fields of an electromagnetic wave mutually perpendicular?

Why are the wave number $\mathbf k$ and the electric and magnetic fields $\mathbf E$ and $\mathbf B$ are perpendicular to each other? I know it but I haven't thought about it deeply. How can I prove ...
3answers
2k views

### Derivation of the speed of light using the integral forms of Maxwell's Equations

Having just finished physics 2, I've been (slightly) exposed to showing that light is a wave with speed $1/\sqrt{\mu _0 \epsilon _0 }$ using the differential forms of Maxwell's equations, though this ...
4answers
477 views

### The necessity of the B field

It is fairly easy using basic special relativity to arrive at the conclusion that the magnetic force effect on nearby charges of wires carrying currents on nearby charges is only due to the length ...
2answers
320 views

### Comparison of covariant form of Maxwell equations with Einstein's GR

We know, the the vector form of Maxwell equations \begin{align} \vec\nabla\cdot\vec{E} &= 4\pi\rho \label{Diff I}\\ \vec\nabla\times\vec{B} &= \dfrac{4\pi}{c} \vec{j}+\dfrac{1}{c}\dfrac{\...
4answers
974 views

### Exactly how is the constant measured velocity of light deduced from Maxwell's equation?

For electromagnetic radiation the velocity of propagation is $c = 1/\sqrt{\mu_0 \epsilon_0}$. Since both $\mu_0$ and $\epsilon_0$ do not vary in any inertial frame, then $c$ must be constant in any ...
1answer
216 views

### Maxwell's equation in free space from wave equations of electric and magnetic field

How to go from the wave equations of electric and magnetic field and $$\boldsymbol{\nabla}\cdot \mathbf E = 0 \quad \text{ and } \quad \ 0 = \boldsymbol{\nabla}\cdot\mathbf B,$$ to the remaining ...
2answers
171 views

### Confusion on Maxwells equations and Gauge Transformations

I know a little bit about electrodynamics but I don't understand the validity of Gauge Transformations. In particular I am confused on how the theory can be consistent among different gauges, in ...
2answers
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1answer
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### Would Michelson-Morkey experiment measure wind in non-vacuum?

If we derive the speed of light from the Maxwell equations we will find it's a function of the permittivity and permeability of the medium. Now let's play with the thought that we are living in a ...
1answer
463 views

### Is light transverse electromagnetic (TEM) or transverse magnetic (TM) wave?

My apologies if this is a duplicate. I have been trying to understand the differences between Maxwell's solutions. So far I gathered that TEM requires free current and at least 2 conductors ...